‘metafor’ package method comparison
Reed Sorensen
November 2018
Estimated values for ‘age_mid’, SE on ‘age_mid’ and tau:
## method coef_age_mid se_age_mid tau
## DL DerSimonian-Laird 0.03237247 0.005760840 0.2704670
## HE Hedges 0.03491691 0.003141985 0.0000000
## HS Hunter-Schmidt 0.03258684 0.005473454 0.2428638
## SJ Sidik-Jonkman 0.03187053 0.006740894 0.3647296
## ML Maximum likelihood 0.03260873 0.005446262 0.2402608
## REML Restricted maximum likelihood 0.03249271 0.005594528 0.2544748
## EB Empirical Bayes 0.03296726 0.005037788 0.2014678
## PM Paule-Mandel 0.03296727 0.005037782 0.2014672## DL
## [1] "-- DerSimonian-Laird"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: DL)
##
## logLik deviance AIC BIC AICc
## -21.0273 53.5456 48.0547 52.8052 48.8047
##
## tau^2 (estimated amount of residual heterogeneity): 0.0732 (SE = 0.0399)
## tau (square root of estimated tau^2 value): 0.2705
## I^2 (residual heterogeneity / unaccounted variability): 66.75%
## H^2 (unaccounted variability / sampling variability): 3.01
## R^2 (amount of heterogeneity accounted for): 61.36%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 31.5777, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.5617 0.3640 -1.5432 0.1228 -1.2750 0.1517
## age_mid 0.0324 0.0058 5.6194 <.0001 0.0211 0.0437 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## HE
## [1] "-- Hedges"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: HE)
##
## logLik deviance AIC BIC AICc
## -45.3816 102.2542 96.7632 101.5138 97.5132
##
## tau^2 (estimated amount of residual heterogeneity): 0 (SE = 0.3136)
## tau (square root of estimated tau^2 value): 0
## I^2 (residual heterogeneity / unaccounted variability): 0.00%
## H^2 (unaccounted variability / sampling variability): 1.00
## R^2 (amount of heterogeneity accounted for): 100.00%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 123.4990, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.8321 0.1881 -4.4240 <.0001 -1.2008 -0.4635 ***
## age_mid 0.0349 0.0031 11.1130 <.0001 0.0288 0.0411 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## HS
## [1] "-- Hunter-Schmidt"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: HS)
##
## logLik deviance AIC BIC AICc
## -20.8965 53.2840 47.7931 52.5436 48.5431
##
## tau^2 (estimated amount of residual heterogeneity): 0.0590 (SE = 0.0277)
## tau (square root of estimated tau^2 value): 0.2429
## I^2 (residual heterogeneity / unaccounted variability): 61.81%
## H^2 (unaccounted variability / sampling variability): 2.62
## R^2 (amount of heterogeneity accounted for): 65.08%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 35.4455, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.5837 0.3452 -1.6911 0.0908 -1.2602 0.0928 .
## age_mid 0.0326 0.0055 5.9536 <.0001 0.0219 0.0433 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## SJ
## [1] "-- Sidik-Jonkman"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: SJ)
##
## logLik deviance AIC BIC AICc
## -22.5830 56.6570 51.1661 55.9166 51.9161
##
## tau^2 (estimated amount of residual heterogeneity): 0.1330 (SE = 0.0670)
## tau (square root of estimated tau^2 value): 0.3647
## I^2 (residual heterogeneity / unaccounted variability): 78.50%
## H^2 (unaccounted variability / sampling variability): 4.65
## R^2 (amount of heterogeneity accounted for): 50.25%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 22.3534, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.5059 0.4272 -1.1842 0.2363 -1.3432 0.3314
## age_mid 0.0319 0.0067 4.7279 <.0001 0.0187 0.0451 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ML
## [1] "-- Maximum likelihood"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: ML)
##
## logLik deviance AIC BIC AICc
## -20.8955 53.2818 47.7909 52.5415 48.5409
##
## tau^2 (estimated amount of residual heterogeneity): 0.0577 (SE = 0.0286)
## tau (square root of estimated tau^2 value): 0.2403
## I^2 (residual heterogeneity / unaccounted variability): 61.30%
## H^2 (unaccounted variability / sampling variability): 2.58
## R^2 (amount of heterogeneity accounted for): 68.95%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 35.8485, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.5859 0.3434 -1.7064 0.0879 -1.2589 0.0871 .
## age_mid 0.0326 0.0054 5.9874 <.0001 0.0219 0.0433 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## REML
## [1] "-- Restricted maximum likelihood"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -20.7780 41.5560 47.5560 52.1351 48.3560
##
## tau^2 (estimated amount of residual heterogeneity): 0.0648 (SE = 0.0327)
## tau (square root of estimated tau^2 value): 0.2545
## I^2 (residual heterogeneity / unaccounted variability): 63.99%
## H^2 (unaccounted variability / sampling variability): 2.78
## R^2 (amount of heterogeneity accounted for): 66.72%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 33.7322, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.5741 0.3531 -1.6258 0.1040 -1.2662 0.1180
## age_mid 0.0325 0.0056 5.8079 <.0001 0.0215 0.0435 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## EB
## [1] "-- Empirical Bayes"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: EB)
##
## logLik deviance AIC BIC AICc
## -21.1766 53.8442 48.3533 53.1038 49.1033
##
## tau^2 (estimated amount of residual heterogeneity): 0.0406 (SE = 0.0299)
## tau (square root of estimated tau^2 value): 0.2015
## I^2 (residual heterogeneity / unaccounted variability): 52.69%
## H^2 (unaccounted variability / sampling variability): 2.11
## R^2 (amount of heterogeneity accounted for): 76.72%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 42.8239, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.6220 0.3163 -1.9665 0.0492 -1.2420 -0.0021 *
## age_mid 0.0330 0.0050 6.5440 <.0001 0.0231 0.0428 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## PM
## [1] "-- Paule-Mandel"
##
## Mixed-Effects Model (k = 36; tau^2 estimator: PM)
##
## logLik deviance AIC BIC AICc
## -21.1766 53.8442 48.3533 53.1038 49.1033
##
## tau^2 (estimated amount of residual heterogeneity): 0.0406 (SE = 0.0299)
## tau (square root of estimated tau^2 value): 0.2015
## I^2 (residual heterogeneity / unaccounted variability): 52.69%
## H^2 (unaccounted variability / sampling variability): 2.11
## R^2 (amount of heterogeneity accounted for): 76.72%
##
## Test for Residual Heterogeneity:
## QE(df = 34) = 102.2542, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 42.8240, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.6220 0.3163 -1.9665 0.0492 -1.2420 -0.0021 *
## age_mid 0.0330 0.0050 6.5440 <.0001 0.0231 0.0428 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1