Inproceedings: an article in a conference proceedings.
How small can a sample size be for a structural equation model?
Title of the conference
Congress of the Swiss Psychological Society, Basel, Switzerland
There are several rules of thumb regarding the minimum sample size or ratio of sample size to estimated coefficients in structural equation models. for example, Bentler and Chou (1985) argue that the ratio of sample size to estimated parameters should be minimum 5:1. To examine under what conditions this rule-of-thumb holds, we ran Monte-Carlo simulations for a structural-equation model with three exogenous latent variables that predicted a dependent variable via an endogenous regressor. We varied (a) the number of observations (from 40 to 200 by increment of 20), (b), the number of latent variables indicators (from 2 to 6 in increment of 1), and (c) the correlations between independent variables, ranging from low to highly collinear (i.e., from .1 to .8 by increment of .1). Our results show that ml estimates are still consistent even in very small sample conditions; however, model convergence rates were very low in low sample size conditions. We found that the chi-square test of model fit tends to over-reject correctly specified models when the parameter to sample size ratio is very small. We also found that a correction to the chi-square proposed by Swain (1975) better approximates the chi-square distribution at small sample sizes and reduced rejection rates close to the type i error rate; that is, across all sample conditions, 5.01% of correctly specified models were rejected using the Swain-corrected statistic whereas rejection rates for the chi-square averaged 14.32%. at the smallest sample size to parameter ratio (i.e., n=40 with 6 indicators), the average rejection for the Swain-correct chi-square was 11.92%; however, it was 76.81% for the chi-square test. Finally, we examined the power of the Hausman (1978) test to detect endogenous regressors. We found that the test has a very low power at small sample sizes. Based on these results we make several recommendations for applied researchers.
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