When sparse data have to be fitted to a log-linear or latent class model, one cannot use the theoretical chi-square distribution to evaluate model fit, because with sparse data the observed cross-table has too many cells in relation to the number of observations to use a distribution that only holds asymptotically. The choice of a theoretical distribution is also difficult when model-expected frequencies are 0 or when model probabilities are estimated 0 or 1. The authors propose to solve these problems by estimating the distribution of a fit measure, using bootstrap methods. An algorithm is presented for estimating this distribution by drawing bootstrap samples from the model-expected proportions, the so-called nonnaive bootstrap method. For the first time the method is applied to empirical data of varying sparseness, from five different data sets. Results show that the asymptotic chi-square distribution is not at all valid for sparse data.
The advantages of latent class analysis for cross-cultural research in psychology are discussed. The basic principles of multigroup latent class analysis are described and illustrated by an empirical study comparing satisfaction-with-life-domain profiles across two nations (China, United States). In particular, it is shown how various assumptions of measurement invariance across cultures can be tested statistically in the latent class framework.
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.
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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.
The focus of this article is on Markov models for the analysis of panel data and, more specifically, on data obtained from repeated measurements of one categorical variable at several consecutive points in time. We first review developments in the field that attack the two main problems of the simple Markov model. The Mixed Markov model extends the simple model by allowing for population heterogeneity; the Latent Markov model incorporates measurement error and latent change into the simple model. Second, we present the more general Latent Mixed Markov model and show how both the Mixed Markov model and the Latent Markov model, as well as several more specific models, relate to this more general model. Finally, we reanalyze the Los Angeles panel data on depression with a focus on stability and change.
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.
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