The Effect of Model Size and Sample size on the Fit Indices in structural Equation Modeling: Simulation Study

Abstract

This study investigated the effect of the most important factors of the experimental design in structural equation modelling. These factors include model size as the number of observed variables per factor (p/f), the sample size and their interactions on general fit indices: χ2, the absolute fit indices: GFI, RMSEA, SRMR, and the incremental fit indices: CFI, NFI. Through a simulation, various conditions of different confirmatory factorial models were created by manipulating the number of latent factors:1-3-5, the number of observed variables; 3-5-10-15, and through different conditions of sample sizes: 200-400-600-800-1000. Using continuous data under normal distribution, these models were estimated using the Maximum Likelihood Estimation Method (ML). The results showed that there are main significant effects of the model size (p/f), the sample size and their interaction on all the fit indices. The GFI, SRMR, and the NFI were the most effected indices by these factors while RMSEA is the least affected and its value became better as the model size increased. The study recommended to be aware of the of model's characteristics when dealing with fit indices.