Approaches of Model Specification for Testing Factor Mean Differences in Higher-order CFA Models

Because the mean structure part of a higher-order CFA model is generally not identified, it is often a challenge in model specification for testing factor mean differences in multi-group higher-order CFA models. Three different parameter constraint approaches (Approaches A, B, and C) are usually proposed to address the identification problems in such modeling. This study is to discuss and demonstrate applications of the three approaches to testing invariance of factor intercepts/means across groups. The Brief Symptom Inventory 18 (BSI-18) will be used for modeling with two samples of rural drug using populations recruited from Ohio (n=248) and Kentucky (n=225). After the invariance of factorial structure of the BSI-18 is confirmed, invariance of the measurement parameters (e.g., factor loadings, item intercepts, and error variances/covariacnes) and structural parameters (e.g., factor variances/covariances and factor means) are examined across the two drug using populations. Statistical package Mplus is used for modeling.