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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 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
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