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tips:rma_vs_lm_lme_lmer

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tips:rma_vs_lm_lme_lmer [2021/11/08 13:31] – Wolfgang Viechtbauertips:rma_vs_lm_lme_lmer [2022/08/03 11:37] – Wolfgang Viechtbauer
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 I^2 (total heterogeneity / total variability):   60.69% I^2 (total heterogeneity / total variability):   60.69%
 H^2 (total variability / sampling variability):  2.54 H^2 (total variability / sampling variability):  2.54
-                                                                                                                          + 
-Test for Heterogeneity:                                                                                                  +Test for Heterogeneity:
 Q(df = 15) = 38.1595, p-val = 0.0009 Q(df = 15) = 38.1595, p-val = 0.0009
  
 Model Results: Model Results:
  
-estimate      se    zval    pval   ci.lb   ci.ub  +estimate      se    zval    pval   ci.lb   ci.ub 
-  0.1252  0.0170  7.3642  <.0001  0.0919  0.1585  *** +  0.1252  0.0170  7.3642  <.0001  0.0919  0.1585  ***
  
 --- ---
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 Weighted Residuals: Weighted Residuals:
-    Min      1Q  Median      3Q     Max  +    Min      1Q  Median      3Q     Max 
--3.1919 -1.0719  0.6674  1.3173  2.4695 +-3.1919 -1.0719  0.6674  1.3173  2.4695
  
 Coefficients: Coefficients:
-            Estimate Std. Error t value Pr(>|t|)    +            Estimate Std. Error t value Pr(>|t|)
 (Intercept)  0.12518    0.02711   4.617 0.000335 *** (Intercept)  0.12518    0.02711   4.617 0.000335 ***
 --- ---
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 This can be demonstrated by extracting the estimated error variance from the ''lm'' object, multiplying the sampling variances by that value, and re-fitting the model with the ''rma()'' function: This can be demonstrated by extracting the estimated error variance from the ''lm'' object, multiplying the sampling variances by that value, and re-fitting the model with the ''rma()'' function:
 <code rsplus> <code rsplus>
-rma(yi, vi*summary(res.lm)$sigma^2, data=dat, method="EE")+rma(yi, vi*sigma(res.lm)^2, data=dat, method="EE")
 </code> </code>
 <code output> <code output>
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 H^2 (total variability / sampling variability):  2.61 H^2 (total variability / sampling variability):  2.61
  
-Test for Heterogeneity: +Test for Heterogeneity:
 Q(df = 15) = 38.1595, p-val = 0.0009 Q(df = 15) = 38.1595, p-val = 0.0009
  
 Model Results: Model Results:
  
-estimate       se     zval     pval    ci.lb    ci.ub           +estimate       se     zval     pval    ci.lb    ci.ub 
-  0.1499   0.0316   4.7501   <.0001   0.0881   0.2118      *** +  0.1499   0.0316   4.7501   <.0001   0.0881   0.2118      ***
  
 --- ---
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 <code output> <code output>
 Linear mixed-effects model fit by REML Linear mixed-effects model fit by REML
- Data: dat + Data: dat
         AIC       BIC   logLik         AIC       BIC   logLik
   -8.781569 -6.657418 7.390784   -8.781569 -6.657418 7.390784
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 Variance function: Variance function:
  Structure: fixed weights  Structure: fixed weights
- Formula: ~vi  + Formula: ~vi 
-Fixed effects: yi ~ 1 +Fixed effects: yi ~ 1
                 Value  Std.Error DF  t-value p-value                 Value  Std.Error DF  t-value p-value
 (Intercept) 0.1415557 0.03071906 16 4.608073   3e-04 (Intercept) 0.1415557 0.03071906 16 4.608073   3e-04
  
 Standardized Within-Group Residuals: Standardized Within-Group Residuals:
-       Min         Q1        Med         Q3        Max  +       Min         Q1        Med         Q3        Max 
--1.1596768 -0.6903414  0.1964221  0.7117538  1.4616798 +-1.1596768 -0.6903414  0.1964221  0.7117538  1.4616798
  
 Number of Observations: 16 Number of Observations: 16
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 <code rsplus> <code rsplus>
 library(lme4) library(lme4)
-res.lmer <- lmer(yi ~ 1 + (1 | study), weights = 1/vi, data=dat, +res.lmer <- lmer(yi ~ 1 + (1 | study), weights = 1/vi, data=dat,
                  control=lmerControl(check.nobs.vs.nlev="ignore", check.nobs.vs.nRE="ignore"))                  control=lmerControl(check.nobs.vs.nlev="ignore", check.nobs.vs.nRE="ignore"))
 summary(res.lmer) summary(res.lmer)
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    Data: dat    Data: dat
 Weights: 1/vi Weights: 1/vi
-Control: +Control:
 lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore") lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
  
 REML criterion at convergence: -14.8 REML criterion at convergence: -14.8
  
-Scaled residuals:  +Scaled residuals: 
-    Min      1Q  Median      3Q     Max  +    Min      1Q  Median      3Q     Max 
--1.1597 -0.6903  0.1964  0.7117  1.4617 +-1.1597 -0.6903  0.1964  0.7117  1.4617
  
 Random effects: Random effects:
  Groups   Name        Variance Std.Dev.  Groups   Name        Variance Std.Dev.
- study    (Intercept) 0.004649 0.06818  + study    (Intercept) 0.004649 0.06818 
- Residual             1.586461 1.25955 + Residual             1.586461 1.25955
 Number of obs: 16, groups:  study, 16 Number of obs: 16, groups:  study, 16
  
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 H^2 (total variability / sampling variability):  1.58 H^2 (total variability / sampling variability):  1.58
  
-Test for Heterogeneity: +Test for Heterogeneity:
 Q(df = 15) = 24.0532, p-val = 0.0642 Q(df = 15) = 24.0532, p-val = 0.0642
  
 Model Results: Model Results:
  
-estimate       se     zval     pval    ci.lb    ci.ub           +estimate       se     zval     pval    ci.lb    ci.ub 
-  0.1416   0.0307   4.6081   <.0001   0.0813   0.2018      *** +  0.1416   0.0307   4.6081   <.0001   0.0813   0.2018      ***
  
 --- ---
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 <code output> <code output>
 Linear mixed-effects model fit by REML Linear mixed-effects model fit by REML
- Data: dat  + Data: dat 
-        AIC      BIC   logLik +        AIC      BIC   logLik
   -10.44653 -9.03043 7.223265   -10.44653 -9.03043 7.223265
  
 Random effects: Random effects:
  Formula:  ~ 1 | study  Formula:  ~ 1 | study
-        (Intercept) Residual +        (Intercept) Residual
 StdDev:  0.09005302        1 StdDev:  0.09005302        1
  
 Variance function: Variance function:
  Structure: fixed weights  Structure: fixed weights
- Formula:  ~ vi  + Formula:  ~ vi 
-Fixed effects: yi ~ 1  +Fixed effects: yi ~ 1 
-                Value  Std.Error DF  t-value p-value +                Value  Std.Error DF  t-value p-value
 (Intercept) 0.1499171 0.03155994 16 4.750234  0.0002 (Intercept) 0.1499171 0.03155994 16 4.750234  0.0002
  
 Standardized Within-Group Residuals: Standardized Within-Group Residuals:
-       Min         Q1        Med        Q3      Max +       Min         Q1        Med        Q3      Max
  -1.222824 -0.5462851 0.09989517 0.6159687 1.305632  -1.222824 -0.5462851 0.09989517 0.6159687 1.305632
  
tips/rma_vs_lm_lme_lmer.txt · Last modified: 2023/11/14 08:00 by Wolfgang Viechtbauer