The Effects of Sample Size, Reliability, Number of Indicators Per Factor and Estimation Method on Fit Indices

Abstract

A simulation study was conducted to evaluate the effects of sample size (N), reliability/loading (L), Number of indicators per factor (p/m) and estimation method (E) on seven fit indices, including three frequently used fit indices: Chi-square (χ2), Normed Fit Index (NFI) and Nonnormed of Fit Index (NNFI), and four recently proposed fit indices: Noncentrality d index, Centrality m index, Relative Noncentrality Index (RNI) and Comparative Fit Index (CFI). The performance of these indices were examined over four levels of N (50, 100, 200 and 500), three levels of L (0.50, 0.70 and 0.90), five levels of p/m (2, 3, 4, 5 and 6), and two levels of estimation method (GLS and ML). The results of this study indicated that: 1) All seven indices showed downward bias when sample sizes were small. However, RNI and CFI were relatively less affected by sample size than other indices. 2) Reliability/Loading did not have strong effects on these fit indices (except NFI) in general. 3) All seven fit indices showed downward bias when p/m ratio increased. This effect is much more severe on χ2 NFI, d and m then on NNFI, RNI and CFI. 4) All seven fit indices were found to be estimation method specific. The interaction effects of these influence factors were strong. The effect of p/m ratio on fit indices is related to the parsimony problem. The correctness of parsimony justification of these indices was also investigated and discussed.