## 7.5 Related issues

Before moving to the demonstrations with the metaSEM package in R, this section discusses some issues related to MASEM. We first compare the multiple-group SEM versus MASEM in analyzing a pool of correlation (or covariance) matrices and then compare and contrast the two fixed-effects models—the TSSEM and the GLS approaches. After this, we address alternative random-effects models for MASEM. Finally, we discuss topics such as the use of ML or restricted (or residual) maximum likelihood (REML) in MASEM, the use of correlation coefficient versus Fisher's *z* score, and the correction for unreliability in MASEM.

### 7.5.1 Multiple-group structural equation modeling versus meta-analytic structural equation modeling

Multiple-group SEM may be used to analyze data with missing data for independent groups (e.g., Allison, 1987; Muthén et al., 1987). The general idea is to partition the data into data sets that contains both complete data and several data sets with different missing-data patterns. By hypothesizing that the same model holds across the complete and incomplete data sets, the whole model can be estimated by applying appropriate equality constraints among different samples.

Let us illustrate the idea with an example. Suppose that we are fitting a two-factor CFA model with two indicators per factor. and are missing in some cases. We may partition the data into two ...