The effects of challenge and threat states on performance: An updated review and meta-analysis of recent findings
Maciej Behnke & Adrian Hase
2024-03-28
This is code for and the results of analysis included in the manuscript:
Link to OSF:
1. Loading and installing all needed packages
# Clear the environment
rm(list = ls())
# Function to check, install (if necessary), and load the required packages
load_required_packages <- function(packages) {
# Function to install and load a package
install_and_load <- function(package) {
if (!require(package, character.only = TRUE)) {
install.packages(package, dependencies = TRUE)
library(package, character.only = TRUE)
}
}
# Iterate through the list of packages and install/load them
sapply(packages, install_and_load)
}
# List of required packages
packages <- c("metafor"
,"robumeta"
,"ggplot2"
,"readxl"
,"clubSandwich",
"esc",
"robvis")
# Call the function to install and load the required packages
load_required_packages(packages)## Ładowanie wymaganego pakietu: metafor## Warning: pakiet 'metafor' został zbudowany w wersji R 4.3.3## Ładowanie wymaganego pakietu: Matrix## Warning: pakiet 'Matrix' został zbudowany w wersji R 4.3.3## Ładowanie wymaganego pakietu: metadat## Ładowanie wymaganego pakietu: numDeriv##
## Loading the 'metafor' package (version 4.6-0). For an
## introduction to the package please type: help(metafor)## Ładowanie wymaganego pakietu: robumeta## Warning: pakiet 'robumeta' został zbudowany w wersji R 4.3.3## Ładowanie wymaganego pakietu: ggplot2## Warning: pakiet 'ggplot2' został zbudowany w wersji R 4.3.3## Ładowanie wymaganego pakietu: readxl## Warning: pakiet 'readxl' został zbudowany w wersji R 4.3.3## Ładowanie wymaganego pakietu: clubSandwich## Warning: pakiet 'clubSandwich' został zbudowany w wersji R 4.3.3## Registered S3 method overwritten by 'clubSandwich':
## method from
## bread.mlm sandwich## Ładowanie wymaganego pakietu: esc## Ładowanie wymaganego pakietu: robvis## Warning: pakiet 'robvis' został zbudowany w wersji R 4.3.3## $metafor
## NULL
##
## $robumeta
## NULL
##
## $ggplot2
## NULL
##
## $readxl
## NULL
##
## $clubSandwich
## NULL
##
## $esc
## NULL
##
## $robvis
## NULL2. Loading data
### set working directory
setwd("C:/Users/macbe/OneDrive/Behnke Dropbox/MA CHT")
#import and store data from excel file
Data <- read_excel("C:/Users/macbe/OneDrive/Behnke Dropbox/MA CHT/Data.xlsx", sheet = "coding")## New names:
## • `title` -> `title...5`
## • `title` -> `title...8`
## • `` -> `...31`#View(Data)
Data <- as.data.frame(Data)
#drop non numeric data
#Data <- Data2 %>% select(-c(Date_Lab1,
#
# ))3. Risk of bias
## New names:
## • `` -> `...1`## # A tibble: 5 × 7
## Study `Randomisation process` Deviations from intende…¹ `Missing outcome data`
## <chr> <chr> <chr> <chr>
## 1 2 Low Low Low
## 2 4 Low Low Low
## 3 14 Low Low Low
## 4 15 Low Low Low
## 5 55 Low Low Low
## # ℹ abbreviated name: ¹`Deviations from intended interventions`
## # ℹ 3 more variables: `Measurement of the outcome` <chr>,
## # `Selection of the reported result` <chr>, Overall <chr>## Warning in ggplot2::geom_point(shape = 1, colour = "black", size = psize, : All aesthetics have length 1, but the data has 30 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.## png
## 2## New names:
## • `` -> `...1`## # A tibble: 6 × 8
## Study Selection of participant…¹ Confounding variable…² Measurement of expos…³
## <chr> <chr> <chr> <chr>
## 1 1 Low Low Low
## 2 3 Low Low Low
## 3 5 Low Low Low
## 4 6 Low Low Low
## 5 7 <NA> <NA> <NA>
## 6 8 Low Low Low
## # ℹ abbreviated names: ¹`Selection of participants`, ²`Confounding variables`,
## # ³`Measurement of exposure`
## # ℹ 4 more variables: `Blinding of outcome assessments` <chr>,
## # `Incomplete outcome data` <chr>, `Selective outcome reporting` <chr>,
## # Overall <chr>## Warning in ggplot2::geom_point(shape = 1, colour = "black", size = psize, : All aesthetics have length 1, but the data has 399 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.## Warning: Removed 14 rows containing missing values or values outside the scale range
## (`geom_point()`).
## Removed 14 rows containing missing values or values outside the scale range
## (`geom_point()`).## png
## 2
4. Preparing the data
#z-transform correlation coefficients
Data$CO_cor_Z <- .5 * log((1+Data$CO_cor)/(1-Data$CO_cor))
Data$TPR_cor_Z <- .5 * log((1+Data$TPR_cor)/(1-Data$TPR_cor))
Data$CTI_cor_Z <- .5 * log((1+Data$CTI_cor)/(1-Data$CTI_cor))
Data$Cogni_cor_Z <- .5 * log((1+Data$Cogni_cor)/(1-Data$Cogni_cor))
# calculate z variance
Data$CO_cor_Z_var <- ifelse(is.na(Data$CO_cor), NA, 1 / (Data$n_performance - 3))
Data$TPR_cor_Z_var <- ifelse(is.na(Data$TPR_cor), NA, 1 / (Data$n_performance - 3))
Data$CTI_cor_Z_var <- ifelse(is.na(Data$CTI_cor), NA, 1 / (Data$n_performance - 3))
Data$Cogni_cor_Z_var <- ifelse(is.na(Data$Cogni_cor), NA, 1 / (Data$n_performance - 3))
# calculate z variance squared
Data$CO_cor_Z_var_Sq <- ifelse(is.na(Data$CO_cor), NA, (1 / (Data$n_performance - 3))^2)
Data$TPR_cor_Z_var_Sq <- ifelse(is.na(Data$TPR_cor), NA, (1 / (Data$n_performance - 3))^2)
Data$CTI_cor_Z_var_Sq <- ifelse(is.na(Data$CTI_cor), NA, (1 / (Data$n_performance - 3))^2)
Data$Cogni_cor_Z_var_Sq <- ifelse(is.na(Data$Cogni_cor), NA, (1 / (Data$n_performance - 3))^2)5. Cardiac Output
5.1 Identyfing outliers
# model for outlier analyses and funnel plots
model_fun_CO <- rma(yi = CO_cor_Z, vi= CO_cor_Z_var, data = Data, slab = Ref_APA)## Warning: 94 studies with NAs omitted from model fitting.model_fun_CO##
## Random-Effects Model (k = 68; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0216 (SE = 0.0070)
## tau (square root of estimated tau^2 value): 0.1470
## I^2 (total heterogeneity / total variability): 72.40%
## H^2 (total variability / sampling variability): 3.62
##
## Test for Heterogeneity:
## Q(df = 67) = 151.6929, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.0473 0.0251 1.8842 0.0595 -0.0019 0.0964 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# outliers diagnostics - outlier rstudent > 3.0 #
Out_model_fun_CO <- influence(model_fun_CO)
Out_model_fun_CO##
## rstudent dffits cook.d cov.r tau2.del
## Arthur et al., 2019.1 1.0347 0.0898 0.0081 1.0076 0.0216
## Arthur et al., 2019.2 2.2513 0.1821 0.0327 0.9729 0.0203
## Arthur et al., 2019.3 0.1791 0.0165 0.0003 1.0164 0.0219
## Baumgartner & Schneider, 2023 -0.9394 -0.1317 0.0174 1.0218 0.0217
## Behnke et al., 2020.1 -0.1463 -0.0169 0.0003 1.0421 0.0225
## Behnke et al., 2020.2 0.5616 0.0789 0.0063 1.0355 0.0222
## Behnke et al., 2022 0.1511 0.0295 0.0009 1.0638 0.0229
## Behnke et al., 2024.1 -0.4481 -0.0716 0.0054 1.0577 0.0227
## Behnke et al., 2024.2 0.0193 0.0079 0.0001 1.0656 0.0230
## Brimmell et al., 2019 2.9532 0.3154 0.0902 0.8960 0.0172
## Crowe et al., 2020.1 -0.1674 -0.0169 0.0003 1.0291 0.0222
## Crowe et al., 2020.2 -0.8044 -0.0907 0.0083 1.0183 0.0218
## Crowe et al., 2020.3 0.2848 0.0345 0.0012 1.0285 0.0222
## Crowe et al., 2020.4 -0.4836 -0.0534 0.0029 1.0255 0.0221
## Crowe et al., 2020.5 0.5611 0.0655 0.0043 1.0248 0.0220
## Gurera & Isaacowitz, 2022.1 0.9151 0.1228 0.0151 1.0222 0.0218
## Gurera & Isaacowitz, 2022.3 -0.5247 -0.0613 0.0038 1.0276 0.0221
## Hangen et al., 2019.1 -0.0442 -0.0028 0.0000 1.0571 0.0228
## Hangen et al., 2019.2 0.1425 0.0264 0.0007 1.0567 0.0228
## Hase et al., 2019.1 -1.3587 -0.1669 0.0275 0.9981 0.0210
## Hase et al., 2019.2 -1.1428 -0.1379 0.0189 1.0081 0.0214
## Hase et al., 2019.3 -0.3883 -0.0451 0.0021 1.0307 0.0222
## Hase et al., 2019.4 -0.1056 -0.0102 0.0001 1.0328 0.0223
## Hase et al., 2019.5 -0.7552 -0.0961 0.0093 1.0252 0.0219
## Hase et al., 2019.6 -1.1732 -0.1523 0.0230 1.0078 0.0213
## Hase et al., in preparation.3 -1.1650 -0.1260 0.0158 1.0057 0.0214
## Hase et al., in preparation.4 -1.4301 -0.1537 0.0234 0.9957 0.0210
## Hase et al., in preparation.5 -0.2418 -0.0240 0.0006 1.0251 0.0221
## Hase et al., in preparation.6 -0.7622 -0.0814 0.0066 1.0175 0.0218
## Hase et al., in preparation.7 0.0968 0.0123 0.0002 1.0261 0.0222
## Hase et al., in preparation.8 -0.1995 -0.0194 0.0004 1.0255 0.0221
## Hase et al., in preparation.9 1.5401 0.1587 0.0249 0.9932 0.0209
## Hase et al., in preparation.10 -1.0385 -0.1083 0.0117 1.0093 0.0215
## Hase et al., in preparation.11 -0.0297 -0.0012 0.0000 1.0250 0.0221
## Hase et al., in preparation.12 0.0117 0.0031 0.0000 1.0250 0.0221
## Hase et al., in preparation.13 -0.4023 -0.0405 0.0017 1.0225 0.0220
## Hase et al., in preparation.14 -0.1952 -0.0186 0.0003 1.0244 0.0221
## Jewiss et al., 2023 (Study 1) 1.4804 0.1636 0.0264 0.9948 0.0209
## Jewiss et al., 2023 (Study 2).1 1.3558 0.1530 0.0232 1.0003 0.0211
## Jewiss et al., 2023 (Study 2).2 -0.4416 -0.0489 0.0024 1.0265 0.0221
## Jewiss et al., 2023 (Study 2).3 -0.1687 -0.0172 0.0003 1.0296 0.0222
## Jewiss et al., 2023 (Study 2).4 0.8033 0.0930 0.0087 1.0197 0.0218
## Jewiss et al., 2023 (Study 2).5 0.4719 0.0560 0.0032 1.0267 0.0221
## Jewiss et al., 2023 (Study 2).6 0.1952 0.0246 0.0006 1.0297 0.0222
## Jewiss et al., 2023 (Study 2).7 0.6598 0.0770 0.0060 1.0232 0.0220
## Jewiss et al., 2023 (Study 2).8 0.3791 0.0455 0.0021 1.0280 0.0222
## Jewiss et al., 2024 -0.3899 -0.0422 0.0018 1.0265 0.0221
## Khalaf et al., 2020.1 0.2996 0.0459 0.0022 1.0447 0.0225
## Khalaf et al., 2020.2 0.3568 0.0539 0.0030 1.0438 0.0225
## Moore et al., 2017 1.0957 0.1549 0.0239 1.0157 0.0214
## O'Brien et al., 2022 -0.8356 -0.1052 0.0111 1.0217 0.0218
## Petzel & Casad, 2022.1 5.0892 0.5536 0.1822 0.5913 0.0068
## Petzel & Casad, 2022.2 -0.7755 -0.1015 0.0104 1.0258 0.0219
## Sammy et al., 2017 -0.9385 -0.1166 0.0136 1.0172 0.0217
## Smith et al., 2022.1 -1.4556 -0.1630 0.0262 0.9942 0.0209
## Smith et al., 2022.2 -1.6612 -0.1866 0.0341 0.9845 0.0205
## Smith et al., 2022.3 -2.4387 -0.2758 0.0720 0.9385 0.0188
## Snijdewint & Scheepers, 2023 -0.2693 -0.0357 0.0013 1.0459 0.0225
## Trotman et al., 2018.2 1.4593 0.1946 0.0368 0.9934 0.0207
## Wood et al., 2018 -0.4982 -0.0533 0.0029 1.0235 0.0220
## Scheepers & Keller, 2022 0.3503 0.0557 0.0032 1.0483 0.0226
## Bosshard et al., 2023.2 0.3202 0.0523 0.0028 1.0508 0.0226
## Simms, 2022.1 0.5999 0.0668 0.0045 1.0221 0.0220
## Simms, 2022.2 -1.1956 -0.1307 0.0170 1.0048 0.0213
## Simms, 2022.3 -0.3677 -0.0384 0.0015 1.0249 0.0221
## Simms, 2022.4 1.1624 0.1256 0.0157 1.0074 0.0214
## Simms, 2022.5 -0.4457 -0.0470 0.0022 1.0239 0.0221
## Simms, 2022.6 0.0382 0.0062 0.0000 1.0273 0.0222
## QE.del hat weight dfbs inf
## Arthur et al., 2019.1 150.1654 0.0075 0.7478 0.0898
## Arthur et al., 2019.2 144.9198 0.0071 0.7125 0.1839
## Arthur et al., 2019.3 151.6335 0.0071 0.7125 0.0165
## Baumgartner & Schneider, 2023 149.3719 0.0194 1.9370 -0.1317
## Behnke et al., 2020.1 151.6685 0.0184 1.8358 -0.0169
## Behnke et al., 2020.2 150.6638 0.0184 1.8358 0.0790
## Behnke et al., 2022 150.2281 0.0280 2.8039 0.0299
## Behnke et al., 2024.1 141.1102 0.0286 2.8567 -0.0723
## Behnke et al., 2024.2 151.1877 0.0286 2.8567 0.0080
## Brimmell et al., 2019 136.7619 0.0133 1.3313 0.3193
## Crowe et al., 2020.1 151.6656 0.0127 1.2737 -0.0169
## Crowe et al., 2020.2 150.6703 0.0127 1.2737 -0.0907
## Crowe et al., 2020.3 151.5005 0.0127 1.2737 0.0345
## Crowe et al., 2020.4 151.3490 0.0127 1.2737 -0.0533
## Crowe et al., 2020.5 151.0422 0.0127 1.2737 0.0654
## Gurera & Isaacowitz, 2022.1 149.3577 0.0175 1.7526 0.1228
## Gurera & Isaacowitz, 2022.3 151.2458 0.0142 1.4188 -0.0612
## Hangen et al., 2019.1 151.6911 0.0247 2.4731 -0.0028
## Hangen et al., 2019.2 151.4071 0.0247 2.4731 0.0266
## Hase et al., 2019.1 148.3503 0.0145 1.4511 -0.1671
## Hase et al., 2019.2 149.3862 0.0142 1.4188 -0.1379
## Hase et al., 2019.3 151.4593 0.0145 1.4511 -0.0450
## Hase et al., 2019.4 151.6859 0.0142 1.4188 -0.0102
## Hase et al., 2019.5 150.5634 0.0163 1.6315 -0.0961
## Hase et al., 2019.6 148.8804 0.0163 1.6315 -0.1523
## Hase et al., in preparation.3 149.6406 0.0114 1.1448 -0.1261
## Hase et al., in preparation.4 148.6173 0.0112 1.1214 -0.1541
## Hase et al., in preparation.5 151.6273 0.0112 1.1214 -0.0240
## Hase et al., in preparation.6 150.8412 0.0114 1.1448 -0.0813
## Hase et al., in preparation.7 151.6619 0.0112 1.1214 0.0123
## Hase et al., in preparation.8 151.6520 0.0112 1.1214 -0.0194
## Hase et al., in preparation.9 147.7581 0.0110 1.0973 0.1592
## Hase et al., in preparation.10 150.1305 0.0107 1.0725 -0.1083
## Hase et al., in preparation.11 151.6927 0.0107 1.0725 -0.0012
## Hase et al., in preparation.12 151.6886 0.0107 1.0725 0.0031
## Hase et al., in preparation.13 151.4854 0.0107 1.0725 -0.0404
## Hase et al., in preparation.14 151.6548 0.0107 1.0725 -0.0186
## Jewiss et al., 2023 (Study 1) 147.7007 0.0125 1.2535 0.1639
## Jewiss et al., 2023 (Study 2).1 148.2297 0.0129 1.2933 0.1532
## Jewiss et al., 2023 (Study 2).2 151.4083 0.0129 1.2933 -0.0488
## Jewiss et al., 2023 (Study 2).3 151.6648 0.0129 1.2933 -0.0171
## Jewiss et al., 2023 (Study 2).4 150.4054 0.0129 1.2933 0.0929
## Jewiss et al., 2023 (Study 2).5 151.2130 0.0129 1.2933 0.0559
## Jewiss et al., 2023 (Study 2).6 151.5895 0.0129 1.2933 0.0246
## Jewiss et al., 2023 (Study 2).7 150.8021 0.0129 1.2933 0.0770
## Jewiss et al., 2023 (Study 2).8 151.3698 0.0129 1.2933 0.0454
## Jewiss et al., 2024 151.4819 0.0125 1.2535 -0.0422
## Khalaf et al., 2020.1 151.2775 0.0201 2.0148 0.0460
## Khalaf et al., 2020.2 151.1331 0.0201 2.0148 0.0541
## Moore et al., 2017 147.6524 0.0197 1.9710 0.1548
## O'Brien et al., 2022 150.3460 0.0158 1.5809 -0.1052
## Petzel & Casad, 2022.1 113.1970 0.0172 1.7219 0.5598 *
## Petzel & Casad, 2022.2 150.4113 0.0172 1.7219 -0.1015
## Sammy et al., 2017 150.0421 0.0153 1.5262 -0.1166
## Smith et al., 2022.1 148.3529 0.0121 1.2117 -0.1634
## Smith et al., 2022.2 147.3424 0.0121 1.2117 -0.1873
## Smith et al., 2022.3 142.4886 0.0121 1.2117 -0.2787
## Snijdewint & Scheepers, 2023 151.5308 0.0207 2.0708 -0.0358
## Trotman et al., 2018.2 145.9160 0.0180 1.8004 0.1943
## Wood et al., 2018 151.3417 0.0119 1.1900 -0.0532
## Scheepers & Keller, 2022 150.9690 0.0223 2.2250 0.0560
## Bosshard et al., 2023.2 150.9722 0.0231 2.3134 0.0526
## Simms, 2022.1 151.0057 0.0117 1.1677 0.0667
## Simms, 2022.2 149.5031 0.0117 1.1677 -0.1308
## Simms, 2022.3 151.5156 0.0117 1.1677 -0.0383
## Simms, 2022.4 149.2972 0.0117 1.1677 0.1257
## Simms, 2022.5 151.4207 0.0117 1.1677 -0.0469
## Simms, 2022.6 151.6821 0.0117 1.1677 0.0062rank_corr_test_CO <- ranktest(model_fun_CO)## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościamirank_corr_test_CO##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = -0.0541, p = 0.5210# leave one out analysis #
leave1out(model_fun_CO)##
## estimate se zval pval ci.lb ci.ub
## Arthur et al., 2019.1 0.0450 0.0252 1.7877 0.0738 -0.0043 0.0943
## Arthur et al., 2019.2 0.0427 0.0247 1.7270 0.0842 -0.0058 0.0912
## Arthur et al., 2019.3 0.0468 0.0253 1.8526 0.0639 -0.0027 0.0964
## Baumgartner & Schneider, 2023 0.0506 0.0253 1.9945 0.0461 0.0009 0.1002
## Behnke et al., 2020.1 0.0477 0.0256 1.8625 0.0625 -0.0025 0.0979
## Behnke et al., 2020.2 0.0453 0.0255 1.7734 0.0762 -0.0048 0.0953
## Behnke et al., 2022 0.0465 0.0259 1.7974 0.0723 -0.0042 0.0972
## Behnke et al., 2024.1 0.0491 0.0258 1.9034 0.0570 -0.0015 0.0996
## Behnke et al., 2024.2 0.0470 0.0259 1.8174 0.0692 -0.0037 0.0978
## Brimmell et al., 2019 0.0397 0.0237 1.6733 0.0943 -0.0068 0.0862
## Crowe et al., 2020.1 0.0477 0.0254 1.8741 0.0609 -0.0022 0.0975
## Crowe et al., 2020.2 0.0495 0.0253 1.9573 0.0503 -0.0001 0.0991
## Crowe et al., 2020.3 0.0464 0.0254 1.8236 0.0682 -0.0035 0.0962
## Crowe et al., 2020.4 0.0486 0.0254 1.9137 0.0557 -0.0012 0.0984
## Crowe et al., 2020.5 0.0456 0.0254 1.7963 0.0724 -0.0042 0.0954
## Gurera & Isaacowitz, 2022.1 0.0442 0.0254 1.7419 0.0815 -0.0055 0.0939
## Gurera & Isaacowitz, 2022.3 0.0488 0.0254 1.9196 0.0549 -0.0010 0.0986
## Hangen et al., 2019.1 0.0473 0.0258 1.8354 0.0664 -0.0032 0.0979
## Hangen et al., 2019.2 0.0466 0.0258 1.8067 0.0708 -0.0039 0.0971
## Hase et al., 2019.1 0.0514 0.0251 2.0519 0.0402 0.0023 0.1005
## Hase et al., 2019.2 0.0507 0.0252 2.0136 0.0441 0.0014 0.1000
## Hase et al., 2019.3 0.0484 0.0255 1.9007 0.0573 -0.0015 0.0983
## Hase et al., 2019.4 0.0475 0.0255 1.8642 0.0623 -0.0024 0.0975
## Hase et al., 2019.5 0.0497 0.0254 1.9563 0.0504 -0.0001 0.0994
## Hase et al., 2019.6 0.0511 0.0252 2.0280 0.0426 0.0017 0.1004
## Hase et al., in preparation.3 0.0504 0.0251 2.0042 0.0450 0.0011 0.0997
## Hase et al., in preparation.4 0.0511 0.0250 2.0416 0.0412 0.0020 0.1001
## Hase et al., in preparation.5 0.0479 0.0254 1.8848 0.0595 -0.0019 0.0976
## Hase et al., in preparation.6 0.0493 0.0253 1.9488 0.0513 -0.0003 0.0989
## Hase et al., in preparation.7 0.0469 0.0254 1.8479 0.0646 -0.0028 0.0967
## Hase et al., in preparation.8 0.0477 0.0254 1.8800 0.0601 -0.0020 0.0975
## Hase et al., in preparation.9 0.0433 0.0250 1.7324 0.0832 -0.0057 0.0923
## Hase et al., in preparation.10 0.0500 0.0252 1.9833 0.0473 0.0006 0.0993
## Hase et al., in preparation.11 0.0473 0.0254 1.8623 0.0626 -0.0025 0.0970
## Hase et al., in preparation.12 0.0472 0.0254 1.8580 0.0632 -0.0026 0.0969
## Hase et al., in preparation.13 0.0483 0.0254 1.9036 0.0570 -0.0014 0.0980
## Hase et al., in preparation.14 0.0477 0.0254 1.8802 0.0601 -0.0020 0.0975
## Jewiss et al., 2023 (Study 1) 0.0432 0.0250 1.7262 0.0843 -0.0058 0.0922
## Jewiss et al., 2023 (Study 2).1 0.0434 0.0251 1.7318 0.0833 -0.0057 0.0926
## Jewiss et al., 2023 (Study 2).2 0.0485 0.0254 1.9082 0.0564 -0.0013 0.0983
## Jewiss et al., 2023 (Study 2).3 0.0477 0.0254 1.8740 0.0609 -0.0022 0.0976
## Jewiss et al., 2023 (Study 2).4 0.0449 0.0253 1.7736 0.0761 -0.0047 0.0945
## Jewiss et al., 2023 (Study 2).5 0.0458 0.0254 1.8041 0.0712 -0.0040 0.0956
## Jewiss et al., 2023 (Study 2).6 0.0466 0.0254 1.8325 0.0669 -0.0032 0.0965
## Jewiss et al., 2023 (Study 2).7 0.0453 0.0254 1.7863 0.0740 -0.0044 0.0950
## Jewiss et al., 2023 (Study 2).8 0.0461 0.0254 1.8133 0.0698 -0.0037 0.0959
## Jewiss et al., 2024 0.0483 0.0254 1.9017 0.0572 -0.0015 0.0981
## Khalaf et al., 2020.1 0.0461 0.0256 1.7979 0.0722 -0.0042 0.0963
## Khalaf et al., 2020.2 0.0459 0.0256 1.7908 0.0733 -0.0043 0.0961
## Moore et al., 2017 0.0434 0.0253 1.7163 0.0861 -0.0062 0.0929
## O'Brien et al., 2022 0.0499 0.0253 1.9685 0.0490 0.0002 0.0996
## Petzel & Casad, 2022.1 0.0365 0.0193 1.8954 0.0580 -0.0012 0.0743
## Petzel & Casad, 2022.2 0.0498 0.0254 1.9610 0.0499 0.0000 0.0996
## Sammy et al., 2017 0.0502 0.0253 1.9839 0.0473 0.0006 0.0997
## Smith et al., 2022.1 0.0513 0.0250 2.0521 0.0402 0.0023 0.1003
## Smith et al., 2022.2 0.0519 0.0249 2.0852 0.0371 0.0031 0.1006
## Smith et al., 2022.3 0.0540 0.0243 2.2220 0.0263 0.0064 0.1016
## Snijdewint & Scheepers, 2023 0.0482 0.0256 1.8778 0.0604 -0.0021 0.0984
## Trotman et al., 2018.2 0.0424 0.0250 1.6980 0.0895 -0.0065 0.0914
## Wood et al., 2018 0.0486 0.0254 1.9153 0.0554 -0.0011 0.0983
## Scheepers & Keller, 2022 0.0458 0.0257 1.7850 0.0743 -0.0045 0.0962
## Bosshard et al., 2023.2 0.0459 0.0257 1.7862 0.0741 -0.0045 0.0963
## Simms, 2022.1 0.0456 0.0254 1.7975 0.0723 -0.0041 0.0953
## Simms, 2022.2 0.0505 0.0251 2.0098 0.0445 0.0013 0.0998
## Simms, 2022.3 0.0482 0.0254 1.8993 0.0575 -0.0015 0.0980
## Simms, 2022.4 0.0441 0.0252 1.7524 0.0797 -0.0052 0.0934
## Simms, 2022.5 0.0484 0.0254 1.9088 0.0563 -0.0013 0.0982
## Simms, 2022.6 0.0471 0.0254 1.8529 0.0639 -0.0027 0.0969
## Q Qp tau2 I2 H2
## Arthur et al., 2019.1 150.1654 0.0000 0.0216 72.6522 3.6566
## Arthur et al., 2019.2 144.9198 0.0000 0.0203 71.4010 3.4966
## Arthur et al., 2019.3 151.6335 0.0000 0.0219 72.9742 3.7002
## Baumgartner & Schneider, 2023 149.3719 0.0000 0.0217 72.5101 3.6377
## Behnke et al., 2020.1 151.6685 0.0000 0.0225 73.2766 3.7420
## Behnke et al., 2020.2 150.6638 0.0000 0.0222 73.0548 3.7112
## Behnke et al., 2022 150.2281 0.0000 0.0229 70.5962 3.4009
## Behnke et al., 2024.1 141.1102 0.0000 0.0227 67.6273 3.0890
## Behnke et al., 2024.2 151.1877 0.0000 0.0230 67.9185 3.1171
## Brimmell et al., 2019 136.7619 0.0000 0.0172 67.8293 3.1084
## Crowe et al., 2020.1 151.6656 0.0000 0.0222 73.1543 3.7250
## Crowe et al., 2020.2 150.6703 0.0000 0.0218 72.7846 3.6744
## Crowe et al., 2020.3 151.5005 0.0000 0.0222 73.1341 3.7222
## Crowe et al., 2020.4 151.3490 0.0000 0.0221 73.0294 3.7077
## Crowe et al., 2020.5 151.0422 0.0000 0.0220 73.0065 3.7046
## Gurera & Isaacowitz, 2022.1 149.3577 0.0000 0.0218 72.6528 3.6567
## Gurera & Isaacowitz, 2022.3 151.2458 0.0000 0.0221 73.0279 3.7075
## Hangen et al., 2019.1 151.6911 0.0000 0.0228 73.0550 3.7113
## Hangen et al., 2019.2 151.4071 0.0000 0.0228 73.0407 3.7093
## Hase et al., 2019.1 148.3503 0.0000 0.0210 71.9739 3.5681
## Hase et al., 2019.2 149.3862 0.0000 0.0214 72.3501 3.6166
## Hase et al., 2019.3 151.4593 0.0000 0.0222 73.1168 3.7198
## Hase et al., 2019.4 151.6859 0.0000 0.0223 73.2059 3.7322
## Hase et al., 2019.5 150.5634 0.0000 0.0219 72.8294 3.6804
## Hase et al., 2019.6 148.8804 0.0000 0.0213 72.2188 3.5996
## Hase et al., in preparation.3 149.6406 0.0000 0.0214 72.4063 3.6240
## Hase et al., in preparation.4 148.6173 0.0000 0.0210 72.0565 3.5787
## Hase et al., in preparation.5 151.6273 0.0000 0.0221 73.0915 3.7163
## Hase et al., in preparation.6 150.8412 0.0000 0.0218 72.8177 3.6789
## Hase et al., in preparation.7 151.6619 0.0000 0.0222 73.1234 3.7207
## Hase et al., in preparation.8 151.6520 0.0000 0.0221 73.1019 3.7177
## Hase et al., in preparation.9 147.7581 0.0000 0.0209 71.9754 3.5683
## Hase et al., in preparation.10 150.1305 0.0000 0.0215 72.5660 3.6451
## Hase et al., in preparation.11 151.6927 0.0000 0.0221 73.1089 3.7187
## Hase et al., in preparation.12 151.6886 0.0000 0.0221 73.1101 3.7189
## Hase et al., in preparation.13 151.4854 0.0000 0.0220 73.0235 3.7069
## Hase et al., in preparation.14 151.6548 0.0000 0.0221 73.0875 3.7158
## Jewiss et al., 2023 (Study 1) 147.7007 0.0000 0.0209 71.9587 3.5662
## Jewiss et al., 2023 (Study 2).1 148.2297 0.0000 0.0211 72.1366 3.5889
## Jewiss et al., 2023 (Study 2).2 151.4083 0.0000 0.0221 73.0567 3.7115
## Jewiss et al., 2023 (Study 2).3 151.6648 0.0000 0.0222 73.1596 3.7257
## Jewiss et al., 2023 (Study 2).4 150.4054 0.0000 0.0218 72.8229 3.6796
## Jewiss et al., 2023 (Study 2).5 151.2130 0.0000 0.0221 73.0613 3.7121
## Jewiss et al., 2023 (Study 2).6 151.5895 0.0000 0.0222 73.1622 3.7261
## Jewiss et al., 2023 (Study 2).7 150.8021 0.0000 0.0220 72.9419 3.6957
## Jewiss et al., 2023 (Study 2).8 151.3698 0.0000 0.0222 73.1051 3.7182
## Jewiss et al., 2024 151.4819 0.0000 0.0221 73.0737 3.7138
## Khalaf et al., 2020.1 151.2775 0.0000 0.0225 73.2321 3.7358
## Khalaf et al., 2020.2 151.1331 0.0000 0.0225 73.2002 3.7314
## Moore et al., 2017 147.6524 0.0000 0.0214 72.2692 3.6061
## O'Brien et al., 2022 150.3460 0.0000 0.0218 72.7381 3.6681
## Petzel & Casad, 2022.1 113.1970 0.0003 0.0068 45.3167 1.8287
## Petzel & Casad, 2022.2 150.4113 0.0000 0.0219 72.7981 3.6762
## Sammy et al., 2017 150.0421 0.0000 0.0217 72.6139 3.6515
## Smith et al., 2022.1 148.3529 0.0000 0.0209 71.9580 3.5661
## Smith et al., 2022.2 147.3424 0.0000 0.0205 71.5968 3.5207
## Smith et al., 2022.3 142.4886 0.0000 0.0188 69.7777 3.3088
## Snijdewint & Scheepers, 2023 151.5308 0.0000 0.0225 73.2258 3.7349
## Trotman et al., 2018.2 145.9160 0.0000 0.0207 71.5844 3.5192
## Wood et al., 2018 151.3417 0.0000 0.0220 73.0045 3.7043
## Scheepers & Keller, 2022 150.9690 0.0000 0.0226 73.1537 3.7249
## Bosshard et al., 2023.2 150.9722 0.0000 0.0226 73.1250 3.7209
## Simms, 2022.1 151.0057 0.0000 0.0220 72.9651 3.6989
## Simms, 2022.2 149.5031 0.0000 0.0213 72.3604 3.6180
## Simms, 2022.3 151.5156 0.0000 0.0221 73.0622 3.7123
## Simms, 2022.4 149.2972 0.0000 0.0214 72.4551 3.6304
## Simms, 2022.5 151.4207 0.0000 0.0221 73.0272 3.7074
## Simms, 2022.6 151.6821 0.0000 0.0222 73.1412 3.7232# Egger#
model_fun_CO_OutEgger <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, random = ~ 1 | paper_id/effect_size_id, mod = ~sqrt(CO_cor_Z_var), tdist=TRUE, data = Data)## Warning: 94 rows with NAs omitted from model fitting.model_fun_CO_OutEgger##
## Multivariate Meta-Analysis Model (k = 68; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0154 0.1241 28 no paper_id
## sigma^2.2 0.0113 0.1064 68 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 66) = 150.9737, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 66) = 0.0342, p-val = 0.8539
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.0472 0.0872 0.5410 66 0.5904 -0.1269 0.2213
## sqrt(CO_cor_Z_var) 0.1167 0.6310 0.1849 66 0.8539 -1.1432 1.3766
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Run trim-and-fill analysis for the right side
model_fun_CO_tf_right <- trimfill(model_fun_CO, side = "right")
# Run trim-and-fill analysis for the left side
model_fun_CO_tf_left <- trimfill(model_fun_CO, side = "left")
# Print the trim-and-fill model results
print(model_fun_CO_tf_right)##
## Estimated number of missing studies on the right side: 13 (SE = 5.4346)
##
## Random-Effects Model (k = 81; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0342 (SE = 0.0088)
## tau (square root of estimated tau^2 value): 0.1848
## I^2 (total heterogeneity / total variability): 78.76%
## H^2 (total variability / sampling variability): 4.71
##
## Test for Heterogeneity:
## Q(df = 80) = 224.7476, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.1032 0.0266 3.8850 0.0001 0.0511 0.1553 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(model_fun_CO_tf_left)##
## Estimated number of missing studies on the left side: 0 (SE = 4.4280)
##
## Random-Effects Model (k = 68; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0216 (SE = 0.0070)
## tau (square root of estimated tau^2 value): 0.1470
## I^2 (total heterogeneity / total variability): 72.40%
## H^2 (total variability / sampling variability): 3.62
##
## Test for Heterogeneity:
## Q(df = 67) = 151.6929, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.0473 0.0251 1.8842 0.0595 -0.0019 0.0964 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Combine the number of studies imputed from both sides
total_imputed_studies <- model_fun_CO_tf_right$k0 + model_fun_CO_tf_left$k0
cat("Total number of imputed studies (both sides) for CO:", total_imputed_studies, "\n")## Total number of imputed studies (both sides) for CO: 13# Generate funnel plots only for right side
#par(mfrow=c(1, 3))
#funnel(model_fun_CO, main="Original Model")
funnel(model_fun_CO_tf_right, main="Trim-and-Fill Right", xlab = 'CO')
#funnel(model_fun_CO_tf_left, main="Trim-and-Fill Left")5.2 Multilevel Model
model_CO_multilevel <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML")## Warning: 94 rows with NAs omitted from model fitting.model_CO_multilevel##
## Multivariate Meta-Analysis Model (k = 68; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0134 0.1158 28 no paper_id
## sigma^2.2 0.0114 0.1068 68 no paper_id/effect_size_id
##
## Test for Heterogeneity:
## Q(df = 67) = 151.6929, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.0610 0.0325 1.8779 67 0.0647 -0.0038 0.1258 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1convert_z2r(0.0919)## [1] 0.09164215forest.rma(model_CO_multilevel, header = "CO",slab = Data$Ref_APA, alim=c(-0.8,1.5))
# Prediction Intervals
predict_CO <- predict(model_CO_multilevel, digits=3, transf=transf.ztor, level = 95)
predict_CO##
## pred ci.lb ci.ub pi.lb pi.ub
## 0.061 -0.004 0.125 -0.254 0.364# Additional Parameters for the Multilevel Model
######## list 1 ########
list_CO <- Data$CO_cor_Z_var
############ sum 1#####################
sum_CO <- sum(list_CO, na.rm = TRUE)
###################### sum 2 #####################
sum2_CO <- (sum_CO)^2
####################### list 2 ##############
list_In_CO <- Data$CO_cor_Z_var_Sq
#################### sum 3 #######################
sum_In_CO<- sum(list_In_CO, na.rm = TRUE)
############### numerator ##############
numerator_CO<- (model_CO_multilevel$k-1)*sum_CO
############# denominator #############
denominator_CO<- sum2_CO - sum_In_CO
############## eps ################
EPS_CO<- numerator_CO / denominator_CO
EPS_CO## [1] 39.89371############### i2 1 level ##################
I2_1_CO <- (EPS_CO) / (model_CO_multilevel$sigma2[1] + model_CO_multilevel$sigma2[2] + EPS_CO) *100
I2_1_CO## [1] 99.93783############## i2 2 level #################
I2_2_CO <- (model_CO_multilevel$sigma2[1]) / (model_CO_multilevel$sigma2[1] + model_CO_multilevel$sigma2[2] + EPS_CO) *100
I2_2_CO## [1] 0.03357787########### I2 level 3
I2_3_CO <- (model_CO_multilevel$sigma2[2]) / (model_CO_multilevel$sigma2[1] + model_CO_multilevel$sigma2[2] + EPS_CO) *100
I2_3_CO## [1] 0.0285909############### ML without level 2 ##########
model_CO_multilevel_2 <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(0,NA), tdist=TRUE,data = Data)## Warning: 94 rows with NAs omitted from model fitting.############# ml without level 3 ###########
model_CO_multilevel_3 <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(NA,0), tdist=TRUE,data = Data)## Warning: 94 rows with NAs omitted from model fitting.##################### sig level 2 #######################
anova12_CO <- anova(model_CO_multilevel,model_CO_multilevel_2)
anova12_CO##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 -10.5180 -3.9039 -10.1371 8.2590 151.6929
## Reduced 2 -9.5398 -5.1304 -9.3523 6.7699 2.9782 0.0844 151.6929###############sig level 3v #################
anova13_CO <- anova(model_CO_multilevel,model_CO_multilevel_3)
anova13_CO##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 -10.5180 -3.9039 -10.1371 8.2590 151.6929
## Reduced 2 -4.7673 -0.3579 -4.5798 4.3836 7.7507 0.0054 151.69296. Total Peripheral Resistance
6.1 Identyfing outliers
model_fun_TPR <- rma(yi = TPR_cor_Z, vi= TPR_cor_Z_var, data = Data, slab = Ref_APA)## Warning: 101 studies with NAs omitted from model fitting.model_fun_TPR##
## Random-Effects Model (k = 61; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0130 (SE = 0.0060)
## tau (square root of estimated tau^2 value): 0.1139
## I^2 (total heterogeneity / total variability): 49.04%
## H^2 (total variability / sampling variability): 1.96
##
## Test for Heterogeneity:
## Q(df = 60) = 117.8564, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -0.0799 0.0240 -3.3272 0.0009 -0.1270 -0.0328 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# outliers diagnostics - outlier rstudent > 3.0 #
Out_model_fun_TPR <- influence(model_fun_TPR)
Out_model_fun_TPR##
## rstudent dffits cook.d cov.r tau2.del
## Arthur et al., 2019.1 -1.1454 -0.1023 0.0104 1.0036 0.0128
## Arthur et al., 2019.2 -0.5555 -0.0455 0.0021 1.0117 0.0131
## Arthur et al., 2019.3 0.7127 0.0634 0.0040 1.0123 0.0131
## Baumgartner & Schneider, 2023 0.0651 0.0216 0.0005 1.0501 0.0137
## Behnke et al., 2024.1 1.2704 0.2657 0.0668 1.0211 0.0122
## Brimmell et al., 2019 -2.5624 -0.3573 0.1197 0.9319 0.0106
## Crowe et al., 2020.1 -0.3022 -0.0304 0.0009 1.0272 0.0133
## Crowe et al., 2020.2 0.2982 0.0425 0.0018 1.0286 0.0134
## Crowe et al., 2020.3 0.8475 0.1047 0.0110 1.0206 0.0131
## Crowe et al., 2020.4 0.0994 0.0189 0.0004 1.0294 0.0134
## Crowe et al., 2020.5 0.5967 0.0768 0.0059 1.0253 0.0133
## Hangen et al., 2019.1 0.5387 0.1113 0.0130 1.0616 0.0137
## Hangen et al., 2019.2 0.6168 0.1247 0.0162 1.0587 0.0137
## Hase et al., 2019.1 2.2108 0.2551 0.0620 0.9615 0.0114
## Hase et al., 2019.2 1.2757 0.1600 0.0254 1.0094 0.0128
## Hase et al., 2019.3 0.6282 0.0874 0.0077 1.0290 0.0133
## Hase et al., 2019.4 0.2224 0.0363 0.0013 1.0331 0.0135
## Hase et al., 2019.5 0.5259 0.0811 0.0067 1.0356 0.0134
## Hase et al., 2019.6 0.5942 0.0900 0.0082 1.0343 0.0134
## Hase et al., in preparation.3 0.1865 0.0271 0.0007 1.0257 0.0134
## Hase et al., in preparation.4 -0.1398 -0.0099 0.0001 1.0246 0.0133
## Hase et al., in preparation.5 -0.0933 -0.0046 0.0000 1.0248 0.0133
## Hase et al., in preparation.6 0.7473 0.0877 0.0077 1.0201 0.0132
## Hase et al., in preparation.7 1.4549 0.1558 0.0241 1.0020 0.0127
## Hase et al., in preparation.8 -0.0468 0.0007 0.0000 1.0250 0.0133
## Hase et al., in preparation.9 -1.5782 -0.1818 0.0326 0.9913 0.0124
## Hase et al., in preparation.10 0.4486 0.0536 0.0029 1.0223 0.0133
## Hase et al., in preparation.11 -1.0838 -0.1189 0.0141 1.0076 0.0128
## Hase et al., in preparation.12 0.6286 0.0722 0.0052 1.0203 0.0132
## Hase et al., in preparation.13 0.6286 0.0722 0.0052 1.0203 0.0132
## Hase et al., in preparation.14 -0.6451 -0.0671 0.0045 1.0175 0.0131
## Jewiss et al., 2023 (Study 1) -1.9260 -0.2474 0.0594 0.9731 0.0118
## Jewiss et al., 2023 (Study 2).1 -0.6691 -0.0779 0.0061 1.0215 0.0132
## Jewiss et al., 2023 (Study 2).2 -0.5116 -0.0574 0.0033 1.0247 0.0133
## Jewiss et al., 2023 (Study 2).3 0.1505 0.0253 0.0006 1.0298 0.0134
## Jewiss et al., 2023 (Study 2).4 -0.5116 -0.0574 0.0033 1.0247 0.0133
## Jewiss et al., 2023 (Study 2).5 -0.2029 -0.0181 0.0003 1.0287 0.0134
## Jewiss et al., 2023 (Study 2).6 -0.2029 -0.0181 0.0003 1.0287 0.0134
## Jewiss et al., 2023 (Study 2).7 0.6023 0.0782 0.0062 1.0257 0.0133
## Jewiss et al., 2023 (Study 2).8 0.9066 0.1121 0.0126 1.0195 0.0131
## Jewiss et al., 2024 0.5910 0.0754 0.0057 1.0249 0.0133
## Khalaf et al., 2020.1 0.0270 0.0162 0.0003 1.0529 0.0138
## Khalaf et al., 2020.2 -0.1737 -0.0166 0.0003 1.0515 0.0137
## Moore et al., 2017 -1.6109 -0.2845 0.0763 0.9802 0.0116
## O'Brien et al., 2022 -1.3518 -0.1951 0.0374 0.9997 0.0124
## Petzel & Casad, 2022.1 -3.6025 -0.7086 0.3951 0.8075 0.0070
## Petzel & Casad, 2022.2 -0.1086 -0.0062 0.0000 1.0423 0.0136
## Sammy et al., 2017 1.6013 0.2029 0.0403 0.9948 0.0123
## Smith et al., 2022.1 -0.9429 -0.1098 0.0121 1.0131 0.0130
## Smith et al., 2022.2 -0.5772 -0.0635 0.0041 1.0216 0.0132
## Smith et al., 2022.3 -1.3001 -0.1565 0.0243 1.0015 0.0126
## Trotman et al., 2018.2 -1.3110 -0.2069 0.0419 1.0024 0.0124
## Wood et al., 2018 0.5727 0.0710 0.0051 1.0237 0.0133
## Scheepers & Keller, 2022 0.4492 0.0885 0.0081 1.0557 0.0137
## Bosshard et al., 2023.2 0.5133 0.1017 0.0108 1.0569 0.0137
## Simms, 2022.1 -0.1623 -0.0126 0.0002 1.0257 0.0133
## Simms, 2022.2 1.2756 0.1423 0.0202 1.0078 0.0128
## Simms, 2022.3 0.2972 0.0399 0.0016 1.0258 0.0133
## Simms, 2022.4 -0.9424 -0.1073 0.0115 1.0125 0.0130
## Simms, 2022.5 0.5332 0.0659 0.0044 1.0237 0.0133
## Simms, 2022.6 0.4199 0.0535 0.0029 1.0249 0.0133
## QE.del hat weight dfbs inf
## Arthur et al., 2019.1 115.6011 0.0076 0.7646 -0.1024
## Arthur et al., 2019.2 117.1407 0.0072 0.7246 -0.0454
## Arthur et al., 2019.3 117.5669 0.0072 0.7246 0.0633
## Baumgartner & Schneider, 2023 117.6039 0.0242 2.4209 0.0216
## Behnke et al., 2024.1 92.0135 0.0431 4.3115 0.2616
## Brimmell et al., 2019 106.2089 0.0149 1.4947 -0.3610
## Crowe et al., 2020.1 117.3103 0.0142 1.4163 -0.0303
## Crowe et al., 2020.2 117.8563 0.0142 1.4163 0.0424
## Crowe et al., 2020.3 117.4306 0.0142 1.4163 0.1046
## Crowe et al., 2020.4 117.7928 0.0142 1.4163 0.0188
## Crowe et al., 2020.5 117.7337 0.0142 1.4163 0.0767
## Hangen et al., 2019.1 117.8382 0.0344 3.4352 0.1124
## Hangen et al., 2019.2 117.7661 0.0344 3.4352 0.1258
## Hase et al., 2019.1 112.5643 0.0166 1.6627 0.2561
## Hase et al., 2019.2 116.4717 0.0162 1.6167 0.1600
## Hase et al., 2019.3 117.7173 0.0166 1.6627 0.0874
## Hase et al., 2019.4 117.8387 0.0162 1.6167 0.0362
## Hase et al., 2019.5 117.8068 0.0193 1.9289 0.0811
## Hase et al., 2019.6 117.7582 0.0193 1.9289 0.0900
## Hase et al., in preparation.3 117.8420 0.0125 1.2463 0.0271
## Hase et al., in preparation.4 117.6082 0.0122 1.2161 -0.0099
## Hase et al., in preparation.5 117.6596 0.0122 1.2161 -0.0046
## Hase et al., in preparation.6 117.5648 0.0125 1.2463 0.0876
## Hase et al., in preparation.7 115.9999 0.0122 1.2161 0.1561
## Hase et al., in preparation.8 117.7050 0.0122 1.2161 0.0007
## Hase et al., in preparation.9 113.2293 0.0119 1.1854 -0.1826
## Hase et al., in preparation.10 117.8169 0.0115 1.1540 0.0535
## Hase et al., in preparation.11 115.3756 0.0115 1.1540 -0.1190
## Hase et al., in preparation.12 117.6904 0.0115 1.1540 0.0721
## Hase et al., in preparation.13 117.6904 0.0115 1.1540 0.0721
## Hase et al., in preparation.14 116.7107 0.0115 1.1540 -0.0671
## Jewiss et al., 2023 (Study 1) 110.8684 0.0139 1.3892 -0.2488
## Jewiss et al., 2023 (Study 2).1 116.4399 0.0144 1.4429 -0.0778
## Jewiss et al., 2023 (Study 2).2 116.8568 0.0144 1.4429 -0.0573
## Jewiss et al., 2023 (Study 2).3 117.8186 0.0144 1.4429 0.0252
## Jewiss et al., 2023 (Study 2).4 116.8568 0.0144 1.4429 -0.0573
## Jewiss et al., 2023 (Study 2).5 117.4657 0.0144 1.4429 -0.0181
## Jewiss et al., 2023 (Study 2).6 117.4657 0.0144 1.4429 -0.0181
## Jewiss et al., 2023 (Study 2).7 117.7303 0.0144 1.4429 0.0781
## Jewiss et al., 2023 (Study 2).8 117.3334 0.0144 1.4429 0.1121
## Jewiss et al., 2024 117.7372 0.0139 1.3892 0.0753
## Khalaf et al., 2020.1 117.5001 0.0256 2.5553 0.0163
## Khalaf et al., 2020.2 117.0312 0.0256 2.5553 -0.0166
## Moore et al., 2017 109.1560 0.0248 2.4792 -0.2826
## O'Brien et al., 2022 112.9972 0.0185 1.8526 -0.1952
## Petzel & Casad, 2022.1 94.5681 0.0207 2.0689 -0.7069 *
## Petzel & Casad, 2022.2 117.4207 0.0207 2.0689 -0.0062
## Sammy et al., 2017 115.3210 0.0177 1.7715 0.2031
## Smith et al., 2022.1 115.6715 0.0133 1.3336 -0.1098
## Smith et al., 2022.2 116.7635 0.0133 1.3336 -0.0634
## Smith et al., 2022.3 114.2596 0.0133 1.3336 -0.1568
## Trotman et al., 2018.2 112.3381 0.0219 2.1941 -0.2066
## Wood et al., 2018 117.7475 0.0131 1.3051 0.0709
## Scheepers & Keller, 2022 117.8562 0.0294 2.9391 0.0891
## Bosshard et al., 2023.2 117.8441 0.0311 3.1102 0.1025
## Simms, 2022.1 117.5671 0.0128 1.2760 -0.0126
## Simms, 2022.2 116.5156 0.0128 1.2760 0.1424
## Simms, 2022.3 117.8564 0.0128 1.2760 0.0398
## Simms, 2022.4 115.7351 0.0128 1.2760 -0.1073
## Simms, 2022.5 117.7748 0.0128 1.2760 0.0657
## Simms, 2022.6 117.8334 0.0128 1.2760 0.0534ranktest(model_fun_TPR)## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = -0.0117, p = 0.8957# leave one out analysis #
leave1out(model_fun_TPR)##
## estimate se zval pval ci.lb ci.ub
## Arthur et al., 2019.1 -0.0775 0.0241 -3.2192 0.0013 -0.1246 -0.0303
## Arthur et al., 2019.2 -0.0788 0.0242 -3.2626 0.0011 -0.1262 -0.0315
## Arthur et al., 2019.3 -0.0815 0.0242 -3.3701 0.0008 -0.1288 -0.0341
## Baumgartner & Schneider, 2023 -0.0805 0.0246 -3.2681 0.0011 -0.1287 -0.0322
## Behnke et al., 2024.1 -0.0861 0.0243 -3.5484 0.0004 -0.1337 -0.0386
## Brimmell et al., 2019 -0.0716 0.0232 -3.0882 0.0020 -0.1171 -0.0262
## Crowe et al., 2020.1 -0.0792 0.0243 -3.2527 0.0011 -0.1269 -0.0315
## Crowe et al., 2020.2 -0.0810 0.0244 -3.3227 0.0009 -0.1287 -0.0332
## Crowe et al., 2020.3 -0.0824 0.0243 -3.3973 0.0007 -0.1300 -0.0349
## Crowe et al., 2020.4 -0.0804 0.0244 -3.2981 0.0010 -0.1281 -0.0326
## Crowe et al., 2020.5 -0.0818 0.0243 -3.3620 0.0008 -0.1295 -0.0341
## Hangen et al., 2019.1 -0.0827 0.0248 -3.3396 0.0008 -0.1312 -0.0341
## Hangen et al., 2019.2 -0.0830 0.0247 -3.3574 0.0008 -0.1314 -0.0345
## Hase et al., 2019.1 -0.0859 0.0236 -3.6472 0.0003 -0.1321 -0.0397
## Hase et al., 2019.2 -0.0838 0.0241 -3.4704 0.0005 -0.1311 -0.0365
## Hase et al., 2019.3 -0.0820 0.0244 -3.3666 0.0008 -0.1298 -0.0343
## Hase et al., 2019.4 -0.0808 0.0244 -3.3093 0.0009 -0.1287 -0.0329
## Hase et al., 2019.5 -0.0819 0.0244 -3.3497 0.0008 -0.1298 -0.0340
## Hase et al., 2019.6 -0.0821 0.0244 -3.3608 0.0008 -0.1300 -0.0342
## Hase et al., in preparation.3 -0.0806 0.0243 -3.3121 0.0009 -0.1283 -0.0329
## Hase et al., in preparation.4 -0.0797 0.0243 -3.2772 0.0010 -0.1273 -0.0320
## Hase et al., in preparation.5 -0.0798 0.0243 -3.2821 0.0010 -0.1275 -0.0322
## Hase et al., in preparation.6 -0.0820 0.0243 -3.3813 0.0007 -0.1296 -0.0345
## Hase et al., in preparation.7 -0.0837 0.0240 -3.4790 0.0005 -0.1308 -0.0365
## Hase et al., in preparation.8 -0.0799 0.0243 -3.2870 0.0010 -0.1276 -0.0323
## Hase et al., in preparation.9 -0.0756 0.0239 -3.1604 0.0016 -0.1225 -0.0287
## Hase et al., in preparation.10 -0.0812 0.0243 -3.3439 0.0008 -0.1288 -0.0336
## Hase et al., in preparation.11 -0.0771 0.0241 -3.1964 0.0014 -0.1243 -0.0298
## Hase et al., in preparation.12 -0.0817 0.0243 -3.3655 0.0008 -0.1292 -0.0341
## Hase et al., in preparation.13 -0.0817 0.0243 -3.3655 0.0008 -0.1292 -0.0341
## Hase et al., in preparation.14 -0.0783 0.0242 -3.2318 0.0012 -0.1258 -0.0308
## Jewiss et al., 2023 (Study 1) -0.0741 0.0237 -3.1258 0.0018 -0.1205 -0.0276
## Jewiss et al., 2023 (Study 2).1 -0.0780 0.0243 -3.2148 0.0013 -0.1256 -0.0305
## Jewiss et al., 2023 (Study 2).2 -0.0785 0.0243 -3.2300 0.0012 -0.1262 -0.0309
## Jewiss et al., 2023 (Study 2).3 -0.0805 0.0244 -3.3037 0.0010 -0.1283 -0.0328
## Jewiss et al., 2023 (Study 2).4 -0.0785 0.0243 -3.2300 0.0012 -0.1262 -0.0309
## Jewiss et al., 2023 (Study 2).5 -0.0795 0.0244 -3.2624 0.0011 -0.1272 -0.0317
## Jewiss et al., 2023 (Study 2).6 -0.0795 0.0244 -3.2624 0.0011 -0.1272 -0.0317
## Jewiss et al., 2023 (Study 2).7 -0.0818 0.0243 -3.3628 0.0008 -0.1295 -0.0341
## Jewiss et al., 2023 (Study 2).8 -0.0826 0.0243 -3.4064 0.0007 -0.1302 -0.0351
## Jewiss et al., 2024 -0.0817 0.0243 -3.3612 0.0008 -0.1294 -0.0341
## Khalaf et al., 2020.1 -0.0803 0.0246 -3.2587 0.0011 -0.1286 -0.0320
## Khalaf et al., 2020.2 -0.0795 0.0246 -3.2283 0.0012 -0.1278 -0.0312
## Moore et al., 2017 -0.0733 0.0238 -3.0816 0.0021 -0.1199 -0.0267
## O'Brien et al., 2022 -0.0753 0.0240 -3.1343 0.0017 -0.1224 -0.0282
## Petzel & Casad, 2022.1 -0.0648 0.0216 -3.0031 0.0027 -0.1071 -0.0225
## Petzel & Casad, 2022.2 -0.0798 0.0245 -3.2529 0.0011 -0.1278 -0.0317
## Sammy et al., 2017 -0.0847 0.0240 -3.5372 0.0004 -0.1317 -0.0378
## Smith et al., 2022.1 -0.0773 0.0242 -3.1965 0.0014 -0.1247 -0.0299
## Smith et al., 2022.2 -0.0784 0.0243 -3.2288 0.0012 -0.1260 -0.0308
## Smith et al., 2022.3 -0.0762 0.0240 -3.1690 0.0015 -0.1233 -0.0291
## Trotman et al., 2018.2 -0.0750 0.0241 -3.1189 0.0018 -0.1221 -0.0279
## Wood et al., 2018 -0.0816 0.0243 -3.3588 0.0008 -0.1293 -0.0340
## Scheepers & Keller, 2022 -0.0821 0.0247 -3.3261 0.0009 -0.1305 -0.0337
## Bosshard et al., 2023.2 -0.0824 0.0247 -3.3373 0.0008 -0.1308 -0.0340
## Simms, 2022.1 -0.0796 0.0243 -3.2728 0.0011 -0.1273 -0.0319
## Simms, 2022.2 -0.0833 0.0241 -3.4558 0.0005 -0.1306 -0.0361
## Simms, 2022.3 -0.0809 0.0243 -3.3246 0.0009 -0.1286 -0.0332
## Simms, 2022.4 -0.0773 0.0242 -3.1999 0.0014 -0.1247 -0.0300
## Simms, 2022.5 -0.0815 0.0243 -3.3538 0.0008 -0.1291 -0.0339
## Simms, 2022.6 -0.0812 0.0243 -3.3396 0.0008 -0.1289 -0.0336
## Q Qp tau2 I2 H2
## Arthur et al., 2019.1 115.6011 0.0000 0.0128 49.1178 1.9653
## Arthur et al., 2019.2 117.1407 0.0000 0.0131 49.6122 1.9846
## Arthur et al., 2019.3 117.5669 0.0000 0.0131 49.6447 1.9859
## Baumgartner & Schneider, 2023 117.6039 0.0000 0.0137 50.2527 2.0102
## Behnke et al., 2024.1 92.0135 0.0038 0.0122 38.7534 1.6327
## Brimmell et al., 2019 106.2089 0.0002 0.0106 44.0855 1.7884
## Crowe et al., 2020.1 117.3103 0.0000 0.0133 49.9444 1.9978
## Crowe et al., 2020.2 117.8563 0.0000 0.0134 50.0218 2.0009
## Crowe et al., 2020.3 117.4306 0.0000 0.0131 49.5710 1.9830
## Crowe et al., 2020.4 117.7928 0.0000 0.0134 50.0627 2.0025
## Crowe et al., 2020.5 117.7337 0.0000 0.0133 49.8377 1.9935
## Hangen et al., 2019.1 117.8382 0.0000 0.0137 49.1716 1.9674
## Hangen et al., 2019.2 117.7661 0.0000 0.0137 49.0087 1.9611
## Hase et al., 2019.1 112.5643 0.0000 0.0114 45.8380 1.8463
## Hase et al., 2019.2 116.4717 0.0000 0.0128 48.7662 1.9518
## Hase et al., 2019.3 117.7173 0.0000 0.0133 49.8336 1.9934
## Hase et al., 2019.4 117.8387 0.0000 0.0135 50.1028 2.0041
## Hase et al., 2019.5 117.8068 0.0000 0.0134 49.9603 1.9984
## Hase et al., 2019.6 117.7582 0.0000 0.0134 49.8840 1.9954
## Hase et al., in preparation.3 117.8420 0.0000 0.0134 49.9966 1.9999
## Hase et al., in preparation.4 117.6082 0.0000 0.0133 49.9588 1.9984
## Hase et al., in preparation.5 117.6596 0.0000 0.0133 49.9720 1.9989
## Hase et al., in preparation.6 117.5648 0.0000 0.0132 49.6817 1.9873
## Hase et al., in preparation.7 115.9999 0.0000 0.0127 48.6767 1.9484
## Hase et al., in preparation.8 117.7050 0.0000 0.0133 49.9821 1.9993
## Hase et al., in preparation.9 113.2293 0.0000 0.0124 48.0697 1.9257
## Hase et al., in preparation.10 117.8169 0.0000 0.0133 49.8813 1.9953
## Hase et al., in preparation.11 115.3756 0.0000 0.0128 49.0463 1.9626
## Hase et al., in preparation.12 117.6904 0.0000 0.0132 49.7712 1.9909
## Hase et al., in preparation.13 117.6904 0.0000 0.0132 49.7712 1.9909
## Hase et al., in preparation.14 116.7107 0.0000 0.0131 49.6099 1.9845
## Jewiss et al., 2023 (Study 1) 110.8684 0.0001 0.0118 46.8025 1.8798
## Jewiss et al., 2023 (Study 2).1 116.4399 0.0000 0.0132 49.6015 1.9842
## Jewiss et al., 2023 (Study 2).2 116.8568 0.0000 0.0133 49.7797 1.9912
## Jewiss et al., 2023 (Study 2).3 117.8186 0.0000 0.0134 50.0669 2.0027
## Jewiss et al., 2023 (Study 2).4 116.8568 0.0000 0.0133 49.7797 1.9912
## Jewiss et al., 2023 (Study 2).5 117.4657 0.0000 0.0134 50.0065 2.0003
## Jewiss et al., 2023 (Study 2).6 117.4657 0.0000 0.0134 50.0065 2.0003
## Jewiss et al., 2023 (Study 2).7 117.7303 0.0000 0.0133 49.8365 1.9935
## Jewiss et al., 2023 (Study 2).8 117.3334 0.0000 0.0131 49.4903 1.9798
## Jewiss et al., 2024 117.7372 0.0000 0.0133 49.8387 1.9936
## Khalaf et al., 2020.1 117.5001 0.0000 0.0138 50.2441 2.0098
## Khalaf et al., 2020.2 117.0312 0.0000 0.0137 50.1680 2.0067
## Moore et al., 2017 109.1560 0.0001 0.0116 46.1263 1.8562
## O'Brien et al., 2022 112.9972 0.0000 0.0124 47.9867 1.9226
## Petzel & Casad, 2022.1 94.5681 0.0023 0.0070 34.2352 1.5206
## Petzel & Casad, 2022.2 117.4207 0.0000 0.0136 50.1916 2.0077
## Sammy et al., 2017 115.3210 0.0000 0.0123 47.7699 1.9146
## Smith et al., 2022.1 115.6715 0.0000 0.0130 49.2172 1.9692
## Smith et al., 2022.2 116.7635 0.0000 0.0132 49.6983 1.9880
## Smith et al., 2022.3 114.2596 0.0000 0.0126 48.5472 1.9435
## Trotman et al., 2018.2 112.3381 0.0000 0.0124 47.7982 1.9156
## Wood et al., 2018 117.7475 0.0000 0.0133 49.8392 1.9936
## Scheepers & Keller, 2022 117.8562 0.0000 0.0137 49.8700 1.9948
## Bosshard et al., 2023.2 117.8441 0.0000 0.0137 49.6472 1.9860
## Simms, 2022.1 117.5671 0.0000 0.0133 49.9714 1.9989
## Simms, 2022.2 116.5156 0.0000 0.0128 48.9619 1.9593
## Simms, 2022.3 117.8564 0.0000 0.0133 49.9799 1.9992
## Simms, 2022.4 115.7351 0.0000 0.0130 49.2307 1.9697
## Simms, 2022.5 117.7748 0.0000 0.0133 49.8618 1.9945
## Simms, 2022.6 117.8334 0.0000 0.0133 49.9288 1.9972# Egger#
model_fun_TPR_OutEgger <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, random = ~ 1 | paper_id/effect_size_id, mod = ~sqrt(TPR_cor_Z_var), tdist=TRUE, data = Data)## Warning: 101 rows with NAs omitted from model fitting.model_fun_TPR_OutEgger##
## Multivariate Meta-Analysis Model (k = 61; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0169 0.1299 24 no paper_id
## sigma^2.2 0.0000 0.0000 61 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 59) = 94.1233, p-val = 0.0025
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 59) = 1.3928, p-val = 0.2427
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.0011 0.0901 0.0119 59 0.9906 -0.1793 0.1815
## sqrt(TPR_cor_Z_var) -0.7579 0.6422 -1.1802 59 0.2427 -2.0430 0.5272
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Run trim-and-fill analysis for the right side
model_fun_TPR_tf_right <- trimfill(model_fun_TPR, side = "right")
# Run trim-and-fill analysis for the left side
model_fun_TPR_tf_left <- trimfill(model_fun_TPR, side = "left")
# Print the trim-and-fill model results
print(model_fun_TPR_tf_right)##
## Estimated number of missing studies on the right side: 0 (SE = 4.4372)
##
## Random-Effects Model (k = 61; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0130 (SE = 0.0060)
## tau (square root of estimated tau^2 value): 0.1139
## I^2 (total heterogeneity / total variability): 49.04%
## H^2 (total variability / sampling variability): 1.96
##
## Test for Heterogeneity:
## Q(df = 60) = 117.8564, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -0.0799 0.0240 -3.3272 0.0009 -0.1270 -0.0328 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(model_fun_TPR_tf_left)##
## Estimated number of missing studies on the left side: 4 (SE = 4.9501)
##
## Random-Effects Model (k = 65; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0174 (SE = 0.0068)
## tau (square root of estimated tau^2 value): 0.1321
## I^2 (total heterogeneity / total variability): 55.84%
## H^2 (total variability / sampling variability): 2.26
##
## Test for Heterogeneity:
## Q(df = 64) = 145.0705, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -0.1015 0.0250 -4.0679 <.0001 -0.1505 -0.0526 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Combine the number of studies imputed from both sides
total_imputed_studies <- model_fun_TPR_tf_right$k0 + model_fun_TPR_tf_left$k0
cat("Total number of imputed studies (both sides) for TPR:", total_imputed_studies, "\n")## Total number of imputed studies (both sides) for TPR: 4# Generate funnel plots only lef
#par(mfrow=c(1, 3))
#funnel(model_fun_TPR, main="Original Model")
#funnel(model_fun_TPR_tf_right, main="Trim-and-Fill Right")
funnel(model_fun_TPR_tf_left, main="Trim-and-Fill Left", xlab = 'TPR')
# Return to single plot layout
#par(mfrow=c(1, 1))6.2 Multilevel Model
model_TPR_multilevel <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML")## Warning: 101 rows with NAs omitted from model fitting.model_TPR_multilevel##
## Multivariate Meta-Analysis Model (k = 61; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0174 0.1319 24 no paper_id
## sigma^2.2 0.0000 0.0000 61 no paper_id/effect_size_id
##
## Test for Heterogeneity:
## Q(df = 60) = 117.8564, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## -0.0980 0.0341 -2.8734 60 0.0056 -0.1662 -0.0298 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1convert_z2r(-0.1042)## [1] -0.1038245predict_TPR <- predict(model_TPR_multilevel, digits=3, transf=transf.ztor, level = 95)
predict_TPR##
## pred ci.lb ci.ub pi.lb pi.ub
## -0.098 -0.165 -0.030 -0.354 0.173forest.rma(model_TPR_multilevel, header = "TPR",slab = Data$Ref_APA, alim=c(-1, 1))
######## list 1 ########
list_TPR <- Data$TPR_cor_Z_var
############ sum 1#####################
sum_TPR <- sum(list_TPR, na.rm = TRUE)
###################### sum 2 #####################
sum2_TPR <- (sum_TPR)^2
####################### list 2 ##############
list_In_TPR <- Data$TPR_cor_Z_var_Sq
#################### sum 3 #######################
sum_In_TPR<- sum(list_In_TPR, na.rm = TRUE)
################ numerator ##############
numerator_TPR<- (model_TPR_multilevel$k-1)*sum_TPR
############# denominator #############
denominator_TPR<- sum2_TPR - sum_In_TPR
############## eps ################
EPS_TPR<- numerator_TPR / denominator_TPR
############### i2 1 level ##################
I2_1_TPR <- (EPS_TPR) / (model_TPR_multilevel$sigma2[1] + model_TPR_multilevel$sigma2[2] + EPS_TPR) *100
I2_1_TPR## [1] 99.95343############## i2 2 level #################
I2_2_TPR <- (model_TPR_multilevel$sigma2[1]) / (model_TPR_multilevel$sigma2[1] + model_TPR_multilevel$sigma2[2] + EPS_TPR) *100
I2_2_TPR## [1] 0.04656649########### I2 level 3
I2_3_TPR <- (model_TPR_multilevel$sigma2[2]) / (model_TPR_multilevel$sigma2[1] + model_TPR_multilevel$sigma2[2] + EPS_TPR) *100
I2_3_TPR## [1] 6.142443e-11############### ML without level 2 ##########
model_TPR_multilevel_2 <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(0,NA), tdist=TRUE,data = Data)## Warning: 101 rows with NAs omitted from model fitting.############# ml without level 3 ###########
model_TPR_multilevel_3 <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(NA,0), tdist=TRUE,data = Data)## Warning: 101 rows with NAs omitted from model fitting.##################### sig level 2 #######################
anova12_TPR <- anova(model_TPR_multilevel,model_TPR_multilevel_2)
anova12_TPR##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 -26.9774 -20.6943 -26.5488 16.4887 117.8564
## Reduced 2 -24.9796 -20.7909 -24.7691 14.4898 3.9978 0.0456 117.8564###############sig level 3v #################
anova13_TPR <- anova(model_TPR_multilevel,model_TPR_multilevel_3)
anova13_TPR##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 -26.9774 -20.6943 -26.5488 16.4887 117.8564
## Reduced 2 -28.9774 -24.7887 -28.7668 16.4887 0.0000 1.0000 117.85647. Cardiovascular Challenge and Threat Index
7.1 Identyfing outliers
# CTI
model_fun_CTI <- rma(yi = CTI_cor_Z, vi= CTI_cor_Z_var, data = Data, slab = Ref_APA)## Warning: 89 studies with NAs omitted from model fitting.model_fun_CTI##
## Random-Effects Model (k = 73; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0293 (SE = 0.0088)
## tau (square root of estimated tau^2 value): 0.1710
## I^2 (total heterogeneity / total variability): 66.76%
## H^2 (total variability / sampling variability): 3.01
##
## Test for Heterogeneity:
## Q(df = 72) = 195.5175, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.0966 0.0273 3.5456 0.0004 0.0432 0.1501 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# outliers diagnostics - outlier rstudent > 3.0 #
Out_model_fun_CTI <- influence(model_fun_CTI)
Out_model_fun_CTI##
## rstudent dffits cook.d cov.r tau2.del
## Arthur et al., 2019.1 0.9248 0.0835 0.0070 1.0093 0.0293
## Arthur et al., 2019.2 1.4709 0.1301 0.0169 0.9987 0.0288
## Arthur et al., 2019.3 -0.5593 -0.0500 0.0025 1.0134 0.0295
## Behnke et al., 2024.1 -0.8577 -0.1373 0.0191 1.0322 0.0296
## Brimmell et al., 2019 2.3027 0.2735 0.0710 0.9574 0.0264
## Crowe et al., 2020.1 -0.0691 -0.0090 0.0001 1.0266 0.0299
## Crowe et al., 2020.2 -0.4474 -0.0523 0.0028 1.0241 0.0298
## Crowe et al., 2020.3 -0.7859 -0.0908 0.0083 1.0185 0.0295
## Crowe et al., 2020.4 0.1002 0.0105 0.0001 1.0265 0.0299
## Crowe et al., 2020.5 -0.6160 -0.0715 0.0051 1.0217 0.0297
## Dixon et al., 2019 1.4682 0.1672 0.0276 0.9979 0.0285
## Hangen et al., 2019.1 -0.3652 -0.0563 0.0033 1.0428 0.0303
## Hangen et al., 2019.2 -0.3102 -0.0481 0.0024 1.0436 0.0303
## Hase et al., 2019.1 -0.7277 -0.0890 0.0080 1.0220 0.0296
## Hase et al., 2019.2 0.1610 0.0183 0.0003 1.0288 0.0300
## Hase et al., 2019.3 -0.8196 -0.1001 0.0101 1.0199 0.0295
## Hase et al., 2019.4 -0.3606 -0.0444 0.0020 1.0274 0.0299
## Hase et al., 2019.5 -0.3961 -0.0516 0.0027 1.0304 0.0300
## Hase et al., 2019.6 -0.2932 -0.0386 0.0015 1.0315 0.0300
## Hase et al., in preparation.3 -0.8314 -0.0915 0.0084 1.0160 0.0295
## Hase et al., in preparation.4 -0.3439 -0.0382 0.0015 1.0225 0.0298
## Hase et al., in preparation.5 -0.0654 -0.0080 0.0001 1.0238 0.0299
## Hase et al., in preparation.6 -1.2063 -0.1317 0.0173 1.0069 0.0290
## Hase et al., in preparation.7 0.2567 0.0271 0.0007 1.0230 0.0298
## Hase et al., in preparation.8 0.0546 0.0050 0.0000 1.0238 0.0299
## Hase et al., in preparation.9 1.9726 0.2134 0.0444 0.9789 0.0276
## Hase et al., in preparation.10 -1.0078 -0.1073 0.0115 1.0115 0.0293
## Hase et al., in preparation.11 0.4944 0.0521 0.0027 1.0200 0.0297
## Hase et al., in preparation.12 -0.4151 -0.0450 0.0020 1.0210 0.0297
## Hase et al., in preparation.13 -0.4931 -0.0533 0.0029 1.0202 0.0297
## Hase et al., in preparation.14 0.3320 0.0346 0.0012 1.0216 0.0298
## Jewiss et al., 2023 (Study 1) 1.4638 0.1679 0.0278 0.9980 0.0285
## Jewiss et al., 2023 (Study 2).1 0.9973 0.1154 0.0133 1.0132 0.0292
## Jewiss et al., 2023 (Study 2).2 -0.1120 -0.0140 0.0002 1.0269 0.0299
## Jewiss et al., 2023 (Study 2).3 -0.2813 -0.0335 0.0011 1.0260 0.0299
## Jewiss et al., 2023 (Study 2).4 0.5813 0.0666 0.0045 1.0222 0.0297
## Jewiss et al., 2023 (Study 2).5 0.2298 0.0256 0.0007 1.0262 0.0299
## Jewiss et al., 2023 (Study 2).6 0.1008 0.0106 0.0001 1.0268 0.0299
## Jewiss et al., 2023 (Study 2).7 -0.1120 -0.0140 0.0002 1.0269 0.0299
## Jewiss et al., 2023 (Study 2).8 -0.3235 -0.0384 0.0015 1.0257 0.0299
## Jewiss et al., 2024 -0.4026 -0.0469 0.0022 1.0242 0.0298
## Khalaf et al., 2020.1 0.0747 0.0089 0.0001 1.0389 0.0302
## Khalaf et al., 2020.2 0.1620 0.0210 0.0005 1.0385 0.0302
## Miller et al., 2021.1 1.1413 0.1217 0.0148 1.0077 0.0291
## Miller et al., 2021.2 0.8737 0.0929 0.0086 1.0139 0.0294
## Miller et al., 2021.3 0.1721 0.0175 0.0003 1.0225 0.0298
## Miller et al., 2021.4 0.6184 0.0654 0.0043 1.0183 0.0296
## Miller et al., 2021.5 -0.0271 -0.0042 0.0000 1.0270 0.0299
## Miller et al., 2021.6 -0.9208 -0.1067 0.0114 1.0157 0.0294
## Miller et al., 2021.7 -0.3761 -0.0409 0.0017 1.0214 0.0298
## Miller et al., 2021.8 1.9509 0.2088 0.0426 0.9803 0.0277
## Miller et al., 2021.9 -0.3761 -0.0409 0.0017 1.0214 0.0298
## Miller et al., 2021.10 -0.2203 -0.0244 0.0006 1.0224 0.0298
## Moore et al., 2017 0.9692 0.1340 0.0180 1.0198 0.0293
## O'Brien et al., 2022 -0.5412 -0.0691 0.0048 1.0274 0.0298
## Petzel & Casad, 2022.1 5.8298 0.9133 0.4847 0.6332 0.0108
## Petzel & Casad, 2022.2 -1.2444 -0.1623 0.0261 1.0081 0.0288
## Sammy et al., 2017 -1.2714 -0.1573 0.0245 1.0063 0.0288
## Scheepers, 2017 0.9215 0.1283 0.0165 1.0219 0.0294
## Slater et al., 2018 -0.5718 -0.0777 0.0061 1.0305 0.0299
## Smith et al., 2022.1 -0.7689 -0.0869 0.0076 1.0181 0.0295
## Smith et al., 2022.2 -1.5973 -0.1775 0.0310 0.9939 0.0283
## Smith et al., 2022.3 -2.3473 -0.2571 0.0632 0.9597 0.0266
## Trotman et al., 2018.2 1.0254 0.1368 0.0187 1.0164 0.0292
## Wood et al., 2018 -0.5571 -0.0629 0.0040 1.0213 0.0297
## Scheepers & Keller, 2022 -0.1555 -0.0240 0.0006 1.0418 0.0303
## Bosshard et al., 2023.2 0.0194 0.0012 0.0000 1.0435 0.0304
## Simms, 2022.1 0.2447 0.0262 0.0007 1.0239 0.0298
## Simms, 2022.2 -1.2819 -0.1410 0.0198 1.0048 0.0289
## Simms, 2022.3 -0.4876 -0.0547 0.0030 1.0219 0.0297
## Simms, 2022.4 0.8089 0.0892 0.0080 1.0163 0.0295
## Simms, 2022.5 -0.6135 -0.0685 0.0047 1.0202 0.0297
## Simms, 2022.6 -0.2691 -0.0307 0.0010 1.0239 0.0298
## QE.del hat weight dfbs inf
## Arthur et al., 2019.1 193.6978 0.0081 0.8097 0.0835
## Arthur et al., 2019.2 191.6006 0.0077 0.7745 0.1304
## Arthur et al., 2019.3 195.3182 0.0077 0.7745 -0.0499
## Behnke et al., 2024.1 163.7671 0.0250 2.5040 -0.1376
## Brimmell et al., 2019 182.3373 0.0135 1.3534 0.2741
## Crowe et al., 2020.1 195.4559 0.0130 1.3027 -0.0090
## Crowe et al., 2020.2 195.4307 0.0130 1.3027 -0.0523
## Crowe et al., 2020.3 194.9129 0.0130 1.3027 -0.0907
## Crowe et al., 2020.4 195.2761 0.0130 1.3027 0.0105
## Crowe et al., 2020.5 195.2306 0.0130 1.3027 -0.0715
## Dixon et al., 2019 189.8045 0.0127 1.2664 0.1673
## Hangen et al., 2019.1 195.4956 0.0225 2.2456 -0.0566
## Hangen et al., 2019.2 195.5171 0.0225 2.2456 -0.0483
## Hase et al., 2019.1 194.9966 0.0146 1.4570 -0.0890
## Hase et al., 2019.2 195.1223 0.0143 1.4293 0.0183
## Hase et al., 2019.3 194.7758 0.0146 1.4570 -0.1001
## Hase et al., 2019.4 195.4910 0.0143 1.4293 -0.0444
## Hase et al., 2019.5 195.4728 0.0161 1.6080 -0.0517
## Hase et al., 2019.6 195.5158 0.0161 1.6080 -0.0386
## Hase et al., in preparation.3 194.8445 0.0119 1.1871 -0.0915
## Hase et al., in preparation.4 195.4930 0.0117 1.1657 -0.0382
## Hase et al., in preparation.5 195.4679 0.0117 1.1657 -0.0080
## Hase et al., in preparation.6 193.7563 0.0119 1.1871 -0.1317
## Hase et al., in preparation.7 195.0806 0.0117 1.1657 0.0270
## Hase et al., in preparation.8 195.3685 0.0117 1.1657 0.0050
## Hase et al., in preparation.9 186.9705 0.0114 1.1436 0.2141
## Hase et al., in preparation.10 194.4289 0.0112 1.1207 -0.1073
## Hase et al., in preparation.11 194.5921 0.0112 1.1207 0.0520
## Hase et al., in preparation.12 195.4525 0.0112 1.1207 -0.0450
## Hase et al., in preparation.13 195.3885 0.0112 1.1207 -0.0532
## Hase et al., in preparation.14 194.9626 0.0112 1.1207 0.0346
## Jewiss et al., 2023 (Study 1) 189.7397 0.0128 1.2848 0.1681
## Jewiss et al., 2023 (Study 2).1 192.3278 0.0132 1.3201 0.1154
## Jewiss et al., 2023 (Study 2).2 195.4813 0.0132 1.3201 -0.0140
## Jewiss et al., 2023 (Study 2).3 195.5145 0.0132 1.3201 -0.0335
## Jewiss et al., 2023 (Study 2).4 194.0983 0.0132 1.3201 0.0666
## Jewiss et al., 2023 (Study 2).5 195.0488 0.0132 1.3201 0.0256
## Jewiss et al., 2023 (Study 2).6 195.2694 0.0132 1.3201 0.0106
## Jewiss et al., 2023 (Study 2).7 195.4813 0.0132 1.3201 -0.0140
## Jewiss et al., 2023 (Study 2).8 195.5041 0.0132 1.3201 -0.0384
## Jewiss et al., 2024 195.4640 0.0128 1.2848 -0.0468
## Khalaf et al., 2020.1 194.9610 0.0191 1.9114 0.0089
## Khalaf et al., 2020.2 194.6647 0.0191 1.9114 0.0211
## Miller et al., 2021.1 192.2049 0.0112 1.1207 0.1217
## Miller et al., 2021.2 193.3667 0.0112 1.1207 0.0928
## Miller et al., 2021.3 195.2354 0.0112 1.1207 0.0175
## Miller et al., 2021.4 194.2466 0.0112 1.1207 0.0653
## Miller et al., 2021.5 195.4195 0.0132 1.3201 -0.0042
## Miller et al., 2021.6 194.5699 0.0132 1.3201 -0.1067
## Miller et al., 2021.7 195.4763 0.0112 1.1207 -0.0409
## Miller et al., 2021.8 187.2771 0.0112 1.1207 0.2095
## Miller et al., 2021.9 195.4763 0.0112 1.1207 -0.0409
## Miller et al., 2021.10 195.5174 0.0112 1.1207 -0.0243
## Moore et al., 2017 189.4170 0.0188 1.8779 0.1340
## O'Brien et al., 2022 195.3179 0.0157 1.5662 -0.0691
## Petzel & Casad, 2022.1 130.2561 0.0168 1.6817 0.8829 *
## Petzel & Casad, 2022.2 192.7979 0.0168 1.6817 -0.1621
## Sammy et al., 2017 193.0300 0.0152 1.5205 -0.1573
## Scheepers, 2017 189.5262 0.0191 1.9114 0.1284
## Slater et al., 2018 195.2356 0.0178 1.7794 -0.0778
## Smith et al., 2022.1 194.9636 0.0125 1.2475 -0.0869
## Smith et al., 2022.2 191.9771 0.0125 1.2475 -0.1778
## Smith et al., 2022.3 187.2598 0.0125 1.2475 -0.2582
## Trotman et al., 2018.2 190.0914 0.0174 1.7445 0.1368
## Wood et al., 2018 195.3168 0.0123 1.2279 -0.0628
## Scheepers & Keller, 2022 195.3955 0.0207 2.0683 -0.0241
## Bosshard et al., 2023.2 194.8221 0.0213 2.1324 0.0012
## Simms, 2022.1 195.0811 0.0121 1.2078 0.0262
## Simms, 2022.2 193.4535 0.0121 1.2078 -0.1411
## Simms, 2022.3 195.3939 0.0121 1.2078 -0.0547
## Simms, 2022.4 193.4523 0.0121 1.2078 0.0891
## Simms, 2022.5 195.2421 0.0121 1.2078 -0.0685
## Simms, 2022.6 195.5150 0.0121 1.2078 -0.0307ranktest(model_fun_CTI)## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.0362, p = 0.6596# leave one out analysis #
leave1out(model_fun_CTI)##
## estimate se zval pval ci.lb ci.ub
## Arthur et al., 2019.1 0.0944 0.0274 3.4462 0.0006 0.0407 0.1480
## Arthur et al., 2019.2 0.0931 0.0272 3.4181 0.0006 0.0397 0.1465
## Arthur et al., 2019.3 0.0980 0.0274 3.5718 0.0004 0.0442 0.1518
## Behnke et al., 2024.1 0.1004 0.0277 3.6257 0.0003 0.0461 0.1547
## Brimmell et al., 2019 0.0894 0.0267 3.3513 0.0008 0.0371 0.1417
## Crowe et al., 2020.1 0.0969 0.0276 3.5083 0.0005 0.0428 0.1510
## Crowe et al., 2020.2 0.0981 0.0276 3.5556 0.0004 0.0440 0.1521
## Crowe et al., 2020.3 0.0991 0.0275 3.6033 0.0003 0.0452 0.1530
## Crowe et al., 2020.4 0.0964 0.0276 3.4891 0.0005 0.0422 0.1505
## Crowe et al., 2020.5 0.0986 0.0276 3.5788 0.0003 0.0446 0.1526
## Dixon et al., 2019 0.0921 0.0272 3.3831 0.0007 0.0388 0.1455
## Hangen et al., 2019.1 0.0982 0.0278 3.5281 0.0004 0.0436 0.1528
## Hangen et al., 2019.2 0.0980 0.0278 3.5185 0.0004 0.0434 0.1525
## Hase et al., 2019.1 0.0991 0.0276 3.5956 0.0003 0.0451 0.1531
## Hase et al., 2019.2 0.0961 0.0276 3.4775 0.0005 0.0420 0.1503
## Hase et al., 2019.3 0.0994 0.0275 3.6102 0.0003 0.0454 0.1533
## Hase et al., 2019.4 0.0979 0.0276 3.5421 0.0004 0.0437 0.1520
## Hase et al., 2019.5 0.0981 0.0277 3.5442 0.0004 0.0438 0.1523
## Hase et al., 2019.6 0.0977 0.0277 3.5293 0.0004 0.0434 0.1520
## Hase et al., in preparation.3 0.0991 0.0275 3.6085 0.0003 0.0453 0.1530
## Hase et al., in preparation.4 0.0977 0.0276 3.5444 0.0004 0.0437 0.1517
## Hase et al., in preparation.5 0.0969 0.0276 3.5121 0.0004 0.0428 0.1509
## Hase et al., in preparation.6 0.1002 0.0274 3.6643 0.0002 0.0466 0.1538
## Hase et al., in preparation.7 0.0959 0.0276 3.4787 0.0005 0.0419 0.1499
## Hase et al., in preparation.8 0.0965 0.0276 3.4992 0.0005 0.0425 0.1506
## Hase et al., in preparation.9 0.0909 0.0270 3.3706 0.0007 0.0380 0.1438
## Hase et al., in preparation.10 0.0996 0.0274 3.6321 0.0003 0.0458 0.1533
## Hase et al., in preparation.11 0.0952 0.0275 3.4590 0.0005 0.0413 0.1492
## Hase et al., in preparation.12 0.0979 0.0275 3.5537 0.0004 0.0439 0.1519
## Hase et al., in preparation.13 0.0981 0.0275 3.5633 0.0004 0.0441 0.1521
## Hase et al., in preparation.14 0.0957 0.0275 3.4736 0.0005 0.0417 0.1497
## Jewiss et al., 2023 (Study 1) 0.0921 0.0272 3.3822 0.0007 0.0387 0.1455
## Jewiss et al., 2023 (Study 2).1 0.0935 0.0274 3.4078 0.0007 0.0397 0.1473
## Jewiss et al., 2023 (Study 2).2 0.0970 0.0276 3.5128 0.0004 0.0429 0.1512
## Jewiss et al., 2023 (Study 2).3 0.0976 0.0276 3.5337 0.0004 0.0434 0.1517
## Jewiss et al., 2023 (Study 2).4 0.0948 0.0276 3.4407 0.0006 0.0408 0.1488
## Jewiss et al., 2023 (Study 2).5 0.0959 0.0276 3.4746 0.0005 0.0418 0.1501
## Jewiss et al., 2023 (Study 2).6 0.0964 0.0276 3.4884 0.0005 0.0422 0.1505
## Jewiss et al., 2023 (Study 2).7 0.0970 0.0276 3.5128 0.0004 0.0429 0.1512
## Jewiss et al., 2023 (Study 2).8 0.0977 0.0276 3.5391 0.0004 0.0436 0.1518
## Jewiss et al., 2024 0.0979 0.0276 3.5500 0.0004 0.0439 0.1520
## Khalaf et al., 2020.1 0.0964 0.0278 3.4697 0.0005 0.0419 0.1509
## Khalaf et al., 2020.2 0.0961 0.0278 3.4584 0.0005 0.0416 0.1505
## Miller et al., 2021.1 0.0933 0.0274 3.4110 0.0006 0.0397 0.1470
## Miller et al., 2021.2 0.0941 0.0274 3.4289 0.0006 0.0403 0.1479
## Miller et al., 2021.3 0.0962 0.0276 3.4890 0.0005 0.0421 0.1502
## Miller et al., 2021.4 0.0949 0.0275 3.4486 0.0006 0.0409 0.1488
## Miller et al., 2021.5 0.0968 0.0276 3.5028 0.0005 0.0426 0.1509
## Miller et al., 2021.6 0.0996 0.0275 3.6241 0.0003 0.0457 0.1534
## Miller et al., 2021.7 0.0978 0.0275 3.5490 0.0004 0.0438 0.1518
## Miller et al., 2021.8 0.0910 0.0270 3.3728 0.0007 0.0381 0.1439
## Miller et al., 2021.9 0.0978 0.0275 3.5490 0.0004 0.0438 0.1518
## Miller et al., 2021.10 0.0973 0.0276 3.5308 0.0004 0.0433 0.1513
## Moore et al., 2017 0.0930 0.0275 3.3783 0.0007 0.0390 0.1469
## O'Brien et al., 2022 0.0985 0.0276 3.5666 0.0004 0.0444 0.1527
## Petzel & Casad, 2022.1 0.0777 0.0217 3.5807 0.0003 0.0352 0.1202
## Petzel & Casad, 2022.2 0.1010 0.0274 3.6922 0.0002 0.0474 0.1547
## Sammy et al., 2017 0.1009 0.0273 3.6905 0.0002 0.0473 0.1545
## Scheepers, 2017 0.0931 0.0276 3.3802 0.0007 0.0391 0.1471
## Slater et al., 2018 0.0988 0.0277 3.5699 0.0004 0.0445 0.1530
## Smith et al., 2022.1 0.0990 0.0275 3.6003 0.0003 0.0451 0.1529
## Smith et al., 2022.2 0.1014 0.0272 3.7331 0.0002 0.0482 0.1547
## Smith et al., 2022.3 0.1035 0.0267 3.8759 0.0001 0.0512 0.1558
## Trotman et al., 2018.2 0.0929 0.0275 3.3813 0.0007 0.0391 0.1468
## Wood et al., 2018 0.0984 0.0275 3.5709 0.0004 0.0444 0.1524
## Scheepers & Keller, 2022 0.0973 0.0278 3.4977 0.0005 0.0428 0.1518
## Bosshard et al., 2023.2 0.0966 0.0278 3.4697 0.0005 0.0420 0.1512
## Simms, 2022.1 0.0959 0.0276 3.4780 0.0005 0.0419 0.1500
## Simms, 2022.2 0.1005 0.0273 3.6773 0.0002 0.0469 0.1540
## Simms, 2022.3 0.0981 0.0276 3.5619 0.0004 0.0441 0.1521
## Simms, 2022.4 0.0942 0.0275 3.4284 0.0006 0.0404 0.1481
## Simms, 2022.5 0.0985 0.0275 3.5785 0.0003 0.0446 0.1525
## Simms, 2022.6 0.0975 0.0276 3.5345 0.0004 0.0434 0.1515
## Q Qp tau2 I2 H2
## Arthur et al., 2019.1 193.6978 0.0000 0.0293 67.0244 3.0325
## Arthur et al., 2019.2 191.6006 0.0000 0.0288 66.6342 2.9971
## Arthur et al., 2019.3 195.3182 0.0000 0.0295 67.2019 3.0490
## Behnke et al., 2024.1 163.7671 0.0000 0.0296 59.1347 2.4471
## Brimmell et al., 2019 182.3373 0.0000 0.0264 64.5720 2.8226
## Crowe et al., 2020.1 195.4559 0.0000 0.0299 67.3830 3.0659
## Crowe et al., 2020.2 195.4307 0.0000 0.0298 67.2881 3.0570
## Crowe et al., 2020.3 194.9129 0.0000 0.0295 67.0806 3.0377
## Crowe et al., 2020.4 195.2761 0.0000 0.0299 67.3787 3.0655
## Crowe et al., 2020.5 195.2306 0.0000 0.0297 67.1992 3.0487
## Dixon et al., 2019 189.8045 0.0000 0.0285 66.3075 2.9680
## Hangen et al., 2019.1 195.4956 0.0000 0.0303 66.4471 2.9804
## Hangen et al., 2019.2 195.5171 0.0000 0.0303 66.4788 2.9832
## Hase et al., 2019.1 194.9966 0.0000 0.0296 67.0995 3.0395
## Hase et al., 2019.2 195.1223 0.0000 0.0300 67.3749 3.0651
## Hase et al., 2019.3 194.7758 0.0000 0.0295 67.0200 3.0321
## Hase et al., 2019.4 195.4910 0.0000 0.0299 67.3227 3.0602
## Hase et al., 2019.5 195.4728 0.0000 0.0300 67.2866 3.0569
## Hase et al., 2019.6 195.5158 0.0000 0.0300 67.3296 3.0609
## Hase et al., in preparation.3 194.8445 0.0000 0.0295 67.0619 3.0360
## Hase et al., in preparation.4 195.4930 0.0000 0.0298 67.3188 3.0599
## Hase et al., in preparation.5 195.4679 0.0000 0.0299 67.3677 3.0644
## Hase et al., in preparation.6 193.7563 0.0000 0.0290 66.7147 3.0043
## Hase et al., in preparation.7 195.0806 0.0000 0.0298 67.3367 3.0615
## Hase et al., in preparation.8 195.3685 0.0000 0.0299 67.3671 3.0644
## Hase et al., in preparation.9 186.9705 0.0000 0.0276 65.6274 2.9093
## Hase et al., in preparation.10 194.4289 0.0000 0.0293 66.9308 3.0240
## Hase et al., in preparation.11 194.5921 0.0000 0.0297 67.2513 3.0536
## Hase et al., in preparation.12 195.4525 0.0000 0.0297 67.2912 3.0573
## Hase et al., in preparation.13 195.3885 0.0000 0.0297 67.2612 3.0545
## Hase et al., in preparation.14 194.9626 0.0000 0.0298 67.3112 3.0592
## Jewiss et al., 2023 (Study 1) 189.7397 0.0000 0.0285 66.2999 2.9674
## Jewiss et al., 2023 (Study 2).1 192.3278 0.0000 0.0292 66.8663 3.0181
## Jewiss et al., 2023 (Study 2).2 195.4813 0.0000 0.0299 67.3808 3.0657
## Jewiss et al., 2023 (Study 2).3 195.5145 0.0000 0.0299 67.3485 3.0626
## Jewiss et al., 2023 (Study 2).4 194.0983 0.0000 0.0297 67.2072 3.0494
## Jewiss et al., 2023 (Study 2).5 195.0488 0.0000 0.0299 67.3568 3.0634
## Jewiss et al., 2023 (Study 2).6 195.2694 0.0000 0.0299 67.3799 3.0656
## Jewiss et al., 2023 (Study 2).7 195.4813 0.0000 0.0299 67.3808 3.0657
## Jewiss et al., 2023 (Study 2).8 195.5041 0.0000 0.0299 67.3358 3.0615
## Jewiss et al., 2024 195.4640 0.0000 0.0298 67.3064 3.0587
## Khalaf et al., 2020.1 194.9610 0.0000 0.0302 67.2527 3.0537
## Khalaf et al., 2020.2 194.6647 0.0000 0.0302 67.2364 3.0522
## Miller et al., 2021.1 192.2049 0.0000 0.0291 66.7858 3.0108
## Miller et al., 2021.2 193.3667 0.0000 0.0294 67.0223 3.0324
## Miller et al., 2021.3 195.2354 0.0000 0.0298 67.3478 3.0626
## Miller et al., 2021.4 194.2466 0.0000 0.0296 67.1901 3.0479
## Miller et al., 2021.5 195.4195 0.0000 0.0299 67.3860 3.0662
## Miller et al., 2021.6 194.5699 0.0000 0.0294 66.9614 3.0268
## Miller et al., 2021.7 195.4763 0.0000 0.0298 67.3043 3.0585
## Miller et al., 2021.8 187.2771 0.0000 0.0277 65.6962 2.9151
## Miller et al., 2021.9 195.4763 0.0000 0.0298 67.3043 3.0585
## Miller et al., 2021.10 195.5174 0.0000 0.0298 67.3432 3.0621
## Moore et al., 2017 189.4170 0.0000 0.0293 66.5833 2.9925
## O'Brien et al., 2022 195.3179 0.0000 0.0298 67.2132 3.0500
## Petzel & Casad, 2022.1 130.2561 0.0000 0.0108 42.4154 1.7366
## Petzel & Casad, 2022.2 192.7979 0.0000 0.0288 66.3660 2.9732
## Sammy et al., 2017 193.0300 0.0000 0.0288 66.4475 2.9804
## Scheepers, 2017 189.5262 0.0000 0.0294 66.6147 2.9953
## Slater et al., 2018 195.2356 0.0000 0.0299 67.1155 3.0409
## Smith et al., 2022.1 194.9636 0.0000 0.0295 67.1010 3.0396
## Smith et al., 2022.2 191.9771 0.0000 0.0283 66.1631 2.9554
## Smith et al., 2022.3 187.2598 0.0000 0.0266 64.7484 2.8368
## Trotman et al., 2018.2 190.0914 0.0000 0.0292 66.6214 2.9959
## Wood et al., 2018 195.3168 0.0000 0.0297 67.2348 3.0520
## Scheepers & Keller, 2022 195.3955 0.0000 0.0303 67.0576 3.0356
## Bosshard et al., 2023.2 194.8221 0.0000 0.0304 66.9462 3.0254
## Simms, 2022.1 195.0811 0.0000 0.0298 67.3442 3.0622
## Simms, 2022.2 193.4535 0.0000 0.0289 66.6186 2.9957
## Simms, 2022.3 195.3939 0.0000 0.0297 67.2680 3.0551
## Simms, 2022.4 193.4523 0.0000 0.0295 67.0602 3.0358
## Simms, 2022.5 195.2421 0.0000 0.0297 67.2044 3.0492
## Simms, 2022.6 195.5150 0.0000 0.0298 67.3434 3.0622# Egger#
model_fun_CTI_OutEgger <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, random = ~ 1 | paper_id/effect_size_id, mod = ~sqrt(CTI_cor_Z_var), tdist=TRUE, data = Data)## Warning: 89 rows with NAs omitted from model fitting.model_fun_CTI_OutEgger##
## Multivariate Meta-Analysis Model (k = 73; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0044 0.0664 28 no paper_id
## sigma^2.2 0.0266 0.1630 73 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 71) = 171.9220, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 71) = 0.2902, p-val = 0.5918
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.0501 0.1003 0.5001 71 0.6185 -0.1498 0.2501
## sqrt(CTI_cor_Z_var) 0.3488 0.6474 0.5387 71 0.5918 -0.9421 1.6397
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Run trim-and-fill analysis for the right side
model_fun_CTI_tf_right <- trimfill(model_fun_CTI, side = "right")
# Run trim-and-fill analysis for the left side
model_fun_CTI_tf_left <- trimfill(model_fun_CTI, side = "left")
# Print the trim-and-fill model results
print(model_fun_CTI_tf_right)##
## Estimated number of missing studies on the right side: 13 (SE = 5.6241)
##
## Random-Effects Model (k = 86; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0393 (SE = 0.0098)
## tau (square root of estimated tau^2 value): 0.1983
## I^2 (total heterogeneity / total variability): 71.71%
## H^2 (total variability / sampling variability): 3.54
##
## Test for Heterogeneity:
## Q(df = 85) = 280.9697, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.1508 0.0276 5.4701 <.0001 0.0968 0.2048 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(model_fun_CTI_tf_left)##
## Estimated number of missing studies on the left side: 0 (SE = 4.4604)
##
## Random-Effects Model (k = 73; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0293 (SE = 0.0088)
## tau (square root of estimated tau^2 value): 0.1710
## I^2 (total heterogeneity / total variability): 66.76%
## H^2 (total variability / sampling variability): 3.01
##
## Test for Heterogeneity:
## Q(df = 72) = 195.5175, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.0966 0.0273 3.5456 0.0004 0.0432 0.1501 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Combine the number of studies imputed from both sides
total_imputed_studies <- model_fun_CTI_tf_right$k0 + model_fun_CTI_tf_left$k0
cat("Total number of imputed studies (both sides) for CTI:", total_imputed_studies, "\n")## Total number of imputed studies (both sides) for CTI: 13# Generate funnel plots only right
#par(mfrow=c(1, 3))
#funnel(model_fun_CTI, main="Original Model")
funnel(model_fun_CTI_tf_right, main="Trim-and-Fill Right", xlab = 'CTI')
#funnel(model_fun_CTI_tf_left, main="Trim-and-Fill Left")
# Return to single plot layout
#par(mfrow=c(1, 1))7.2 Multilevel Model
model_CTI_multilevel <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML")## Warning: 89 rows with NAs omitted from model fitting.model_CTI_multilevel##
## Multivariate Meta-Analysis Model (k = 73; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 28 no paper_id
## sigma^2.2 0.0293 0.1710 73 no paper_id/effect_size_id
##
## Test for Heterogeneity:
## Q(df = 72) = 195.5175, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.0966 0.0273 3.5456 72 0.0007 0.0423 0.1510 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1convert_z2r(0.1150)## [1] 0.1144957predict_CTI <-predict(model_CTI_multilevel, digits=3, transf=transf.ztor, level = 95)
predict_CTI##
## pred ci.lb ci.ub pi.lb pi.ub
## 0.096 0.042 0.150 -0.244 0.415forest.rma(model_CTI_multilevel, header = "CTI",slab = Data$Ref_APA, alim=c(-1,1.6))
######## list 1 ########
list_CTI <- Data$CTI_cor_Z_var
############ sum 1#####################
sum_CTI <- sum(list_CTI, na.rm = TRUE)
###################### sum 2 #####################
sum2_CTI <- (sum_CTI)^2
####################### list 2 ##############
list_In_CTI <- Data$CTI_cor_Z_var_Sq
#################### sum 3 #######################
sum_In_CTI<- sum(list_In_CTI, na.rm = TRUE)
############### numerator ##############
numerator_CTI<- (model_CTI_multilevel$k-1)*sum_CTI
############# denominator #############
denominator_CTI<- sum2_CTI - sum_In_CTI
############## eps ################
EPS_CTI<- numerator_CTI / denominator_CTI
############### i2 1 level ##################
I2_1_CTI <- (EPS_CTI) / (model_CTI_multilevel$sigma2[1] + model_CTI_multilevel$sigma2[2] + EPS_CTI) *100
I2_1_CTI## [1] 99.91892############## i2 2 level #################
I2_2_CTI <- (model_CTI_multilevel$sigma2[1]) / (model_CTI_multilevel$sigma2[1] + model_CTI_multilevel$sigma2[2] + EPS_CTI) *100
I2_2_CTI## [1] 9.976715e-10########### I2 level 3
I2_3_CTI <- (model_CTI_multilevel$sigma2[2]) / (model_CTI_multilevel$sigma2[1] + model_CTI_multilevel$sigma2[2] + EPS_CTI) *100
I2_3_CTI## [1] 0.08107815############### ML without level 2 ##########
model_CTI_multilevel_2 <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(0,NA), tdist=TRUE,data = Data)## Warning: 89 rows with NAs omitted from model fitting.############# ml without level 3 ###########
model_CTI_multilevel_3 <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(NA,0), tdist=TRUE,data = Data)## Warning: 89 rows with NAs omitted from model fitting.##################### sig level 2 #######################
anova12_CTI <- anova(model_CTI_multilevel,model_CTI_multilevel_2)
anova12_CTI##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 0.9258 7.7558 1.2787 2.5371 195.5175
## Reduced 2 -1.0742 3.4791 -0.9003 2.5371 0.0000 1.0000 195.5175###############sig level 3v #################
anova13_CTI <- anova(model_CTI_multilevel,model_CTI_multilevel_3)
anova13_CTI##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 0.9258 7.7558 1.2787 2.5371 195.5175
## Reduced 2 17.3488 21.9021 17.5227 -6.6744 18.4230 <.0001 195.51758. Cognitive Challenge and Threat Index
8.1 Identyfing outliers
# Cogni
model_fun_Cogni <- rma(yi = Cogni_cor_Z, vi= Cogni_cor_Z_var, data = Data, slab = Ref_APA)## Warning: 41 studies with NAs omitted from model fitting.model_fun_Cogni##
## Random-Effects Model (k = 121; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0209 (SE = 0.0046)
## tau (square root of estimated tau^2 value): 0.1445
## I^2 (total heterogeneity / total variability): 72.22%
## H^2 (total variability / sampling variability): 3.60
##
## Test for Heterogeneity:
## Q(df = 120) = 377.1303, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.1426 0.0176 8.0869 <.0001 0.1080 0.1771 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# outliers diagnostics - outlier rstudent > 3.0 #
Out_model_fun_Cogni <- influence(model_fun_Cogni)
Out_model_fun_Cogni##
## rstudent dffits cook.d cov.r tau2.del
## Baumgartner & Schneider, 2023 0.6951 0.0742 0.0055 1.0158 0.0211
## Behnke et al., 2020.1 1.0369 0.1010 0.0102 1.0102 0.0209
## Behnke et al., 2020.2 0.2726 0.0338 0.0012 1.0180 0.0212
## Behnke et al., 2022 0.5509 0.0750 0.0057 1.0249 0.0212
## Behnke et al., 2024.1 -0.4259 -0.0425 0.0018 1.0253 0.0212
## Brimmell et al., 2019 1.0899 0.0896 0.0080 1.0069 0.0209
## Cabral et al., 2024.1 -0.0635 0.0014 0.0000 1.0179 0.0212
## Cabral et al., 2024.2 0.0474 0.0122 0.0001 1.0181 0.0212
## Cabral et al., 2024.3 -0.1187 -0.0041 0.0000 1.0178 0.0212
## Carenzo et al., 2020.1 -2.9849 -0.4105 0.1512 0.9269 0.0181
## Carenzo et al., 2020.2 2.9348 0.2503 0.0571 0.9391 0.0185
## Gurera & Isaacowitz, 2022.1 0.0629 0.0133 0.0002 1.0175 0.0212
## Gurera & Isaacowitz, 2022.2 0.9287 0.0899 0.0081 1.0114 0.0210
## Gurera & Isaacowitz, 2022.3 0.1302 0.0170 0.0003 1.0141 0.0211
## Gurera & Isaacowitz, 2022.4 -0.6745 -0.0547 0.0030 1.0100 0.0210
## Hase et al., 2019.1 -0.2894 -0.0196 0.0004 1.0134 0.0211
## Hase et al., 2019.2 0.3804 0.0378 0.0014 1.0135 0.0211
## Hase et al., 2019.3 -2.1304 -0.2053 0.0413 0.9809 0.0200
## Hase et al., 2019.4 -1.2910 -0.1146 0.0131 1.0010 0.0207
## Hase et al., 2019.5 1.1090 0.1007 0.0101 1.0081 0.0209
## Hase et al., 2019.6 1.0580 0.0968 0.0094 1.0089 0.0209
## Hase et al., in preparation.1 -1.9693 -0.1839 0.0333 0.9859 0.0202
## Hase et al., in preparation.2 -0.4694 -0.0355 0.0013 1.0117 0.0210
## Hase et al., in preparation.3 -0.0941 -0.0025 0.0000 1.0111 0.0211
## Hase et al., in preparation.4 0.7580 0.0598 0.0036 1.0088 0.0210
## Hase et al., in preparation.5 1.0974 0.0826 0.0068 1.0059 0.0209
## Hase et al., in preparation.6 -1.4914 -0.1202 0.0144 0.9975 0.0206
## Hase et al., in preparation.7 -0.7349 -0.0538 0.0029 1.0073 0.0209
## Hase et al., in preparation.8 -1.2097 -0.0941 0.0088 1.0018 0.0208
## Hase et al., in preparation.9 -0.7691 -0.0561 0.0031 1.0068 0.0209
## Hase et al., in preparation.10 0.6042 0.0479 0.0023 1.0094 0.0210
## Hase et al., in preparation.11 -0.6767 -0.0480 0.0023 1.0074 0.0210
## Hase et al., in preparation.12 -0.1753 -0.0087 0.0001 1.0102 0.0210
## Hase et al., in preparation.13 -0.0064 0.0040 0.0000 1.0105 0.0211
## Hase et al., in preparation.14 -0.3430 -0.0216 0.0005 1.0096 0.0210
## Jamieson et al., 2022.1 1.7000 0.1788 0.0311 0.9930 0.0202
## Jamieson et al., 2022.2 2.2201 0.2132 0.0430 0.9717 0.0195
## Jamieson et al., 2022.3 1.7107 0.1669 0.0273 0.9939 0.0203
## Journault et al., in preparation.1 1.6881 0.1767 0.0304 0.9936 0.0202
## Journault et al., in preparation.2 0.4541 0.0605 0.0037 1.0234 0.0212
## Journault et al., in preparation.3 1.0794 0.1228 0.0151 1.0128 0.0209
## Khalaf et al., 2020.1 1.2190 0.1213 0.0147 1.0075 0.0208
## Khalaf et al., 2020.2 1.0883 0.1103 0.0122 1.0102 0.0209
## Laurin & Pellet, 2023 -0.1477 -0.0065 0.0000 1.0277 0.0213
## Lee et al., 2019 -0.6117 -0.0655 0.0043 1.0207 0.0211
## Malkoc et al., 2023 -0.5209 -0.0533 0.0029 1.0218 0.0212
## Malkoc et al., 2024 -0.2157 -0.0149 0.0002 1.0253 0.0213
## Moe & Putwain, 2020.1 1.1301 0.1016 0.0103 1.0076 0.0209
## Moe & Putwain, 2020.2 0.4469 0.0463 0.0022 1.0150 0.0211
## Moe & Putwain, 2020.3 0.5825 0.0578 0.0034 1.0141 0.0211
## Moe & Putwain, 2020.4 0.4093 0.0431 0.0019 1.0152 0.0211
## Moe & Putwain, 2020.5 0.5226 0.0527 0.0028 1.0145 0.0211
## Moe & Putwain, 2020.6 0.9793 0.0899 0.0081 1.0098 0.0209
## Moe & Putwain, 2020.7 0.5118 0.0518 0.0027 1.0146 0.0211
## Moore et al., 2017 1.1401 0.1134 0.0128 1.0090 0.0209
## Mosley et al., 2018.1 -0.9855 -0.0854 0.0073 1.0063 0.0209
## Mosley et al., 2018.2 -0.4972 -0.0387 0.0015 1.0120 0.0210
## Mulvenna et al., 2023.1 -0.4669 -0.0457 0.0021 1.0219 0.0212
## Mulvenna et al., 2023.2 -0.2711 -0.0215 0.0005 1.0241 0.0213
## O'Brien et al., 2022 -1.6605 -0.1619 0.0259 0.9927 0.0204
## Sammy et al., 2017 1.6633 0.1368 0.0186 0.9973 0.0205
## Schickel et al., 2023.1 -0.0682 0.0016 0.0000 1.0208 0.0212
## Schickel et al., 2023.2 0.6618 0.0744 0.0056 1.0175 0.0211
## Sharpe et al., 2024.1 0.2546 0.0241 0.0006 1.0112 0.0211
## Sharpe et al., 2024.2 -1.3253 -0.1245 0.0154 1.0005 0.0206
## Sharpe et al., 2024.3 1.9858 0.1311 0.0171 0.9934 0.0205
## Thornton et al., 2020.1 -0.3631 -0.0304 0.0009 1.0189 0.0212
## Thornton et al., 2020.2 -0.5396 -0.0503 0.0025 1.0170 0.0211
## Trotman et al., 2018.1 0.5538 0.0589 0.0035 1.0160 0.0211
## Trotman et al., 2018.2 -0.2277 -0.0150 0.0002 1.0171 0.0212
## Turner et al., 2021.1 0.1059 0.0185 0.0003 1.0191 0.0212
## Turner et al., 2021.2 0.9351 0.0946 0.0090 1.0123 0.0210
## Turner et al., 2021.3 -0.1219 -0.0043 0.0000 1.0187 0.0212
## Wood et al., 2018 1.1312 0.0874 0.0076 1.0058 0.0209
## Scheepers & Keller, 2022 0.6364 0.0743 0.0056 1.0188 0.0211
## Bosshard et al., 2023.1 0.3778 0.0510 0.0026 1.0230 0.0212
## Mansell, 2023.1 -1.1740 -0.1264 0.0159 1.0050 0.0207
## Mansell, 2023.2 -1.3615 -0.1503 0.0223 1.0000 0.0205
## Jamieson et al., 2021.1 1.4866 0.1630 0.0261 1.0008 0.0205
## Jamieson et al., 2021.2 0.9583 0.1139 0.0130 1.0162 0.0210
## Sharpe et al., 2024.4 -1.4100 -0.0962 0.0092 0.9990 0.0207
## Sharpe et al., 2024.5 -0.9652 -0.0634 0.0040 1.0036 0.0209
## Sharpe et al., 2024.6 -0.3155 -0.0177 0.0003 1.0076 0.0210
## Sharpe et al., 2024.7 -0.5930 -0.0369 0.0014 1.0063 0.0210
## Sharpe et al., 2024.8 -1.3708 -0.0933 0.0087 0.9994 0.0207
## Sharpe et al., 2024.9 -1.7281 -0.1204 0.0144 0.9947 0.0206
## Sharpe et al., 2024.10 -0.5745 -0.0356 0.0013 1.0064 0.0210
## Sharpe et al., 2024.11 -0.6189 -0.0387 0.0015 1.0061 0.0210
## Sharpe et al., 2024.12 -0.4763 -0.0198 0.0004 1.0030 0.0209
## Sharpe et al., 2024.13 -0.7951 -0.0345 0.0012 1.0021 0.0209
## Sharpe et al., 2024.14 0.1206 0.0069 0.0000 1.0038 0.0210
## Sharpe et al., 2024.15 -0.2139 -0.0079 0.0001 1.0035 0.0209
## Simms, 2022.1 0.1358 0.0154 0.0002 1.0116 0.0211
## Simms, 2022.2 0.3480 0.0314 0.0010 1.0112 0.0211
## Simms, 2022.3 -0.3100 -0.0197 0.0004 1.0106 0.0210
## Simms, 2022.4 -0.4627 -0.0322 0.0010 1.0097 0.0210
## Simms, 2022.5 -0.0156 0.0037 0.0000 1.0115 0.0211
## Simms, 2022.6 -1.0707 -0.0838 0.0070 1.0038 0.0208
## Marr et al., 2021 0.4656 0.0586 0.0035 1.0213 0.0212
## Conlon et al., 2022.1 1.4311 0.1269 0.0160 1.0022 0.0207
## Conlon et al., 2022.2 0.8707 0.0835 0.0070 1.0118 0.0210
## van Gog et al., 2024.1 -0.5458 -0.0470 0.0022 1.0140 0.0211
## van Gog et al., 2024.2 -0.5993 -0.0525 0.0028 1.0134 0.0210
## van Gog et al., 2024.3 -0.9314 -0.0840 0.0071 1.0078 0.0209
## van Gog et al., 2024.4 -0.6238 -0.0528 0.0028 1.0119 0.0210
## van Gog et al., 2024.5 -0.3600 -0.0266 0.0007 1.0137 0.0211
## van Gog et al., 2024.6 0.1454 0.0192 0.0004 1.0152 0.0211
## van Gog et al., 2024.7 -0.4333 -0.0351 0.0012 1.0147 0.0211
## van Gog et al., 2024.8 -1.1237 -0.1077 0.0116 1.0049 0.0208
## van Gog et al., 2024.9 -1.6375 -0.1571 0.0244 0.9934 0.0204
## van Gog et al., 2024.10 0.4059 0.0417 0.0018 1.0146 0.0211
## van Gog et al., 2024.11 -0.4485 -0.0341 0.0012 1.0123 0.0211
## van Gog et al., 2024.12 -0.3509 -0.0252 0.0006 1.0130 0.0211
## van Gog et al., 2024.13 -0.8418 -0.0759 0.0058 1.0095 0.0209
## van Gog et al., 2024.14 -0.5817 -0.0493 0.0024 1.0128 0.0210
## van Gog et al., 2024.15 -1.2941 -0.1275 0.0161 1.0014 0.0206
## van Gog et al., 2024.16 -0.0618 0.0013 0.0000 1.0170 0.0212
## van Gog et al., 2024.17 -0.7555 -0.0685 0.0047 1.0112 0.0210
## van Gog et al., 2024.18 -1.6826 -0.1726 0.0293 0.9915 0.0203
## van Gog et al., 2024.19 -0.6509 -0.0577 0.0033 1.0127 0.0210
## van Gog et al., 2024.20 0.1551 0.0218 0.0005 1.0172 0.0212
## QE.del hat weight dfbs inf
## Baumgartner & Schneider, 2023 376.0458 0.0098 0.9785 0.0742
## Behnke et al., 2020.1 374.7321 0.0093 0.9263 0.1010
## Behnke et al., 2020.2 377.0359 0.0093 0.9263 0.0338
## Behnke et al., 2022 371.4928 0.0143 1.4307 0.0752
## Behnke et al., 2024.1 360.0503 0.0146 1.4585 -0.0426
## Brimmell et al., 2019 375.2546 0.0067 0.6678 0.0896
## Cabral et al., 2024.1 377.0734 0.0092 0.9173 0.0014
## Cabral et al., 2024.2 377.1268 0.0092 0.9173 0.0122
## Cabral et al., 2024.3 377.0228 0.0092 0.9173 -0.0041
## Carenzo et al., 2020.1 341.0679 0.0114 1.1383 -0.4063 *
## Carenzo et al., 2020.2 345.7446 0.0114 1.1383 0.2481
## Gurera & Isaacowitz, 2022.1 377.1294 0.0088 0.8834 0.0133
## Gurera & Isaacowitz, 2022.2 375.3689 0.0088 0.8834 0.0899
## Gurera & Isaacowitz, 2022.3 377.1242 0.0071 0.7125 0.0170
## Gurera & Isaacowitz, 2022.4 376.0585 0.0071 0.7125 -0.0547
## Hase et al., 2019.1 376.8703 0.0073 0.7290 -0.0196
## Hase et al., 2019.2 376.9498 0.0071 0.7125 0.0377
## Hase et al., 2019.3 367.8462 0.0073 0.7290 -0.2059
## Hase et al., 2019.4 373.5908 0.0071 0.7125 -0.1147
## Hase et al., 2019.5 374.7727 0.0082 0.8213 0.1007
## Hase et al., 2019.6 374.9992 0.0082 0.8213 0.0968
## Hase et al., in preparation.1 369.3800 0.0070 0.7039 -0.1844
## Hase et al., in preparation.2 376.5717 0.0070 0.7039 -0.0355
## Hase et al., in preparation.3 377.0886 0.0057 0.5731 -0.0025
## Hase et al., in preparation.4 376.3613 0.0056 0.5612 0.0598
## Hase et al., in preparation.5 375.4259 0.0056 0.5612 0.0826
## Hase et al., in preparation.6 373.2222 0.0057 0.5731 -0.1203
## Hase et al., in preparation.7 376.1049 0.0056 0.5612 -0.0538
## Hase et al., in preparation.8 374.5367 0.0056 0.5612 -0.0942
## Hase et al., in preparation.9 376.0320 0.0055 0.5490 -0.0560
## Hase et al., in preparation.10 376.6744 0.0054 0.5364 0.0479
## Hase et al., in preparation.11 376.2748 0.0054 0.5364 -0.0479
## Hase et al., in preparation.12 377.0408 0.0054 0.5364 -0.0087
## Hase et al., in preparation.13 377.1226 0.0054 0.5364 0.0040
## Hase et al., in preparation.14 376.8717 0.0054 0.5364 -0.0216
## Jamieson et al., 2022.1 356.9870 0.0130 1.3021 0.1780
## Jamieson et al., 2022.2 352.6334 0.0123 1.2276 0.2118
## Jamieson et al., 2022.3 366.8627 0.0112 1.1165 0.1666
## Journault et al., in preparation.1 358.8824 0.0129 1.2858 0.1760
## Journault et al., in preparation.2 376.2039 0.0128 1.2811 0.0606
## Journault et al., in preparation.3 370.1425 0.0128 1.2817 0.1228
## Khalaf et al., 2020.1 373.0985 0.0102 1.0187 0.1212
## Khalaf et al., 2020.2 373.9681 0.0102 1.0187 0.1103
## Laurin & Pellet, 2023 374.9994 0.0144 1.4383 -0.0065
## Lee et al., 2019 371.1765 0.0136 1.3567 -0.0656
## Malkoc et al., 2023 373.2067 0.0134 1.3370 -0.0534
## Malkoc et al., 2024 376.1061 0.0134 1.3370 -0.0149
## Moe & Putwain, 2020.1 374.7188 0.0081 0.8085 0.1016
## Moe & Putwain, 2020.2 376.8328 0.0081 0.8085 0.0463
## Moe & Putwain, 2020.3 376.5738 0.0081 0.8085 0.0577
## Moe & Putwain, 2020.4 376.8905 0.0081 0.8085 0.0430
## Moe & Putwain, 2020.5 376.6981 0.0081 0.8085 0.0527
## Moe & Putwain, 2020.6 375.3578 0.0081 0.8085 0.0899
## Moe & Putwain, 2020.7 376.7189 0.0081 0.8085 0.0518
## Moore et al., 2017 373.7907 0.0100 0.9960 0.1134
## Mosley et al., 2018.1 374.9393 0.0073 0.7290 -0.0854
## Mosley et al., 2018.2 376.4897 0.0073 0.7290 -0.0386
## Mulvenna et al., 2023.1 374.6075 0.0129 1.2946 -0.0458
## Mulvenna et al., 2023.2 376.0461 0.0129 1.2946 -0.0216
## O'Brien et al., 2022 370.7560 0.0080 0.7953 -0.1621
## Sammy et al., 2017 371.9932 0.0077 0.7673 0.1369
## Schickel et al., 2023.1 377.0414 0.0106 1.0634 0.0016
## Schickel et al., 2023.2 375.9794 0.0106 1.0634 0.0744
## Sharpe et al., 2024.1 377.0726 0.0057 0.5731 0.0241
## Sharpe et al., 2024.2 372.9904 0.0079 0.7885 -0.1246
## Sharpe et al., 2024.3 371.5501 0.0051 0.5103 0.1315
## Thornton et al., 2020.1 376.4190 0.0106 1.0557 -0.0304
## Thornton et al., 2020.2 375.7601 0.0106 1.0557 -0.0503
## Trotman et al., 2018.1 376.5610 0.0091 0.9080 0.0589
## Trotman et al., 2018.2 376.8810 0.0091 0.9080 -0.0150
## Turner et al., 2021.1 377.1292 0.0097 0.9673 0.0185
## Turner et al., 2021.2 375.0714 0.0097 0.9673 0.0946
## Turner et al., 2021.3 377.0060 0.0097 0.9673 -0.0043
## Wood et al., 2018 375.2492 0.0060 0.5960 0.0874
## Scheepers & Keller, 2022 375.9007 0.0113 1.1277 0.0743
## Bosshard et al., 2023.1 376.6850 0.0122 1.2198 0.0510
## Mansell, 2023.1 371.6856 0.0106 1.0557 -0.1263
## Mansell, 2023.2 369.9919 0.0106 1.0557 -0.1502
## Jamieson et al., 2021.1 357.7120 0.0134 1.3411 0.1625
## Jamieson et al., 2021.2 369.5351 0.0134 1.3411 0.1140
## Sharpe et al., 2024.4 374.1431 0.0042 0.4227 -0.0964
## Sharpe et al., 2024.5 375.6769 0.0042 0.4227 -0.0634
## Sharpe et al., 2024.6 376.9371 0.0042 0.4227 -0.0177
## Sharpe et al., 2024.7 376.5420 0.0042 0.4227 -0.0369
## Sharpe et al., 2024.8 374.3001 0.0042 0.4227 -0.0934
## Sharpe et al., 2024.9 372.7159 0.0042 0.4227 -0.1207
## Sharpe et al., 2024.10 376.5750 0.0042 0.4227 -0.0356
## Sharpe et al., 2024.11 376.4942 0.0042 0.4227 -0.0387
## Sharpe et al., 2024.12 376.8276 0.0019 0.1898 -0.0198
## Sharpe et al., 2024.13 376.3362 0.0019 0.1898 -0.0345
## Sharpe et al., 2024.14 377.1225 0.0019 0.1898 0.0069
## Sharpe et al., 2024.15 377.0577 0.0019 0.1898 -0.0079
## Simms, 2022.1 377.1225 0.0058 0.5847 0.0153
## Simms, 2022.2 377.0001 0.0058 0.5847 0.0314
## Simms, 2022.3 376.8966 0.0058 0.5847 -0.0197
## Simms, 2022.4 376.6692 0.0058 0.5847 -0.0322
## Simms, 2022.5 377.1191 0.0058 0.5847 0.0037
## Simms, 2022.6 375.0108 0.0058 0.5847 -0.0839
## Marr et al., 2021 376.4851 0.0117 1.1666 0.0587
## Conlon et al., 2022.1 372.9087 0.0085 0.8510 0.1270
## Conlon et al., 2022.2 375.6734 0.0085 0.8510 0.0835
## van Gog et al., 2024.1 376.1680 0.0088 0.8783 -0.0470
## van Gog et al., 2024.2 375.9976 0.0088 0.8783 -0.0525
## van Gog et al., 2024.3 374.9298 0.0080 0.8020 -0.0840
## van Gog et al., 2024.4 376.0623 0.0080 0.8020 -0.0528
## van Gog et al., 2024.5 376.7364 0.0077 0.7673 -0.0266
## van Gog et al., 2024.6 377.1206 0.0077 0.7673 0.0192
## van Gog et al., 2024.7 376.5062 0.0086 0.8567 -0.0351
## van Gog et al., 2024.8 373.7382 0.0086 0.8567 -0.1077
## van Gog et al., 2024.9 371.1049 0.0077 0.7745 -0.1572
## van Gog et al., 2024.10 376.9044 0.0077 0.7745 0.0417
## van Gog et al., 2024.11 376.5941 0.0073 0.7290 -0.0341
## van Gog et al., 2024.12 376.7752 0.0073 0.7290 -0.0252
## van Gog et al., 2024.13 375.2250 0.0083 0.8274 -0.0759
## van Gog et al., 2024.14 376.1459 0.0083 0.8274 -0.0493
## van Gog et al., 2024.15 372.6448 0.0087 0.8677 -0.1275
## van Gog et al., 2024.16 377.0808 0.0087 0.8677 0.0013
## van Gog et al., 2024.17 375.4537 0.0087 0.8677 -0.0685
## van Gog et al., 2024.18 369.8239 0.0087 0.8677 -0.1727
## van Gog et al., 2024.19 375.8325 0.0087 0.8730 -0.0577
## van Gog et al., 2024.20 377.1173 0.0087 0.8730 0.0218ranktest(model_fun_Cogni)## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = -0.1557, p = 0.0121# leave one out analysis #
leave1out(model_fun_Cogni)##
## estimate se zval pval ci.lb ci.ub
## Baumgartner & Schneider, 2023 0.1412 0.0178 7.9500 0.0000 0.1064 0.1761
## Behnke et al., 2020.1 0.1408 0.0177 7.9452 0.0000 0.1060 0.1755
## Behnke et al., 2020.2 0.1420 0.0178 7.9815 0.0000 0.1071 0.1768
## Behnke et al., 2022 0.1412 0.0178 7.9132 0.0000 0.1062 0.1762
## Behnke et al., 2024.1 0.1433 0.0178 8.0288 0.0000 0.1083 0.1783
## Brimmell et al., 2019 0.1410 0.0177 7.9697 0.0000 0.1063 0.1756
## Cabral et al., 2024.1 0.1425 0.0178 8.0139 0.0000 0.1077 0.1774
## Cabral et al., 2024.2 0.1423 0.0178 8.0024 0.0000 0.1075 0.1772
## Cabral et al., 2024.3 0.1426 0.0178 8.0201 0.0000 0.1078 0.1775
## Carenzo et al., 2020.1 0.1494 0.0170 8.8035 0.0000 0.1161 0.1827
## Carenzo et al., 2020.2 0.1383 0.0171 8.0983 0.0000 0.1049 0.1718
## Gurera & Isaacowitz, 2022.1 0.1423 0.0178 8.0039 0.0000 0.1075 0.1772
## Gurera & Isaacowitz, 2022.2 0.1410 0.0177 7.9516 0.0000 0.1062 0.1757
## Gurera & Isaacowitz, 2022.3 0.1423 0.0178 8.0136 0.0000 0.1075 0.1770
## Gurera & Isaacowitz, 2022.4 0.1435 0.0177 8.1011 0.0000 0.1088 0.1782
## Hase et al., 2019.1 0.1429 0.0177 8.0528 0.0000 0.1081 0.1777
## Hase et al., 2019.2 0.1419 0.0177 7.9951 0.0000 0.1071 0.1767
## Hase et al., 2019.3 0.1461 0.0175 8.3703 0.0000 0.1119 0.1804
## Hase et al., 2019.4 0.1446 0.0176 8.1969 0.0000 0.1100 0.1791
## Hase et al., 2019.5 0.1408 0.0177 7.9542 0.0000 0.1061 0.1755
## Hase et al., 2019.6 0.1408 0.0177 7.9549 0.0000 0.1061 0.1755
## Hase et al., in preparation.1 0.1458 0.0175 8.3283 0.0000 0.1115 0.1801
## Hase et al., in preparation.2 0.1432 0.0177 8.0752 0.0000 0.1084 0.1779
## Hase et al., in preparation.3 0.1426 0.0177 8.0448 0.0000 0.1079 0.1773
## Hase et al., in preparation.4 0.1415 0.0177 7.9918 0.0000 0.1068 0.1762
## Hase et al., in preparation.5 0.1411 0.0177 7.9808 0.0000 0.1064 0.1757
## Hase et al., in preparation.6 0.1447 0.0176 8.2170 0.0000 0.1102 0.1792
## Hase et al., in preparation.7 0.1435 0.0177 8.1112 0.0000 0.1088 0.1782
## Hase et al., in preparation.8 0.1442 0.0176 8.1734 0.0000 0.1096 0.1788
## Hase et al., in preparation.9 0.1435 0.0177 8.1154 0.0000 0.1089 0.1782
## Hase et al., in preparation.10 0.1417 0.0177 8.0016 0.0000 0.1070 0.1764
## Hase et al., in preparation.11 0.1434 0.0177 8.1048 0.0000 0.1087 0.1781
## Hase et al., in preparation.12 0.1427 0.0177 8.0547 0.0000 0.1080 0.1774
## Hase et al., in preparation.13 0.1425 0.0177 8.0406 0.0000 0.1078 0.1772
## Hase et al., in preparation.14 0.1429 0.0177 8.0701 0.0000 0.1082 0.1776
## Jamieson et al., 2022.1 0.1394 0.0176 7.9385 0.0000 0.1050 0.1739
## Jamieson et al., 2022.2 0.1389 0.0174 7.9933 0.0000 0.1048 0.1730
## Jamieson et al., 2022.3 0.1396 0.0176 7.9460 0.0000 0.1052 0.1741
## Journault et al., in preparation.1 0.1395 0.0176 7.9381 0.0000 0.1050 0.1739
## Journault et al., in preparation.2 0.1415 0.0178 7.9335 0.0000 0.1065 0.1764
## Journault et al., in preparation.3 0.1404 0.0177 7.9137 0.0000 0.1056 0.1752
## Khalaf et al., 2020.1 0.1404 0.0177 7.9362 0.0000 0.1057 0.1751
## Khalaf et al., 2020.2 0.1406 0.0177 7.9362 0.0000 0.1059 0.1753
## Laurin & Pellet, 2023 0.1427 0.0179 7.9837 0.0000 0.1076 0.1777
## Lee et al., 2019 0.1437 0.0178 8.0698 0.0000 0.1088 0.1786
## Malkoc et al., 2023 0.1435 0.0178 8.0529 0.0000 0.1086 0.1784
## Malkoc et al., 2024 0.1428 0.0178 8.0013 0.0000 0.1078 0.1778
## Moe & Putwain, 2020.1 0.1408 0.0177 7.9551 0.0000 0.1061 0.1754
## Moe & Putwain, 2020.2 0.1417 0.0178 7.9808 0.0000 0.1069 0.1765
## Moe & Putwain, 2020.3 0.1415 0.0178 7.9730 0.0000 0.1067 0.1763
## Moe & Putwain, 2020.4 0.1418 0.0178 7.9833 0.0000 0.1070 0.1766
## Moe & Putwain, 2020.5 0.1416 0.0178 7.9763 0.0000 0.1068 0.1764
## Moe & Putwain, 2020.6 0.1410 0.0177 7.9578 0.0000 0.1062 0.1757
## Moe & Putwain, 2020.7 0.1416 0.0178 7.9769 0.0000 0.1068 0.1764
## Moore et al., 2017 0.1406 0.0177 7.9380 0.0000 0.1059 0.1753
## Mosley et al., 2018.1 0.1441 0.0177 8.1467 0.0000 0.1094 0.1787
## Mosley et al., 2018.2 0.1432 0.0177 8.0775 0.0000 0.1085 0.1780
## Mulvenna et al., 2023.1 0.1434 0.0178 8.0452 0.0000 0.1084 0.1783
## Mulvenna et al., 2023.2 0.1429 0.0178 8.0127 0.0000 0.1080 0.1779
## O'Brien et al., 2022 0.1454 0.0176 8.2780 0.0000 0.1110 0.1798
## Sammy et al., 2017 0.1402 0.0176 7.9613 0.0000 0.1056 0.1747
## Schickel et al., 2023.1 0.1425 0.0178 8.0026 0.0000 0.1076 0.1774
## Schickel et al., 2023.2 0.1412 0.0178 7.9430 0.0000 0.1064 0.1761
## Sharpe et al., 2024.1 0.1421 0.0177 8.0179 0.0000 0.1074 0.1769
## Sharpe et al., 2024.2 0.1447 0.0176 8.2088 0.0000 0.1102 0.1793
## Sharpe et al., 2024.3 0.1402 0.0176 7.9825 0.0000 0.1058 0.1747
## Thornton et al., 2020.1 0.1431 0.0178 8.0419 0.0000 0.1082 0.1780
## Thornton et al., 2020.2 0.1434 0.0178 8.0692 0.0000 0.1086 0.1783
## Trotman et al., 2018.1 0.1415 0.0178 7.9642 0.0000 0.1067 0.1763
## Trotman et al., 2018.2 0.1428 0.0178 8.0335 0.0000 0.1080 0.1777
## Turner et al., 2021.1 0.1422 0.0178 7.9923 0.0000 0.1073 0.1771
## Turner et al., 2021.2 0.1409 0.0177 7.9432 0.0000 0.1061 0.1756
## Turner et al., 2021.3 0.1426 0.0178 8.0165 0.0000 0.1078 0.1775
## Wood et al., 2018 0.1410 0.0177 7.9763 0.0000 0.1064 0.1757
## Scheepers & Keller, 2022 0.1412 0.0178 7.9378 0.0000 0.1064 0.1761
## Bosshard et al., 2023.1 0.1416 0.0178 7.9448 0.0000 0.1067 0.1766
## Mansell, 2023.1 0.1448 0.0177 8.1924 0.0000 0.1101 0.1794
## Mansell, 2023.2 0.1452 0.0176 8.2364 0.0000 0.1106 0.1797
## Jamieson et al., 2021.1 0.1397 0.0176 7.9221 0.0000 0.1051 0.1743
## Jamieson et al., 2021.2 0.1405 0.0178 7.9087 0.0000 0.1057 0.1754
## Sharpe et al., 2024.4 0.1442 0.0176 8.1872 0.0000 0.1097 0.1788
## Sharpe et al., 2024.5 0.1437 0.0177 8.1357 0.0000 0.1091 0.1783
## Sharpe et al., 2024.6 0.1429 0.0177 8.0740 0.0000 0.1082 0.1775
## Sharpe et al., 2024.7 0.1432 0.0177 8.0984 0.0000 0.1085 0.1779
## Sharpe et al., 2024.8 0.1442 0.0176 8.1824 0.0000 0.1097 0.1787
## Sharpe et al., 2024.9 0.1447 0.0176 8.2286 0.0000 0.1102 0.1791
## Sharpe et al., 2024.10 0.1432 0.0177 8.0967 0.0000 0.1085 0.1778
## Sharpe et al., 2024.11 0.1432 0.0177 8.1008 0.0000 0.1086 0.1779
## Sharpe et al., 2024.12 0.1429 0.0177 8.0946 0.0000 0.1083 0.1775
## Sharpe et al., 2024.13 0.1432 0.0176 8.1131 0.0000 0.1086 0.1777
## Sharpe et al., 2024.14 0.1424 0.0177 8.0648 0.0000 0.1078 0.1770
## Sharpe et al., 2024.15 0.1427 0.0177 8.0807 0.0000 0.1081 0.1773
## Simms, 2022.1 0.1423 0.0177 8.0252 0.0000 0.1075 0.1770
## Simms, 2022.2 0.1420 0.0177 8.0106 0.0000 0.1073 0.1767
## Simms, 2022.3 0.1429 0.0177 8.0640 0.0000 0.1082 0.1776
## Simms, 2022.4 0.1431 0.0177 8.0798 0.0000 0.1084 0.1778
## Simms, 2022.5 0.1425 0.0177 8.0372 0.0000 0.1077 0.1772
## Simms, 2022.6 0.1440 0.0177 8.1550 0.0000 0.1094 0.1786
## Marr et al., 2021 0.1415 0.0178 7.9437 0.0000 0.1066 0.1764
## Conlon et al., 2022.1 0.1403 0.0176 7.9514 0.0000 0.1057 0.1749
## Conlon et al., 2022.2 0.1411 0.0177 7.9564 0.0000 0.1063 0.1758
## van Gog et al., 2024.1 0.1434 0.0178 8.0777 0.0000 0.1086 0.1782
## van Gog et al., 2024.2 0.1435 0.0177 8.0856 0.0000 0.1087 0.1783
## van Gog et al., 2024.3 0.1440 0.0177 8.1391 0.0000 0.1093 0.1787
## van Gog et al., 2024.4 0.1435 0.0177 8.0917 0.0000 0.1087 0.1782
## van Gog et al., 2024.5 0.1430 0.0177 8.0587 0.0000 0.1082 0.1778
## van Gog et al., 2024.6 0.1422 0.0178 8.0072 0.0000 0.1074 0.1770
## van Gog et al., 2024.7 0.1432 0.0178 8.0630 0.0000 0.1084 0.1780
## van Gog et al., 2024.8 0.1444 0.0177 8.1743 0.0000 0.1098 0.1791
## van Gog et al., 2024.9 0.1453 0.0176 8.2701 0.0000 0.1109 0.1797
## van Gog et al., 2024.10 0.1418 0.0178 7.9870 0.0000 0.1070 0.1766
## van Gog et al., 2024.11 0.1432 0.0177 8.0714 0.0000 0.1084 0.1779
## van Gog et al., 2024.12 0.1430 0.0177 8.0598 0.0000 0.1082 0.1778
## van Gog et al., 2024.13 0.1439 0.0177 8.1245 0.0000 0.1092 0.1786
## van Gog et al., 2024.14 0.1434 0.0177 8.0848 0.0000 0.1087 0.1782
## van Gog et al., 2024.15 0.1448 0.0176 8.2083 0.0000 0.1102 0.1794
## van Gog et al., 2024.16 0.1425 0.0178 8.0178 0.0000 0.1077 0.1774
## van Gog et al., 2024.17 0.1438 0.0177 8.1101 0.0000 0.1090 0.1785
## van Gog et al., 2024.18 0.1456 0.0176 8.2933 0.0000 0.1112 0.1800
## van Gog et al., 2024.19 0.1436 0.0177 8.0936 0.0000 0.1088 0.1783
## van Gog et al., 2024.20 0.1422 0.0178 7.9964 0.0000 0.1073 0.1770
## Q Qp tau2 I2 H2
## Baumgartner & Schneider, 2023 376.0458 0.0000 0.0211 72.4433 3.6289
## Behnke et al., 2020.1 374.7321 0.0000 0.0209 72.3024 3.6104
## Behnke et al., 2020.2 377.0359 0.0000 0.0212 72.5477 3.6427
## Behnke et al., 2022 371.4928 0.0000 0.0212 71.0777 3.4575
## Behnke et al., 2024.1 360.0503 0.0000 0.0212 69.6185 3.2915
## Brimmell et al., 2019 375.2546 0.0000 0.0209 72.3371 3.6150
## Cabral et al., 2024.1 377.0734 0.0000 0.0212 72.5518 3.6432
## Cabral et al., 2024.2 377.1268 0.0000 0.0212 72.5575 3.6440
## Cabral et al., 2024.3 377.0228 0.0000 0.0212 72.5464 3.6425
## Carenzo et al., 2020.1 341.0679 0.0000 0.0181 69.1888 3.2456
## Carenzo et al., 2020.2 345.7446 0.0000 0.0185 69.6520 3.2951
## Gurera & Isaacowitz, 2022.1 377.1294 0.0000 0.0212 72.5573 3.6440
## Gurera & Isaacowitz, 2022.2 375.3689 0.0000 0.0210 72.3669 3.6189
## Gurera & Isaacowitz, 2022.3 377.1242 0.0000 0.0211 72.5421 3.6419
## Gurera & Isaacowitz, 2022.4 376.0585 0.0000 0.0210 72.4137 3.6250
## Hase et al., 2019.1 376.8703 0.0000 0.0211 72.5118 3.6379
## Hase et al., 2019.2 376.9498 0.0000 0.0211 72.5248 3.6396
## Hase et al., 2019.3 367.8462 0.0000 0.0200 71.4512 3.5028
## Hase et al., 2019.4 373.5908 0.0000 0.0207 72.1259 3.5876
## Hase et al., 2019.5 374.7727 0.0000 0.0209 72.2950 3.6095
## Hase et al., 2019.6 374.9992 0.0000 0.0209 72.3203 3.6128
## Hase et al., in preparation.1 369.3800 0.0000 0.0202 71.6311 3.5250
## Hase et al., in preparation.2 376.5717 0.0000 0.0210 72.4726 3.6327
## Hase et al., in preparation.3 377.0886 0.0000 0.0211 72.5126 3.6380
## Hase et al., in preparation.4 376.3613 0.0000 0.0210 72.4456 3.6292
## Hase et al., in preparation.5 375.4259 0.0000 0.0209 72.3512 3.6168
## Hase et al., in preparation.6 373.2222 0.0000 0.0206 72.0759 3.5811
## Hase et al., in preparation.7 376.1049 0.0000 0.0209 72.3963 3.6227
## Hase et al., in preparation.8 374.5367 0.0000 0.0208 72.2218 3.5999
## Hase et al., in preparation.9 376.0320 0.0000 0.0209 72.3865 3.6214
## Hase et al., in preparation.10 376.6744 0.0000 0.0210 72.4731 3.6328
## Hase et al., in preparation.11 376.2748 0.0000 0.0210 72.4117 3.6247
## Hase et al., in preparation.12 377.0408 0.0000 0.0210 72.4994 3.6363
## Hase et al., in preparation.13 377.1226 0.0000 0.0211 72.5105 3.6378
## Hase et al., in preparation.14 376.8717 0.0000 0.0210 72.4792 3.6336
## Jamieson et al., 2022.1 356.9870 0.0000 0.0202 71.2499 3.4782
## Jamieson et al., 2022.2 352.6334 0.0000 0.0195 70.7010 3.4131
## Jamieson et al., 2022.3 366.8627 0.0000 0.0203 71.6155 3.5230
## Journault et al., in preparation.1 358.8824 0.0000 0.0202 71.3185 3.4866
## Journault et al., in preparation.2 376.2039 0.0000 0.0212 72.3036 3.6106
## Journault et al., in preparation.3 370.1425 0.0000 0.0209 71.9618 3.5666
## Khalaf et al., 2020.1 373.0985 0.0000 0.0208 72.1490 3.5905
## Khalaf et al., 2020.2 373.9681 0.0000 0.0209 72.2359 3.6018
## Laurin & Pellet, 2023 374.9994 0.0000 0.0213 70.9100 3.4376
## Lee et al., 2019 371.1765 0.0000 0.0211 71.9166 3.5608
## Malkoc et al., 2023 373.2067 0.0000 0.0212 72.0585 3.5789
## Malkoc et al., 2024 376.1061 0.0000 0.0213 72.1678 3.5930
## Moe & Putwain, 2020.1 374.7188 0.0000 0.0209 72.2878 3.6085
## Moe & Putwain, 2020.2 376.8328 0.0000 0.0211 72.5218 3.6392
## Moe & Putwain, 2020.3 376.5738 0.0000 0.0211 72.4935 3.6355
## Moe & Putwain, 2020.4 376.8905 0.0000 0.0211 72.5280 3.6401
## Moe & Putwain, 2020.5 376.6981 0.0000 0.0211 72.5071 3.6373
## Moe & Putwain, 2020.6 375.3578 0.0000 0.0209 72.3590 3.6178
## Moe & Putwain, 2020.7 376.7189 0.0000 0.0211 72.5094 3.6376
## Moore et al., 2017 373.7907 0.0000 0.0209 72.2141 3.5989
## Mosley et al., 2018.1 374.9393 0.0000 0.0209 72.2858 3.6083
## Mosley et al., 2018.2 376.4897 0.0000 0.0210 72.4668 3.6320
## Mulvenna et al., 2023.1 374.6075 0.0000 0.0212 72.2176 3.5994
## Mulvenna et al., 2023.2 376.0461 0.0000 0.0213 72.2856 3.6082
## O'Brien et al., 2022 370.7560 0.0000 0.0204 71.8106 3.5474
## Sammy et al., 2017 371.9932 0.0000 0.0205 71.9767 3.5685
## Schickel et al., 2023.1 377.0414 0.0000 0.0212 72.5347 3.6410
## Schickel et al., 2023.2 375.9794 0.0000 0.0211 72.4315 3.6273
## Sharpe et al., 2024.1 377.0726 0.0000 0.0211 72.5159 3.6385
## Sharpe et al., 2024.2 372.9904 0.0000 0.0206 72.0702 3.5804
## Sharpe et al., 2024.3 371.5501 0.0000 0.0205 71.9701 3.5676
## Thornton et al., 2020.1 376.4190 0.0000 0.0212 72.4809 3.6338
## Thornton et al., 2020.2 375.7601 0.0000 0.0211 72.4207 3.6259
## Trotman et al., 2018.1 376.5610 0.0000 0.0211 72.4971 3.6360
## Trotman et al., 2018.2 376.8810 0.0000 0.0212 72.5309 3.6405
## Turner et al., 2021.1 377.1292 0.0000 0.0212 72.5559 3.6438
## Turner et al., 2021.2 375.0714 0.0000 0.0210 72.3423 3.6156
## Turner et al., 2021.3 377.0060 0.0000 0.0212 72.5439 3.6422
## Wood et al., 2018 375.2492 0.0000 0.0209 72.3338 3.6145
## Scheepers & Keller, 2022 375.9007 0.0000 0.0211 72.4113 3.6247
## Bosshard et al., 2023.1 376.6850 0.0000 0.0212 72.4175 3.6255
## Mansell, 2023.1 371.6856 0.0000 0.0207 72.0380 3.5763
## Mansell, 2023.2 369.9919 0.0000 0.0205 71.8746 3.5555
## Jamieson et al., 2021.1 357.7120 0.0000 0.0205 71.3553 3.4910
## Jamieson et al., 2021.2 369.5351 0.0000 0.0210 71.8600 3.5537
## Sharpe et al., 2024.4 374.1431 0.0000 0.0207 72.1880 3.5956
## Sharpe et al., 2024.5 375.6769 0.0000 0.0209 72.3371 3.6149
## Sharpe et al., 2024.6 376.9371 0.0000 0.0210 72.4644 3.6317
## Sharpe et al., 2024.7 376.5420 0.0000 0.0210 72.4232 3.6262
## Sharpe et al., 2024.8 374.3001 0.0000 0.0207 72.2032 3.5975
## Sharpe et al., 2024.9 372.7159 0.0000 0.0206 72.0510 3.5780
## Sharpe et al., 2024.10 376.5750 0.0000 0.0210 72.4266 3.6267
## Sharpe et al., 2024.11 376.4942 0.0000 0.0210 72.4184 3.6256
## Sharpe et al., 2024.12 376.8276 0.0000 0.0209 72.4098 3.6245
## Sharpe et al., 2024.13 376.3362 0.0000 0.0209 72.3797 3.6205
## Sharpe et al., 2024.14 377.1225 0.0000 0.0210 72.4348 3.6278
## Sharpe et al., 2024.15 377.0577 0.0000 0.0209 72.4258 3.6266
## Simms, 2022.1 377.1225 0.0000 0.0211 72.5216 3.6392
## Simms, 2022.2 377.0001 0.0000 0.0211 72.5114 3.6379
## Simms, 2022.3 376.8966 0.0000 0.0210 72.4911 3.6352
## Simms, 2022.4 376.6692 0.0000 0.0210 72.4643 3.6317
## Simms, 2022.5 377.1191 0.0000 0.0211 72.5192 3.6389
## Simms, 2022.6 375.0108 0.0000 0.0208 72.2760 3.6070
## Marr et al., 2021 376.4851 0.0000 0.0212 72.4430 3.6288
## Conlon et al., 2022.1 372.9087 0.0000 0.0207 72.0907 3.5830
## Conlon et al., 2022.2 375.6734 0.0000 0.0210 72.3976 3.6229
## van Gog et al., 2024.1 376.1680 0.0000 0.0211 72.4506 3.6298
## van Gog et al., 2024.2 375.9976 0.0000 0.0210 72.4317 3.6274
## van Gog et al., 2024.3 374.9298 0.0000 0.0209 72.2978 3.6098
## van Gog et al., 2024.4 376.0623 0.0000 0.0210 72.4281 3.6269
## van Gog et al., 2024.5 376.7364 0.0000 0.0211 72.5013 3.6365
## van Gog et al., 2024.6 377.1206 0.0000 0.0211 72.5484 3.6428
## van Gog et al., 2024.7 376.5062 0.0000 0.0211 72.4858 3.6345
## van Gog et al., 2024.8 373.7382 0.0000 0.0208 72.1739 3.5938
## van Gog et al., 2024.9 371.1049 0.0000 0.0204 71.8460 3.5519
## van Gog et al., 2024.10 376.9044 0.0000 0.0211 72.5266 3.6399
## van Gog et al., 2024.11 376.5941 0.0000 0.0211 72.4791 3.6336
## van Gog et al., 2024.12 376.7752 0.0000 0.0211 72.5005 3.6364
## van Gog et al., 2024.13 375.2250 0.0000 0.0209 72.3365 3.6149
## van Gog et al., 2024.14 376.1459 0.0000 0.0210 72.4414 3.6286
## van Gog et al., 2024.15 372.6448 0.0000 0.0206 72.0532 3.5782
## van Gog et al., 2024.16 377.0808 0.0000 0.0212 72.5511 3.6431
## van Gog et al., 2024.17 375.4537 0.0000 0.0210 72.3696 3.6192
## van Gog et al., 2024.18 369.8239 0.0000 0.0203 71.7300 3.5373
## van Gog et al., 2024.19 375.8325 0.0000 0.0210 72.4127 3.6249
## van Gog et al., 2024.20 377.1173 0.0000 0.0212 72.5559 3.6438# Egger#
model_fun_Cogni_OutEgger <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, random = ~ 1 | paper_id/effect_size_id, mod = ~sqrt(Cogni_cor_Z_var), tdist=TRUE, data = Data)## Warning: 41 rows with NAs omitted from model fitting.model_fun_Cogni_OutEgger##
## Multivariate Meta-Analysis Model (k = 121; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0105 0.1024 39 no paper_id
## sigma^2.2 0.0098 0.0989 121 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 119) = 373.2432, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 119) = 1.5876, p-val = 0.2101
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.2211 0.0505 4.3756 119 <.0001 0.1210 0.3211
## sqrt(Cogni_cor_Z_var) -0.5302 0.4208 -1.2600 119 0.2101 -1.3635 0.3030
##
## intrcpt ***
## sqrt(Cogni_cor_Z_var)
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Run trim-and-fill analysis for the right side
model_fun_Cogni_tf_right <- trimfill(model_fun_Cogni, side = "right")
# Run trim-and-fill analysis for the left side
model_fun_Cogni_tf_left <- trimfill(model_fun_Cogni, side = "left")
# Print the trim-and-fill model results
print(model_fun_Cogni_tf_right)##
## Estimated number of missing studies on the right side: 28 (SE = 7.1995)
##
## Random-Effects Model (k = 149; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0350 (SE = 0.0061)
## tau (square root of estimated tau^2 value): 0.1871
## I^2 (total heterogeneity / total variability): 79.41%
## H^2 (total variability / sampling variability): 4.86
##
## Test for Heterogeneity:
## Q(df = 148) = 584.4407, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2056 0.0191 10.7476 <.0001 0.1681 0.2430 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(model_fun_Cogni_tf_left)##
## Estimated number of missing studies on the left side: 0 (SE = 5.7525)
##
## Random-Effects Model (k = 121; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0209 (SE = 0.0046)
## tau (square root of estimated tau^2 value): 0.1445
## I^2 (total heterogeneity / total variability): 72.22%
## H^2 (total variability / sampling variability): 3.60
##
## Test for Heterogeneity:
## Q(df = 120) = 377.1303, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.1426 0.0176 8.0869 <.0001 0.1080 0.1771 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Combine the number of studies imputed from both sides
total_imputed_studies <- model_fun_Cogni_tf_right$k0 + model_fun_Cogni_tf_left$k0
cat("Total number of imputed studies (both sides) for Cogni:", total_imputed_studies, "\n")## Total number of imputed studies (both sides) for Cogni: 28# Generate funnel plots only left
#par(mfrow=c(1, 3))
funnel(model_fun_Cogni, main="Original Model")
funnel(model_fun_Cogni_tf_right, main="Trim-and-Fill Right")
funnel(model_fun_Cogni_tf_left, main="Trim-and-Fill Left", xlab = 'Cogni')
# Return to single plot layout
#par(mfrow=c(1, 1))8.2 Multilevel Model
model_Cogni_multilevel <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML")## Warning: 41 rows with NAs omitted from model fitting.model_Cogni_multilevel##
## Multivariate Meta-Analysis Model (k = 121; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0122 0.1106 39 no paper_id
## sigma^2.2 0.0093 0.0963 121 no paper_id/effect_size_id
##
## Test for Heterogeneity:
## Q(df = 120) = 377.1303, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.1650 0.0239 6.9040 120 <.0001 0.1177 0.2123 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1convert_z2r(0.1660)## [1] 0.1644919predict_Cogni <- predict(model_Cogni_multilevel, digits=3, transf=transf.ztor, level = 95)
predict_Cogni##
## pred ci.lb ci.ub pi.lb pi.ub
## 0.163 0.117 0.209 -0.128 0.429forest.rma(model_Cogni_multilevel, header = "Cogni",slab = Data$Ref_APA, alim=c(-0.8,1.2))
######## list 1 ########
list_Cogni <- Data$Cogni_cor_Z_var
############ sum 1#####################
sum_Cogni <- sum(list_Cogni, na.rm = TRUE)
###################### sum 2 #####################
sum2_Cogni <- (sum_Cogni)^2
####################### list 2 ##############
list_In_Cogni <- Data$Cogni_cor_Z_var_Sq
#################### sum 3 #######################
sum_In_Cogni<- sum(list_In_Cogni, na.rm = TRUE)
################ numerator ##############
numerator_Cogni<- (model_Cogni_multilevel$k-1)*sum_Cogni
############# denominator #############
denominator_Cogni<- sum2_Cogni - sum_In_Cogni
############## eps ################
EPS_Cogni<- numerator_Cogni / denominator_Cogni
############### i2 1 level ##################
I2_1_Cogni <- (EPS_Cogni) / (model_Cogni_multilevel$sigma2[1] + model_Cogni_multilevel$sigma2[2] + EPS_Cogni) *100
I2_1_Cogni## [1] 99.94956############## i2 2 level #################
I2_2_Cogni <- (model_Cogni_multilevel$sigma2[1]) / (model_Cogni_multilevel$sigma2[1] + model_Cogni_multilevel$sigma2[2] + EPS_Cogni) *100
I2_2_Cogni## [1] 0.02869619########### I2 level 3
I2_3_Cogni <- (model_Cogni_multilevel$sigma2[2]) / (model_Cogni_multilevel$sigma2[1] + model_Cogni_multilevel$sigma2[2] + EPS_Cogni) *100
I2_3_Cogni## [1] 0.02174071############### ML without level 2 ##########
model_Cogni_multilevel_2 <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(0,NA), tdist=TRUE,data = Data)## Warning: 41 rows with NAs omitted from model fitting.############# ml without level 3 ###########
model_Cogni_multilevel_3 <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", sigma2=c(NA,0), tdist=TRUE,data = Data)## Warning: 41 rows with NAs omitted from model fitting.##################### sig level 2 #######################
anova12_Cogni <- anova(model_Cogni_multilevel,model_Cogni_multilevel_2)
anova12_Cogni##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 -64.3029 -55.9404 -64.0960 35.1515 377.1303
## Reduced 2 -47.4700 -41.8950 -47.3674 25.7350 18.8330 <.0001 377.1303###############sig level 3v #################
anova13_Cogni <- anova(model_Cogni_multilevel,model_Cogni_multilevel_3)
anova13_Cogni##
## df AIC BIC AICc logLik LRT pval QE
## Full 3 -64.3029 -55.9404 -64.0960 35.1515 377.1303
## Reduced 2 -42.8638 -37.2888 -42.7612 23.4319 23.4391 <.0001 377.13039. Results table
# Function to perform the calculations and create the result table for a given parameter
create_result_table <- function(parameter_name, cor_col, n_col) {
# Z-transform correlation coefficients
z_col <- .5 * log((1 + Data[[cor_col]]) / (1 - Data[[cor_col]]))
var_col <- 1 / (Data[[n_col]] - 3)
# Add z and variance columns to Data
Data[[paste0(parameter_name, "_cor_Z")]] <- z_col
Data[[paste0(parameter_name, "_cor_Z_var")]] <- var_col
Data[[paste0(parameter_name, "_cor_Z_var_Sq")]] <- var_col^2
# Meta-analysis model
model <- rma.mv(yi = z_col, V = var_col, slab = Data$Ref_APA,
data = Data, random = ~ 1 | paper_id/effect_size_id,
test = "t", method = "REML")
# Prediction intervals
predict_result <- predict(model, transf=transf.ztor, level = 95)
# Additional I2 calculations
EPS <- (model$k - 1) * sum(var_col, na.rm = TRUE) /
((sum(var_col, na.rm = TRUE))^2 - sum(var_col^2, na.rm = TRUE))
I2_1 <- round((EPS) / (model$sigma2[1] + model$sigma2[2] + EPS) * 100, 2)
I2_2 <- round((model$sigma2[1]) / (model$sigma2[1] + model$sigma2[2] + EPS) * 100, 2)
I2_3 <- round((model$sigma2[2]) / (model$sigma2[1] + model$sigma2[2] + EPS) * 100, 2)
# Egger's test
egger_test <- rma.mv(yi = z_col, V = var_col, random = ~ 1 | paper_id/effect_size_id,
mod = ~ sqrt(var_col), tdist = TRUE, data = Data)
egger_result <- round(egger_test$QM, 2)
# Rank correlation test
rank_corr_test <- ranktest(model)
rank_corr_result <- round(as.numeric(rank_corr_test$tau), 2)
# Creating the table
result_table <- data.frame(
Parameter_Name = parameter_name,
Number_of_Effect_Sizes = model$k,
Mean_Effect_Size = round(model$b[1], 2),
CI_95 = paste0(round(model$ci.lb, 2), ", ", round(model$ci.ub, 2)),
PI_95 = paste0(round(predict_result$pi.lb, 2), ", ", round(predict_result$pi.ub, 2)),
Q_Parameter = round(model$QE,2),
I2_Level1 = I2_1,
I2_Level2 = I2_2,
I2_Level3 = I2_3,
Egger_Test_Result = egger_result,
Rank_Corr_Test_Result = rank_corr_result
)
return(result_table)
}
# List of parameters and corresponding column names
parameters <- list(
list(name = "CO", cor_col = "CO_cor", n_col = "n_performance"),
list(name = "TPR", cor_col = "TPR_cor", n_col = "n_performance"),
list(name = "CTI", cor_col = "CTI_cor", n_col = "n_performance"),
list(name = "Cogni", cor_col = "Cogni_cor", n_col = "n_performance")
)
# Apply the function to each parameter and combine the results
result_tables <- lapply(parameters, function(param) {
create_result_table(param$name, param$cor_col, param$n_col)
})## Warning: 94 rows with NAs omitted from model fitting.
## Warning: 94 rows with NAs omitted from model fitting.## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami## Warning: 101 rows with NAs omitted from model fitting.
## Warning: 101 rows with NAs omitted from model fitting.## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami## Warning: 89 rows with NAs omitted from model fitting.
## Warning: 89 rows with NAs omitted from model fitting.## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami## Warning: 41 rows with NAs omitted from model fitting.
## Warning: 41 rows with NAs omitted from model fitting.## Warning in cor.test.default(yi.star, vi, method = "kendall", exact = exact):
## nie można obliczyć dokładnej wartości prawdopodobieństwa z powtórzonymi
## wartościami# Combine all result tables into one data frame
final_result_table <- do.call(rbind, result_tables)
# Print the final result table
print(final_result_table)## Parameter_Name Number_of_Effect_Sizes Mean_Effect_Size CI_95
## 1 CO 68 0.06 0, 0.13
## 2 TPR 61 -0.10 -0.17, -0.03
## 3 CTI 73 0.10 0.04, 0.15
## 4 Cogni 121 0.16 0.12, 0.21
## PI_95 Q_Parameter I2_Level1 I2_Level2 I2_Level3 Egger_Test_Result
## 1 -0.25, 0.36 151.69 99.85 0.08 0.07 0.03
## 2 -0.35, 0.17 117.86 99.88 0.12 0.00 1.39
## 3 -0.24, 0.42 195.52 99.84 0.00 0.16 0.29
## 4 -0.13, 0.43 377.13 99.93 0.04 0.03 1.59
## Rank_Corr_Test_Result
## 1 -0.05
## 2 -0.01
## 3 0.04
## 4 -0.16write.csv(final_result_table, "meta_analysis_results.csv", row.names = FALSE)10. Figures
10.1 Funnel plots
# Run trim-and-fill analysis for the right side
model_fun_CO_tf_right <- trimfill(model_fun_CO, side = "right")
model_fun_TPR_tf_left <- trimfill(model_fun_TPR, side = "left")
model_fun_CTI_tf_right <- trimfill(model_fun_CTI, side = "right")
#model_fun_Cogni_tf_right <- trimfill(model_fun_Cogni, side = "left" )
# Set up 2x2 plotting area
par(mfrow=c(2, 2))
# Generate funnel plots
funnel(model_fun_CO_tf_right, main="", xlab = 'Cardiac Output')
funnel(model_fun_TPR_tf_left, main="", xlab = 'Total Peripheral Resistance')
funnel(model_fun_CTI_tf_right, main="", xlab = 'Challenge Threat Index')
funnel(model_fun_Cogni_tf_right, main="", xlab = 'Cognitive Evaluations')
# Set up the file for output
jpeg("funnel_plots.jpg", width = 16, height = 16, units = "cm", res = 300)
# Set up 2x2 plotting area
par(mfrow=c(2, 2))
# Generate funnel plots
funnel(model_fun_CO_tf_right, main="", xlab = 'Cardiac Output')
funnel(model_fun_TPR_tf_left, main="", xlab = 'Total Peripheral Resistance')
funnel(model_fun_CTI_tf_right, main="", xlab = 'Challenge Threat Index')
funnel(model_fun_Cogni_tf_right, main="", xlab = 'Cognitive Evaluations')
# Close the file
dev.off()## png
## 2# Return to single plot layout
par(mfrow=c(1, 1))10.2 Forest plots
# Save CO forest plot
jpeg("forest_plot_CO.jpg", width = 8, height = 26, units = "cm", res = 300)
forest(model_CO_multilevel, header = "Reference", xlab = 'CO', slab = Data$Ref_APA, alim = c(-0.8, 1), cex = 0.42, shade="zebra")
dev.off()## png
## 2# Save TPR forest plot
jpeg("forest_plot_TPR.jpg", width = 8, height = 26, units = "cm", res = 300)
forest(model_TPR_multilevel, header = "Reference", xlab = 'TPR', slab = Data$Ref_APA, alim = c(-1, .6), cex = 0.42, shade="zebra")
dev.off()## png
## 2# Save CTI forest plot
jpeg("forest_plot_CTI.jpg", width = 8, height = 26, units = "cm", res = 300)
forest(model_CTI_multilevel, header = "Reference", xlab = 'CTI', slab = Data$Ref_APA, alim = c(-1.5, 1.5), cex = 0.42, shade="zebra")
dev.off()## png
## 2# Save Cogni forest plot
jpeg("forest_plot_Cogni.jpg", width = 8, height = 26, units = "cm", res = 300)
forest(model_Cogni_multilevel, header = "Reference", xlab = 'Cognitive Evaluations', slab = Data$Ref_APA, alim = c(-0.8, 1), cex = 0.42, shade="zebra")
dev.off()## png
## 2# Display forest plots
knitr::include_graphics("forest_plot_CO.jpg")
knitr::include_graphics("forest_plot_TPR.jpg")
knitr::include_graphics("forest_plot_CTI.jpg")
knitr::include_graphics("forest_plot_Cogni.jpg")
11 Moderator Analysis
11.1 Moderator Analysis - main code
model_CO_multilevel_BD <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(Cardio_before0_during1)-1, tdist=TRUE)## Warning: 94 rows with NAs omitted from model fitting.model_CO_multilevel_Age <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ age, tdist=TRUE)## Warning: 94 rows with NAs omitted from model fitting.model_CO_multilevel_Sex <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ sex_percent_F, tdist=TRUE)## Warning: 94 rows with NAs omitted from model fitting.model_CO_multilevel_Rob <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(overall_RoB)-1, tdist=TRUE)## Warning: 95 rows with NAs omitted from model fitting.## Warning: Redundant predictors dropped from the model.model_CO_multilevel_BD##
## Multivariate Meta-Analysis Model (k = 68; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0127 0.1127 28 no paper_id
## sigma^2.2 0.0121 0.1099 68 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 66) = 143.8691, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 66) = 2.0653, p-val = 0.1349
##
## Model Results:
##
## estimate se tval df pval ci.lb
## factor(Cardio_before0_during1)0 0.0439 0.0385 1.1396 66 0.2586 -0.0330
## factor(Cardio_before0_during1)1 0.0925 0.0520 1.7786 66 0.0799 -0.0113
## ci.ub
## factor(Cardio_before0_during1)0 0.1209
## factor(Cardio_before0_during1)1 0.1963 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CO_multilevel_Age##
## Multivariate Meta-Analysis Model (k = 68; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0149 0.1219 28 no paper_id
## sigma^2.2 0.0105 0.1022 68 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 66) = 150.6689, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 66) = 1.1833, p-val = 0.2806
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.1632 0.0987 1.6524 66 0.1032 -0.0340 0.3603
## age -0.0043 0.0040 -1.0878 66 0.2806 -0.0123 0.0036
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CO_multilevel_Sex##
## Multivariate Meta-Analysis Model (k = 68; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0147 0.1213 28 no paper_id
## sigma^2.2 0.0115 0.1074 68 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 66) = 148.0255, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 66) = 0.0336, p-val = 0.8552
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.0536 0.0552 0.9702 66 0.3355 -0.0567 0.1638
## sex_percent_F 0.0230 0.1257 0.1833 66 0.8552 -0.2280 0.2740
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CO_multilevel_Rob##
## Multivariate Meta-Analysis Model (k = 67; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0163 0.1277 27 no paper_id
## sigma^2.2 0.0118 0.1087 67 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 65) = 150.0373, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 65) = 1.5413, p-val = 0.2218
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## factor(overall_RoB)1 0.0645 0.0395 1.6334 65 0.1072 -0.0144 0.1433
## factor(overall_RoB)2 0.0485 0.0753 0.6439 65 0.5219 -0.1019 0.1988
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_TPR_multilevel_BD <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(Cardio_before0_during1)-1, tdist=TRUE)## Warning: 101 rows with NAs omitted from model fitting.model_TPR_multilevel_Age <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ age, tdist=TRUE)## Warning: 101 rows with NAs omitted from model fitting.model_TPR_multilevel_Sex <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ sex_percent_F, tdist=TRUE)## Warning: 101 rows with NAs omitted from model fitting.model_TPR_multilevel_Rob <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(overall_RoB)-1, tdist=TRUE)## Warning: 102 rows with NAs omitted from model fitting.
## Warning: Redundant predictors dropped from the model.model_TPR_multilevel_BD##
## Multivariate Meta-Analysis Model (k = 61; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0187 0.1369 24 no paper_id
## sigma^2.2 0.0000 0.0000 61 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 59) = 112.3671, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 59) = 3.9994, p-val = 0.0235
##
## Model Results:
##
## estimate se tval df pval ci.lb
## factor(Cardio_before0_during1)0 -0.0996 0.0397 -2.5082 59 0.0149 -0.1790
## factor(Cardio_before0_during1)1 -0.0971 0.0642 -1.5136 59 0.1355 -0.2255
## ci.ub
## factor(Cardio_before0_during1)0 -0.0201 *
## factor(Cardio_before0_during1)1 0.0313
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_TPR_multilevel_Age##
## Multivariate Meta-Analysis Model (k = 61; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0188 0.1372 24 no paper_id
## sigma^2.2 0.0000 0.0000 61 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 59) = 116.3318, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 59) = 0.0791, p-val = 0.7796
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt -0.0108 0.3157 -0.0342 59 0.9728 -0.6424 0.6208
## age -0.0039 0.0137 -0.2812 59 0.7796 -0.0313 0.0236
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_TPR_multilevel_Sex##
## Multivariate Meta-Analysis Model (k = 61; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0190 0.1378 24 no paper_id
## sigma^2.2 0.0000 0.0000 61 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 59) = 104.7456, p-val = 0.0002
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 59) = 0.0089, p-val = 0.9253
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt -0.0944 0.0612 -1.5421 59 0.1284 -0.2169 0.0281
## sex_percent_F -0.0125 0.1326 -0.0942 59 0.9253 -0.2777 0.2528
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_TPR_multilevel_Rob##
## Multivariate Meta-Analysis Model (k = 60; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0098 0.0989 23 no paper_id
## sigma^2.2 0.0000 0.0000 60 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 58) = 88.9257, p-val = 0.0056
##
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 58) = 9.2274, p-val = 0.0003
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## factor(overall_RoB)1 -0.0511 0.0329 -1.5528 58 0.1259 -0.1169 0.0148
## factor(overall_RoB)2 -0.2504 0.0625 -4.0054 58 0.0002 -0.3755 -0.1253
##
## factor(overall_RoB)1
## factor(overall_RoB)2 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CTI_multilevel_BD <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(Cardio_before0_during1)-1, tdist=TRUE)## Warning: 89 rows with NAs omitted from model fitting.model_CTI_multilevel_Age <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ age, tdist=TRUE)## Warning: 89 rows with NAs omitted from model fitting.model_CTI_multilevel_Sex <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ sex_percent_F, tdist=TRUE)## Warning: 89 rows with NAs omitted from model fitting.model_CTI_multilevel_Rob <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(overall_RoB)-1, tdist=TRUE)## Warning: 90 rows with NAs omitted from model fitting.
## Warning: Redundant predictors dropped from the model.model_CTI_multilevel_BD##
## Multivariate Meta-Analysis Model (k = 73; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 28 no paper_id
## sigma^2.2 0.0290 0.1702 73 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 71) = 181.6539, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 71) = 6.9192, p-val = 0.0018
##
## Model Results:
##
## estimate se tval df pval ci.lb
## factor(Cardio_before0_during1)0 0.0828 0.0300 2.7652 71 0.0072 0.0231
## factor(Cardio_before0_during1)1 0.1607 0.0646 2.4883 71 0.0152 0.0319
## ci.ub
## factor(Cardio_before0_during1)0 0.1426 **
## factor(Cardio_before0_during1)1 0.2895 *
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CTI_multilevel_Age##
## Multivariate Meta-Analysis Model (k = 73; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0018 0.0429 28 no paper_id
## sigma^2.2 0.0286 0.1690 73 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 71) = 195.3210, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 71) = 0.0196, p-val = 0.8891
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.0417 0.4099 0.1016 71 0.9193 -0.7757 0.8590
## age 0.0026 0.0184 0.1399 71 0.8891 -0.0341 0.0392
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CTI_multilevel_Sex##
## Multivariate Meta-Analysis Model (k = 73; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0008 0.0284 28 no paper_id
## sigma^2.2 0.0289 0.1700 73 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 71) = 174.5910, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 71) = 0.3318, p-val = 0.5664
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.0737 0.0502 1.4665 71 0.1469 -0.0265 0.1738
## sex_percent_F 0.0653 0.1134 0.5760 71 0.5664 -0.1609 0.2916
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_CTI_multilevel_Rob##
## Multivariate Meta-Analysis Model (k = 72; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0037 0.0606 27 no paper_id
## sigma^2.2 0.0284 0.1684 72 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 70) = 188.8290, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 70) = 5.3111, p-val = 0.0071
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## factor(overall_RoB)1 0.1013 0.0338 2.9988 70 0.0038 0.0339 0.1687 **
## factor(overall_RoB)2 0.0983 0.0770 1.2764 70 0.2060 -0.0553 0.2518
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_Cogni_multilevel_Year <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ year, tdist=TRUE)## Warning: 41 rows with NAs omitted from model fitting.model_Cogni_multilevel_Age <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ age, tdist=TRUE)## Warning: 43 rows with NAs omitted from model fitting.model_Cogni_multilevel_Sex <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ sex_percent_F, tdist=TRUE)## Warning: 42 rows with NAs omitted from model fitting.model_Cogni_multilevel_Rob <- rma.mv(yi = Cogni_cor_Z, V = Cogni_cor_Z_var, slab = Ref_APA, data = Data, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ factor(overall_RoB)-1, tdist=TRUE)## Warning: 42 rows with NAs omitted from model fitting.model_Cogni_multilevel_Year##
## Multivariate Meta-Analysis Model (k = 121; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0114 0.1066 39 no paper_id
## sigma^2.2 0.0095 0.0974 121 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 119) = 354.1891, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 119) = 1.5059, p-val = 0.2222
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 16.7599 13.5233 1.2393 119 0.2177 -10.0176 43.5374
## year -0.0082 0.0067 -1.2272 119 0.2222 -0.0215 0.0050
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_Cogni_multilevel_Age##
## Multivariate Meta-Analysis Model (k = 119; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0120 0.1094 38 no paper_id
## sigma^2.2 0.0096 0.0981 119 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 117) = 347.1890, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 117) = 0.5320, p-val = 0.4672
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.2017 0.0627 3.2169 117 0.0017 0.0775 0.3259 **
## age -0.0018 0.0025 -0.7294 117 0.4672 -0.0067 0.0031
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_Cogni_multilevel_Sex##
## Multivariate Meta-Analysis Model (k = 120; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0130 0.1140 38 no paper_id
## sigma^2.2 0.0095 0.0976 120 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 118) = 371.1344, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 118) = 0.0013, p-val = 0.9714
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.1653 0.0373 4.4363 118 <.0001 0.0915 0.2390 ***
## sex_percent_F 0.0021 0.0593 0.0359 118 0.9714 -0.1154 0.1196
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_Cogni_multilevel_Rob##
## Multivariate Meta-Analysis Model (k = 120; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0137 0.1169 38 no paper_id
## sigma^2.2 0.0093 0.0966 120 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 117) = 372.4900, p-val < .0001
##
## Test of Moderators (coefficients 1:3):
## F(df1 = 3, df2 = 117) = 14.6794, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## factor(overall_RoB)1 0.1805 0.0321 5.6301 117 <.0001 0.1170 0.2440
## factor(overall_RoB)2 0.1366 0.0404 3.3765 117 0.0010 0.0565 0.2166
## factor(overall_RoB)3 0.1931 0.1500 1.2869 117 0.2007 -0.1041 0.4902
##
## factor(overall_RoB)1 ***
## factor(overall_RoB)2 ***
## factor(overall_RoB)3
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 111.2 Moderator Analysis - Year + Data from Behnke & Kaczmarek, 2019
#import and store data from excel file
Data2 <- read_excel("C:/Users/macbe/OneDrive/Behnke Dropbox/MA CHT/Data.xlsx", sheet = "year_pub_bias")## New names:
## • `title` -> `title...5`
## • `title` -> `title...8`
## • `` -> `...22`
## • `` -> `...31`#View(Data2)
Data2 <- as.data.frame(Data2)
#z-transform correlation coefficients
Data2$CO_cor_Z <- .5 * log((1+Data2$CO_cor)/(1-Data2$CO_cor))
Data2$TPR_cor_Z <- .5 * log((1+Data2$TPR_cor)/(1-Data2$TPR_cor))
Data2$CTI_cor_Z <- .5 * log((1+Data2$CTI_cor)/(1-Data2$CTI_cor))
# calculate z variance
Data2$CO_cor_Z_var <- ifelse(is.na(Data2$CO_cor), NA, 1 / (Data2$n_performance - 3))
Data2$TPR_cor_Z_var <- ifelse(is.na(Data2$TPR_cor), NA, 1 / (Data2$n_performance - 3))
Data2$CTI_cor_Z_var <- ifelse(is.na(Data2$CTI_cor), NA, 1 / (Data2$n_performance - 3))
# calculate z variance squared
Data2$CO_cor_Z_var_Sq <- ifelse(is.na(Data2$CO_cor), NA, (1 / (Data2$n_performance - 3))^2)
Data2$TPR_cor_Z_var_Sq <- ifelse(is.na(Data2$TPR_cor), NA, (1 / (Data2$n_performance - 3))^2)
Data2$CTI_cor_Z_var_Sq <- ifelse(is.na(Data2$CTI_cor), NA, (1 / (Data2$n_performance - 3))^2)
model_CO_multilevel_Year <- rma.mv(yi = CO_cor_Z, V = CO_cor_Z_var, slab = Ref_APA, data = Data2, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ year, tdist=TRUE) #did not converge## Warning: 95 rows with NAs omitted from model fitting.model_TPR_multilevel_Year <- rma.mv(yi = TPR_cor_Z, V = TPR_cor_Z_var, slab = Ref_APA, data = Data2, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ year, tdist=TRUE)## Warning: 102 rows with NAs omitted from model fitting.#model_CTI_multilevel_Year <- rma.mv(yi = CTI_cor_Z, V = CTI_cor_Z_var, slab = Ref_APA, data = Data2, random = ~ 1 | paper_id/effect_size_id, test = "t", method = "REML", mods = ~ year, tdist=TRUE)
model_CO_multilevel_Year #did not converge##
## Multivariate Meta-Analysis Model (k = 86; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0156 0.1250 46 no paper_id
## sigma^2.2 0.0109 0.1042 86 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 84) = 193.2813, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 84) = 3.9173, p-val = 0.0511
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 23.4955 11.8215 1.9875 84 0.0501 -0.0129 47.0039 .
## year -0.0116 0.0059 -1.9792 84 0.0511 -0.0232 0.0001 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_TPR_multilevel_Year##
## Multivariate Meta-Analysis Model (k = 79; method: REML)
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0174 0.1320 42 no paper_id
## sigma^2.2 0.0000 0.0000 79 no paper_id/effect_size_id
##
## Test for Residual Heterogeneity:
## QE(df = 77) = 144.2935, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 77) = 1.5997, p-val = 0.2098
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt -14.2351 11.1563 -1.2760 77 0.2058 -36.4502 7.9800
## year 0.0070 0.0055 1.2648 77 0.2098 -0.0040 0.0180
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#model_CTI_multilevel_Year #did not converge11.3 Table for moderator analysis
# Function to extract the necessary information from the moderator models
extract_mod_results <- function(model) {
mod_F <- round(model$QM, 2)
mod_df <- paste(model$QMdf[1], model$QMdf[2], sep = ", ")
return(list(F = mod_F, df = mod_df))
}
# Creating the summary table
create_summary_table <- function() {
data <- data.frame(
Name = c("CO", "TPR", "CTI", "Cogni"),
ModeratorAge_F = c(
extract_mod_results(model_CO_multilevel_Age)$F,
extract_mod_results(model_TPR_multilevel_Age)$F,
extract_mod_results(model_CTI_multilevel_Age)$F,
extract_mod_results(model_Cogni_multilevel_Age)$F
),
ModeratorAge_df = c(
extract_mod_results(model_CO_multilevel_Age)$df,
extract_mod_results(model_TPR_multilevel_Age)$df,
extract_mod_results(model_CTI_multilevel_Age)$df,
extract_mod_results(model_Cogni_multilevel_Age)$df
),
ModeratorSex_F = c(
extract_mod_results(model_CO_multilevel_Sex)$F,
extract_mod_results(model_TPR_multilevel_Sex)$F,
extract_mod_results(model_CTI_multilevel_Sex)$F,
extract_mod_results(model_Cogni_multilevel_Sex)$F
),
ModeratorSex_df = c(
extract_mod_results(model_CO_multilevel_Sex)$df,
extract_mod_results(model_TPR_multilevel_Sex)$df,
extract_mod_results(model_CTI_multilevel_Sex)$df,
extract_mod_results(model_Cogni_multilevel_Sex)$df
),
ModeratorBD_F = c(
extract_mod_results(model_CO_multilevel_BD)$F,
extract_mod_results(model_TPR_multilevel_BD)$F,
extract_mod_results(model_CTI_multilevel_BD)$F,
NA
),
ModeratorBD_df = c(
extract_mod_results(model_CO_multilevel_BD)$df,
extract_mod_results(model_TPR_multilevel_BD)$df,
extract_mod_results(model_CTI_multilevel_BD)$df,
NA
),
ModeratorYear_F = c(
extract_mod_results(model_CO_multilevel_Year)$F,
extract_mod_results(model_TPR_multilevel_Year)$F,
NA, #did not converge
extract_mod_results(model_Cogni_multilevel_Year)$F
),
ModeratorYear_df = c(
extract_mod_results(model_CO_multilevel_Year)$df,
extract_mod_results(model_TPR_multilevel_Year)$df,
NA, #did not converge
extract_mod_results(model_Cogni_multilevel_Year)$df
),
ModeratorRob_F = c(
extract_mod_results(model_CO_multilevel_Rob)$F,
extract_mod_results(model_TPR_multilevel_Rob)$F,
extract_mod_results(model_CTI_multilevel_Rob)$F,
extract_mod_results(model_Cogni_multilevel_Rob)$F
),
ModeratorRob_df = c(
extract_mod_results(model_CO_multilevel_Rob)$df,
extract_mod_results(model_TPR_multilevel_Rob)$df,
extract_mod_results(model_CTI_multilevel_Rob)$df,
extract_mod_results(model_Cogni_multilevel_Rob)$df
)
)
return(data)
}
# Create and print the summary table
summary_table <- create_summary_table()
print(summary_table)## Name ModeratorAge_F ModeratorAge_df ModeratorSex_F ModeratorSex_df
## 1 CO 1.18 1, 66 0.03 1, 66
## 2 TPR 0.08 1, 59 0.01 1, 59
## 3 CTI 0.02 1, 71 0.33 1, 71
## 4 Cogni 0.53 1, 117 0.00 1, 118
## ModeratorBD_F ModeratorBD_df ModeratorYear_F ModeratorYear_df ModeratorRob_F
## 1 2.07 2, 66 3.92 1, 84 1.54
## 2 4.00 2, 59 1.60 1, 77 9.23
## 3 6.92 2, 71 NA <NA> 5.31
## 4 NA <NA> 1.51 1, 119 14.68
## ModeratorRob_df
## 1 2, 65
## 2 2, 58
## 3 2, 70
## 4 3, 117write.csv(summary_table, "moderator_table.csv", row.names = FALSE)