A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models

Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The literature on the topic has focused on conducting power analyses as well as identifying rules of thumb for deciding an appropriate sample size. Often the advice involves an assumption that sample size requirement is moderated by aspects of the model in question. In this study, an effort was undertaken to extend the findings of Gagné and Hancock (2006) Gagné, P. and Hancock, G. R. 2006. Measurement model quality, sample size, and solution propriety in confirmatory factor analysis. Multivariate Behavioral Research, 41: 65–83. Taylor & Francis Online , Google Scholar on measurement model quality and solution propriety to a broader set of confirmatory factor analysis models. As well, we examined whether Herzog, Boomsma, and Reinecke's (2007) findings for the Swain correction to the χ2 statistic for large models would generalize to models in our study. Our findings suggest that Gagné and Hancock's approach extends to large models with surprisingly little increase in sample size requirements and that the Swain correction to χ2 performs fairly well. We argue that likely rejection or model fit should be taken into account when determining sample size requirements and therefore, provide an updated table of minimum sample size that incorporates Gagné and Hancock's method and model fit.