Evaluating Covariate Effects on ESM Measurement Model Changes with Latent Markov Factor Analysis: A Three-Step Approach

• Published in: Multivariate behavioral research Vol. 58; no. 2; pp. 262 - 291
• Main Authors: Vogelsmeier, Leonie V.D.E., Vermunt, Jeroen K., Bülow, Anne, De Roover, Kim
• Format: Journal Article
• Language: English
• Published: United States Routledge 04.03.2023; Taylor & Francis Ltd
• Subjects: Between-subjects design; Clustering; Data Interpretation, Statistical; Empirical analysis; Evaluation; Experience sampling; Factor analysis; Humans; Invariance; latent Markov modeling; Markov Chains; measurement invariance; Mixtures; Psychological factors; three-step approach; Time Factors; factor analysis; Experience sampling; measurement invariance; three-step approach; latent Markov modeling
• ISSN: 0027-3171; 1532-7906; 1532-7906
• DOI: 10.1080/00273171.2021.1967715

Invariance of the measurement model (MM) between subjects and within subjects over time is a prerequisite for drawing valid inferences when studying dynamics of psychological factors in intensive longitudinal data. To conveniently evaluate this invariance, latent Markov factor analysis (LMFA) was proposed. LMFA combines a latent Markov model with mixture factor analysis: The Markov model captures changes in MMs over time by clustering subjects' observations into a few states and state-specific factor analyses reveal what the MMs look like. However, to estimate the model, Vogelsmeier, Vermunt, van Roekel, and De Roover (2019) introduced a one-step (full information maximum likelihood; FIML) approach that is counterintuitive for applied researchers and entails cumbersome model selection procedures in the presence of many covariates. In this paper, we simplify the complex LMFA estimation and facilitate the exploration of covariate effects on state memberships by splitting the estimation in three intuitive steps: (1) obtain states with mixture factor analysis while treating repeated measures as independent, (2) assign observations to the states, and (3) use these states in a discrete- or continuous-time latent Markov model taking into account classification errors. A real data example demonstrates the empirical value.