META-ANALYSIS OF CORRELATION MATRICES FOR STRUCTURAL EQUATION MODELS: A MULTI-SAMPLE STRUCTURAL EQUATION MODELING APPROACH
 
Cheung, W.L. and Chan, W., The Chinese University of Hong Kong, Hong Kong
 
Meta-analysis, a statistical method for summarizing research findings, is becoming more and more popular in psychology. Structural equation modeling, a multivariate statistical technique combining factor analysis and path analysis, is always used to model the processes or mechanisms of behaviors. Generally, meta-analysts summarize research findings for structural equation models with two-step approaches. In the first step, correlation matrices are pooled together with Hunter-Schmidt's (1990) or Hedges-Olkin's (1985) procedures. In the second step, the pooled correlation matrix is analyzed with structural equation modeling. However, there are several difficulties with these approaches: a) the elements in the correlation matrices are treated as independent though they are correlated; b) the pooled correlation matrix may be non-positive definite as they are usually based on different samples; and most importantly, c) the chi-square statistics and standard errors of parameter estimates are incorrect in model fitting. If we ignore these problems, conclusions drawn from meta-analysis are likely to be incorrect. In responding to these problems, a new multi-sample structural equation modeling is proposed here (e.g., Lee, 1985; Muthn, Kaplan, & Hollis, 1987). The proposed method can tackle two important issues in meta-analysis for structural equation models: a) analysis of incomplete variables; and b) the analysis of correlation. Results show that the proposed method can perform better than the conventional methods. Procedures and applications will also be demonstrated in the present study.