The code for this chapter was provided by
Professor Hoffman from the Department of Psychology of the University of
Nebraska-Lincoln. We thank Professor Hoffman for her contribution to this
chapter.
Page 148, table 8.3 using the data set https://stats.idre.ucla.edu/wp-content/uploads/2016/02/meta20.sas7bdat. SAS
proc mixed is used in all the analyses. The use of the statement parms with
the "hold =" option allows us to perform variance-known analysis.
Model 2: multilevel intercept-only
data practice; set ats.meta20; if study=16 and G=.955 THEN study=17; run; * creating dataset of residual variances to hold constant; * covariance parameters start values need to start at 2 instead of 1; data resvar; set practice; covp = study+1; keep covp varofd; run; * transposing to multivariate; proc transpose data=resvar out=resvar; id covp; idlabel covp; var varofd; run; * renaming transposed variables to use in PARMS statement; * adding in start value for intercept variance as covp1; data resvar; retain covp1; set resvar; drop _name_; array old(20) _2-_21; array new(20) covp2-covp21; do i=1 to 20; new[i]=old[i]; end; drop _2--_21 i; covp1=.14; run; proc mixed data=practice method=reml; class study; * study is categorical variable; model d = / solution ddfm=bw; * empty model for effect size; random intercept / subject=study; * allowing heterogeneity in d; repeated / group=study type=vc; * separate residual variance per study; parms / parmsdata=resvar hold=2 to 21; * hold residual variances at known values; run;Covariance Parameter Estimates Cov Parm Subject Group Estimate Intercept STUDY 0.1446 Residual STUDY 1 0.08600 Residual STUDY 2 0.1060 ... ... Residual STUDY 20 0.1410 Fit Statistics -2 Res Log Likelihood 30.4 AIC (smaller is better) 32.4 AICC (smaller is better) 32.7 BIC (smaller is better) 33.4 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 0.00 0.9533 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 0.5801 0.1080 19 5.37 <.0001
Model 2: multilevel regression
proc mixed data=practice method=reml; class study; * study is categorical variable; model d = weeks / solution cl ddfm=bw; random intercept / subject=study; * allowing heterogeneity in d; repeated / group=study; * separate residual variance per study; parms / parmsdata=resvar hold=2 to 21; * hold residual variances at known values; run;Covariance Parameter Estimates Cov Parm Subject Group Estimate Intercept STUDY 0.03658 Residual STUDY 1 0.08600 Residual STUDY 2 0.1060 ... ... Residual STUDY 20 0.1410 Fit Statistics -2 Res Log Likelihood 22.2 AIC (smaller is better) 24.2 AICC (smaller is better) 24.5 BIC (smaller is better) 25.2 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 2.60 0.1071 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Alpha Lower Upper Intercept -0.2169 0.2043 18 -1.06 0.3023 0.05 -0.6462 0.2123 WEEKS 0.1399 0.03378 18 4.14 0.0006 0.05 0.06895 0.2109
Page 151, table 8.4: Random-effects model and multilevel meta-analyses on example
data
Model 1: Intercept-only (see previous example)
Model 2: Intercept + Ntot
proc mixed data=practice method=reml; class study; model d = ntot / solution ddfm=bw; random intercept / subject=study; repeated / group=study; parms / parmsdata=resvar hold=2 to 21; run;Cov Parm Subject Group Estimate Intercept STUDY 0.1592 Residual STUDY 1 0.08600 Residual STUDY 2 0.1060 ... ... Residual STUDY 20 0.1410 Fit Statistics -2 Res Log Likelihood 38.0 AIC (smaller is better) 40.0 AICC (smaller is better) 40.2 BIC (smaller is better) 41.0 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 0.05 0.8157 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 0.4430 0.5125 18 0.86 0.3988 NTOT 0.002489 0.009005 18 0.28 0.7854
Model 3: intercept + reliability
proc mixed data=practice method=reml; class study; model d = rii / solution ddfm=bw; random intercept / subject=study; repeated / group=study; parms / parmsdata=resvar hold=2 to 21; run;Covariance Parameter Estimates Cov Parm Subject Group Estimate Intercept STUDY 0.1565 Residual STUDY 1 0.08600 Residual STUDY 2 0.1060 ... ... Residual STUDY 20 0.1410 Fit Statistics -2 Res Log Likelihood 27.7 AIC (smaller is better) 29.7 AICC (smaller is better) 30.0 BIC (smaller is better) 30.7 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 0.04 0.8419 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Alpha Lower Upper Intercept 0.1602 1.2273 18 0.13 0.8976 0.05 -2.4182 2.7386 RII 0.5087 1.4773 18 0.34 0.7346 0.05 -2.5950 3.6124
Model 4: intercept + duration
proc mixed data=practice method=reml; class study; model d = weeks / solution ddfm=bw; random intercept / subject=study; repeated / group=study; parms / parmsdata=resvar hold=2 to 21; run;Covariance Parameter Estimates Cov Parm Subject Group Estimate Intercept STUDY 0.03658 Residual STUDY 1 0.08600 Residual STUDY 2 0.1060 ... ... Residual STUDY 20 0.1410 Fit Statistics -2 Res Log Likelihood 22.2 AIC (smaller is better) 24.2 AICC (smaller is better) 24.5 BIC (smaller is better) 25.2 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 2.60 0.1071 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept -0.2169 0.2043 18 -1.06 0.3023 WEEKS 0.1399 0.03378 18 4.14 0.0006
Model 5: intercept + all
proc mixed data=practice method=reml; class study; model d = ntot rii weeks / solution ddfm=bw; random intercept / subject=study; repeated / group=study; parms / parmsdata=resvar hold=2 to 21; run;Covariance Parameter Estimates Cov Parm Subject Group Estimate Intercept STUDY 0.04934 Residual STUDY 1 0.08600 Residual STUDY 2 0.1060 ... ... Residual STUDY 20 0.1410 Fit Statistics -2 Res Log Likelihood 27.6 AIC (smaller is better) 29.6 AICC (smaller is better) 29.9 BIC (smaller is better) 30.6 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 1.67 0.1965 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 0.3843 0.9234 16 0.42 0.6828 NTOT -0.00357 0.007035 16 -0.51 0.6187 RII -0.5510 1.2010 16 -0.46 0.6526 WEEKS 0.1506 0.03755 16 4.01 0.0010