Abstract
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.
Highlights
The field of psychology relies heavily on the use of tools for measuring constructs as varied as cognition, mood, personality, and attitude
The convergence rate was below 100% except for group sample sizes of 500 and 1,000
The purpose of this study was to compare the performance of metric invariance (MI) assessment using several CFA estimation methods in conditions for which their performance might be questionable, namely with small samples and skewed latent traits
Summary
The field of psychology relies heavily on the use of tools for measuring constructs as varied as cognition, mood, personality, and attitude Scores derived from these instruments are frequently used to assist in making decisions about whether a child should receive special educational accommodations, whether a patient may be suffering from depression, what type of employment an applicant may best be suited for, and whether a college student is motivated by an internal or external reward structure, among others. It is crucial that practitioners and researchers know whether the items on the Invariance Small Samples Skewed Traits scale are invariant or the same across theoretically interesting subgroups In this context, invariance refers to the case when individual items have the same statistical characteristics (e.g., relationship to the latent trait being measured by the scale) for members of the various subgroups (e.g., boys and girls).
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