Discrete Latent Markov Models for Normally Distributed Response Data.

Area of Science:

• Psychometrics
• Statistical Modeling
• Developmental Psychology

Background:

• Markov modeling is established for discrete repeated measures.
• Analogical models for continuous responses are under-explored.
• Existing discrete models often assume conditional independence.

Purpose of the Study:

• To present and discuss analogical single indicator models for normally distributed responses.
• To extend Markov modeling frameworks to continuous data.
• To explore models that relax the conditional independence assumption.

Main Methods:

• Formulating models as highly constrained multinormal finite mixture models.
• Relaxing the conditional independence assumption to account for latent classes and within-class dependence.
• Utilizing structural equation modeling for within-class dependence.
• Fitting models using the freely available program Mx.

Main Results:

• Demonstrated the formulation of normal-based Markov models as multinormal finite mixtures.
• Showcased the fitting of these models using the Mx program.
• Applied the models to data on the understanding of conservation of continuous quantity.

Conclusions:

• Normal-based Markov models offer a flexible alternative to discrete models for continuous data.
• These models can capture both latent class structures and within-class dependencies.
• The proposed framework is applicable to psychological constructs like conservation understanding.