Objective: We review two alternative ways of modeling stability and change of longitudinal data by using time-fixed and time-varying covariates for the observed individuals. Both the methods build on the foundation of finite mixture models, and are commonly applied in many fields but they look at the data from different perspectives. Our attempt is to make comparisons when the ordinal nature of the response variable is of interest. Methods: The latent Markov model is based on time-varying latent variables to explain the observable behavior of the individuals. It is proposed in a semiparametric formulation as the latent process has a discrete distribution and 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 Gaussian random variables to account for the variability in the growth factors. We refer to a real data example on self-reported health status to illustrate their peculiarities and differences.

Pennoni, F., Romeo, I. (2017). Latent Markov and growth mixture models for ordinal individual responses with covariates: A comparison. STATISTICAL ANALYSIS AND DATA MINING, 10(1), 29-39 [10.1002/sam.11335].

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

PENNONI, FULVIA
;
2017

Abstract

Objective: We review two alternative ways of modeling stability and change of longitudinal data by using time-fixed and time-varying covariates for the observed individuals. Both the methods build on the foundation of finite mixture models, and are commonly applied in many fields but they look at the data from different perspectives. Our attempt is to make comparisons when the ordinal nature of the response variable is of interest. Methods: The latent Markov model is based on time-varying latent variables to explain the observable behavior of the individuals. It is proposed in a semiparametric formulation as the latent process has a discrete distribution and 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 Gaussian random variables to account for the variability in the growth factors. We refer to a real data example on self-reported health status to illustrate their peculiarities and differences.
Articolo in rivista - Articolo scientifico
dynamic factor model; expectation-maximization algorithm; forward-backward recursions; latent trajectories; maximum likelihood; Monte Carlo methods;
dynamic factor model, expectation-maximization algorithm, forward-backward recursions, latent trajectories, maximum likelihood, Monte Carlo methods
English
29
39
11
hdl:10281/92380
Pennoni, F., Romeo, I. (2017). Latent Markov and growth mixture models for ordinal individual responses with covariates: A comparison. STATISTICAL ANALYSIS AND DATA MINING, 10(1), 29-39 [10.1002/sam.11335].
Pennoni, F; Romeo, I
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/140445
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