Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An overview of latent Markov models for longitudinal categorical data   We provide a comprehensive overview of latent Markov (LM) models for the
analysis of longitudinal categorical data. The main assumption behind these
models is that the response variables are conditionally independent given a
latent process which follows a first-order Markov chain. We first illustrate
the basic LM model in which the conditional distribution of each response
variable given the corresponding latent variable and the initial and transition
probabilities of the latent process are unconstrained. For this model we also
illustrate in detail maximum likelihood estimation through the
Expectation-Maximization algorithm, which may be efficiently implemented by
recursions known in the hidden Markov literature. We then illustrate several
constrained versions of the basic LM model, which make the model more
parsimonious and allow us to include and test hypotheses of interest. These
constraints may be put on the conditional distribution of the response
variables given the latent process (measurement model) or on the distribution
of the latent process (latent model). We also deal with extensions of LM model
for the inclusion of individual covariates and to multilevel data. Covariates
may affect the measurement or the latent model; we discuss the implications of
these two different approaches according to the context of application.
Finally, we outline methods for obtaining standard errors for the parameter
estimates, for selecting the number of states and for path prediction. Models
and related inference are illustrated by the description of relevant
socio-economic applications available in the literature.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg