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

Abstract

Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates Vermunt, J.K.; Langeheine, R.; Bockenholt, U. Publication date: 1995 Link to publicationCitation for published version (APA): Vermunt, J. K., Langeheine, R., & Bockenholt, U. (1995). Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. (WORC Paper / Work and Organization Research Centre (WORC); Vol. 95.06.013/7). Unknown Publisher. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. the observed transitions between two points in time will be pa.rtiall~. spurious. La.tentMarkov models make it possible to separate true change from measurement error. The standard latent Markov model is, however, ra.ther limited~~.hen the aim is to e~plain.individual differences in the probabilit,y of occupying a particular state at a particular point in time. This paper presents a fle~:ible logit regression approach~~-hich allows to regress the la,tent states occupied at the various points in time on both time-constant and time-va.r~.ing covaria.tes. The regression approach combines feat.ures of ca.usal log-linear models and latent class models with explanatory variables. An applica.t.ion is presented in which pupils' interest in physics at different points in time is explained bv the timeconstant cova.riate se~and the~time-varying covariate physics grade.

A Longitudinal Study of Polish Attitudes to Emigration: A Latent Markov Model Approach

“…The initial formulation of the latent Markov (LM) model introduced by Wiggins (1973) has been developed in several directions, and applied in a number of fields (Bartolucci, Montanari & Pandolfi 2015, Genge 2014, van de Pol & Langeheine 1990, Vermunt, Langeheine & Böckenholt 1999, Visser & Speekenbrink 2010). The LM model represents an important class of models for the analysis of longitudinal data when response variables are categorical.…”

“…It can be seen that computation time and computer storage increase with the number of points, which makes the standard EM algorithm impractical or even impossible to apply with more than a few time points (Vermunt, Langeheine & Böckenholt 1999). Therefore, the depmixS4 package of R uses a special variant of the EM algorithm for LM models, called Baum--Welch or forward-backward algorithm (Baum et al 1970, Paas, Vermunt & Bijmolt 2007).…”

Qualitative Longitudinal Analysis of Symptoms in Patients with Primary and Metastatic Brain Tumours

“…τ = (τ rs ), the matrix of time homogeneous transition probabilities between latent states, Pr(Z it = s|Z it−1 = r) = τ rs for t = 2,…,T; Assuming conditional independence between responses, given the latent state, the marginal probability of a response pattern y i is then (1) where the summation is over S T terms, Rijmen et al Page 5 and The multiple-indicator HMM was extended in two ways in this paper. First, observed patient characteristics and symptom attributes were incorporated through a logistic regression model for the conditional response probabilities (Vermunt et al, 1999): (2) where β s indicates the vector of fixed symptom effects within state s, and γ represents the vector of fixed patient effects. The vectors x j and w it contain respectively the values of symptom j on the symptom attributes (e.g.…”

Maximum likelihood estimation of an extended latent Markov model for clustered binary panel data

“…It may be seen as an extension of the latent class model (Lazarsfeld and Henry (1968); Goodman (1974)) in which the response variables are conditionally independent given a latent Markov (LM) chain. This model has been applied in many fields, especially in psychological and educational measurement (Langeheine et al (1994); Vermunt et al (1999)) and sociology (Van de Pol and Langeheine (1990); Mannan and Koval (2003)). Likelihood inference for the LM model was studied by Bartolucci (2006) who considered, in particular, the problem of testing linear hypotheses on the transition probabilities of the latent process.…”

“…It is in practice a finite mixture of LM models which allows the parameters of the latent process to be different between subjects. Moreover, Vermunt et al (1999) introduced a version of the LM model in which the initial and transition probabilities of the latent process depend on individual covariates.…”