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Latent Markov and growth mixture models for ordinal individual responses with covariates: A comparison
Author(s) -
Peni Fulvia,
Romeo Isabella
Publication year - 2017
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11335
Subject(s) - covariate , categorical variable , latent variable , ordinal data , econometrics , latent variable model , markov chain , mixture model , markov model , mathematics , statistics , latent class model , local independence , variable order markov model , markov property , variable (mathematics) , computer science , mathematical analysis
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.