Sample Size Requirement for Unbiased Estimation of Structural Equation Models: A Monte Carlo Study

This is the authors' abstract. We don't add key points for this paper.

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 & Chou, 1987). To examine under what conditions this rule-of-thumb holds, we ran Monte-Carlo simulations for a structural-equation model having three exogenous latent variables that predicted a dependent variable via an endogenous regressor. We varied (a) the number of observations (from 40 to 200); (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.