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Open AccessArticle

Handling Covariates in Markovian Models with a Mixture Transition Distribution Based Approach

by
NCCR LIVES, University of Lausanne, 1015 Lausanne, Switzerland
Current address: Geopolis, University of Lausanne, 1015 Lausanne, Switzerland.
Symmetry 2020, 12(4), 558; https://doi.org/10.3390/sym12040558
Received: 4 February 2020 / Revised: 27 March 2020 / Accepted: 29 March 2020 / Published: 4 April 2020
(This article belongs to the Special Issue The Mixture Transition Distribution Model)
This paper presents and discusses the use of a Mixture Transition Distribution-like model (MTD) to account for covariates in Markovian models. The MTD was introduced in 1985 by Raftery as an approximation of higher order Markov chains. In the MTD, each lag is estimated separately using an additive model, which introduces a kind of symmetrical relationship between the past and the present. Here, using an MTD-based approach, we consider each covariate separately, and we combine the effects of the lags and of the covariates by means of a mixture model. This approach has three main advantages. First, no modification of the estimation procedure is needed. Second, it is parsimonious in terms of freely estimated parameters. Third, the weight parameters of the mixture can be used as an indication of the relevance of the covariate in explaining the time dependence between states. An illustrative example taken from life course studies using a 3-state hidden Markov model and a covariate with three levels shows how to interpret the results of such models. View Full-Text
Keywords: covariates in Markovian modeling; hidden Markov model; MTD model; social sciences covariates in Markovian modeling; hidden Markov model; MTD model; social sciences
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MDPI and ACS Style

Bolano, D. Handling Covariates in Markovian Models with a Mixture Transition Distribution Based Approach. Symmetry 2020, 12, 558. https://doi.org/10.3390/sym12040558

AMA Style

Bolano D. Handling Covariates in Markovian Models with a Mixture Transition Distribution Based Approach. Symmetry. 2020; 12(4):558. https://doi.org/10.3390/sym12040558

Chicago/Turabian Style

Bolano, Danilo. 2020. "Handling Covariates in Markovian Models with a Mixture Transition Distribution Based Approach" Symmetry 12, no. 4: 558. https://doi.org/10.3390/sym12040558

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