Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison

Pennoni, Fulvia and Romeo, Isabella (2016): Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison.

Abstract

We propose a short review between two alternative ways of modeling stability and change of longitudinal data when time-fixed and time-varying covariates referred to the observed individuals are available. They both build on the foundation of the finite mixture models and are commonly applied in many fields. They look at the data by a different perspective and in the literature they have not been compared when the ordinal nature of the response variable is of interest. The latent Markov model is based on time-varying latent variables to explain the observable behavior of the individuals. The model is proposed in a semi-parametric formulation as the latent Markov process has a discrete distribution and it is characterized by a Markov structure. The growth mixture model is based on a latent categorical variable that accounts for the unobserved heterogeneity in the observed trajectories and on a mixture of normally distributed random variable to account for the variability of growth rates. To illustrate the main differences among them we refer to a real data example on the self reported health status.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dynamic factor model, Expectation-Maximization algorithm, Forward-Backward recursions, Latent trajectories, Maximum likelihood, Monte Carlo methods.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C33 - Panel Data Models ; Spatio-temporal Models; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; I - Health, Education, and Welfare > I1 - Health > I11 - Analysis of Health Care Markets; I - Health, Education, and Welfare > I1 - Health > I12 - Health Behavior

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