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Several rules of thumb for the minimum sample size of structural equation models have been proposed. A widely-accepted ratio of sample size to estimated parameters is N:p = 5:1 (Bentler (b) the number of latent variables indicators (from 2 to 6); (c) the correlations between factors (from 0.2 to 0.8) and the degree of endogeneity affecting the endogenous regressor (high or low). Results show that ML estimates are still consistent across-the-board. However, in small sample size conditions model convergence rates were low and the chi-squared test of model fit tended to over-reject correctly specified models. We found that a correction to the chi-squared proposed by Swain (1976) better approximates the chi-squared distribution at small sample sizes and reduced rejection rates close to the Type I error rate (5%). Finally, we found that the Hausman (1978) endogeneity test had very low power at small sample sizes. Based on these results we make several recommendations for applied researchers.
Bastardoz et al. (Wed,) studied this question.