We present a test for cluster bias, which can be used to detect violations of measurement invariance across clusters in 2-level data. We show how measurement invariance assumptions across clusters imply measurement invariance across levels in a 2-level factor model. Cluster bias is investigated by testing whether the within-level factor loadings…

State-space modeling techniques have been compared to structural equation modeling (SEM) techniques in various contexts but their unique strengths have often been overshadowed by their similarities to SEM. In this article, we provide a comprehensive discussion of these 2 approaches' similarities and differences through analytic comparisons and…

In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…

We propose a method to investigate measurement invariance in the multigroup exploratory factor model, subject to target rotation. We consider both oblique and orthogonal target rotation. This method has clear advantages over other approaches, such as the use of congruence measures. We demonstrate that the model can be implemented readily in the…

This article is concerned with the seemingly simple problem of testing whether latent factors are perfectly correlated (i.e., statistically indistinct). In recent literature, researchers have used different approaches, which are not always correct or complete. We discuss the parameter constraints required to obtain such perfectly correlated latent…

A linear latent growth curve mixture model is presented which includes switching between growth curves. Switching is accommodated by means of a Markov transition model. The model is formulated with switching as a highly constrained multivariate mixture model and is fitted using the freely available Mx program. The model is illustrated by analyzing…