Journal
MULTIVARIATE BEHAVIORAL RESEARCH
Volume 58, Issue 2, Pages 262-291Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/00273171.2021.1967715
Keywords
Experience sampling; measurement invariance; factor analysis; latent Markov modeling; three-step approach
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This paper introduces a simplified method for estimating the latent Markov factor analysis (LMFA) and facilitates the exploration of covariate effects. A real data example demonstrates the empirical value of this method.
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.
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