Factor Analysis: Multiple Groups

Abstract

The general factor model, when extended to include mean‐level information, is a very powerful tool for cross‐group and longitudinal comparisons. The multiple‐group mean and covariance structures (MACS) approach is particularly useful for making cross‐group (or cross‐time) comparisons because it allows for (a) simultaneous estimation of all parameters in each group (or at each occasion) and (b) direct statistical comparisons of the estimated parameters across the groups (or occasions). Because the means of measured indicators are included explicitly in the analyses, they provide a basis to make a very strong test of the validity of construct comparisons (i.e., measurement equivalence) across groups and across time. Specifically, strong factorial invariance indicates that constructs are fundamentally similar in each group or across time (i.e., comparable) and hypotheses about the nature of possible group‐ or time‐related influences can be meaningfully tested on any of the constructs' basic moments (means, variances, or covariances) across time or across each group whether the groups are defined on the basis of culture, gender, or any other grouping criteria.

The Teacher Self-Efficacy Scale (TSES) Factorial Structure Evidence Review and New Evidence From Polish-Speaking Samples

“…Several basic forms of factorial invariance have been listed in the literature (Meredith, 1993; Little & Slegers, 2005): (a) Configural factorial invariance ensures that in each group the same factorial structure is observed. (b) Metric (or pattern) invariance (also called weak factorial invariance) requires loadings to be equal across groups.…”

Race/ethnicity and measurement equivalence of the Everyday Discrimination Scale.

“…Our next step was to examine measurement invariance to determine whether the underlying latent constructs are equivalent across four racial/ethnic groups, following procedures and recommendations by Meredith (1993) and Little and Slegers (2005). Results are presented in Table 3.…”

Ten-year stability and latent structure of the DSM–IV schizotypal, borderline, avoidant, and obsessive-compulsive personality disorders.

“…For instances in which the reliable structural components were being evaluated and the chi square difference test is appropriate, concerns of excessive power were addressed by adopting a more stringent p value. For omnibus chi square difference tests, we adopted a value of .005 (see Little & Slegers, 2005). For invariance tests, concerns arise over evaluating the invariance of the measurement parameters when a large number of parameter estimates are involved.…”