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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 (:/), 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 x , 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.

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