Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates

Abstract

Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both time- constant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.

A Latent Markov Model for Detecting Patterns of Criminal Activity

“…Although this is possible in other studies, it has not routinely been carried out. Moreover, our approach appears to be more flexible in terms of allowing not only a limited number of time occasions as in the models that were proposed by Vermunt et al . (1999) and Collins and Wugalter (1992).…”

“…These parameters can provide an interpretation of the latent classes corresponding to the different levels of C t . Note also that the way in which we include the covariates is different from that adopted within the approach of Vermunt et al . (1999), which is based on a logit parameterization of the transition probabilities, and is more similar to that which was used, for instance, by Mooijaart and van Montfort (2006).…”

“…The use of these recursions, which appears to be quite new in the LM literature, makes the model estimable also when the number of time occasions is large. Using more standard approaches, instead, it would not be possible to estimate the model for data sets with more than a few time periods (see also the discussion in Vermunt et al . (1999)).…”

Discrete Time, Discrete State Latent Markov Modelling for Assessing and Predicting Household Acquisitions of Financial Products

“…Below we present the LMM with concomitant variables (Van de Pol and Langeheine, 1990; Vermunt et al. , 1999; Bartolucci et al.…”

Reading Ability Development from Kindergarten to Junior Secondary: Latent Transition Analyses with Growth Mixture Modeling

“…and families (parents, etc.). Another possibility is to treat the covariate as a time-varying variable in multilevel structure (Vermunt et al, 1999; Bartolucci et al, 2011). That means, in our analyses, the social rating recorded at Kindergarten, Spring Grade 1 Spring and Fall Grade 5 can all be treated as multiple indicators affecting the transition at different time points.…”