The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model...

The common maximum likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes model-implied instrumental variable – generalized...

A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in Psychometrika 55:5–18, <CitationRef CitationID="CR11">1990</CitationRef>). In the model, latent variables are assumed to have a multivariate normal...</citationref>

Rubin and Thayer (Psychometrika, 47:69–76, <CitationRef CitationID="CR16">1982</CitationRef>) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations...</citationref>

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor...