Stability of the Data-Model Fit over Increasing Levels of Factorial Invariance for Different Features of Design in Factor Analysis

Abstract

The aim of this study is to provide an empirical evaluation of the influence of different aspects of design in the context of factor analysis in terms of model stability. The overall model stability of factor solutions was evaluated by the examination of the order for testing three levels of Measurement Invariance (MIV) starting with configural invariance (model 0). Model testing was evaluated by the Chi-square difference test ((x2) between two groups, and Root Mean Square Error of Approximation (RMSEA), Comparative Fit Index (CFI), and Tucker-Lewis Index (TLI). Factorial invariance results revealed that the stability of the models was varying over increasing levels of measurement as a function of Variable-To-Factor (VTF) ratio, Subject-To-Variable (STV) ratio, and their interactions. There were invariant factor loadings and invariant intercepts among the groups indicating that measurement invariance was achieved. For VTF ratios 4:1, 7:1, and 10:1, the models started to show stability over the levels of measurement when the STV ratio was 4:1. Yet, the frequency of stability models over 1000 replications increased (from 77% to 91%) as the STV ratio increased. The models showed more stability at or above 32:1 STV.