Comparison of Methods for Factor Invariance Testing of a 1-Factor Model With Small Samples and Skewed Latent Traits

A primary underlying assumption for researchers using a psychological scale is that scores are comparable across individuals from different subgroups within the population. In the absence of invariance, the validity of these scores for inferences about individuals may be questionable. Factor invariance testing refers to the methodological approach to assessing whether specific factor model parameters are indeed equivalent across groups. Though much research has investigated the performance of several techniques for assessing invariance, very little work has examined how methods perform under small sample size, and non-normally distributed latent trait conditions. Therefore, the purpose of this simulation study was to compare invariance assessment Type I error and power rates between (a) the normal based maximum likelihood estimator, (b) a skewed-t distribution maximum likelihood estimator, (c) Bayesian estimation, and (d) the generalized structured component analysis model. The study focused on a 1-factor model. Results of the study demonstrated that the maximum likelihood estimator was robust to violations of normality of the latent trait, and that the Bayesian and generalized component models may be useful in particular situations. Implications of these findings for research and practice are discussed.