Jeroen K. Vermunt

Latent class cluster analysis

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A Poisson log-bilinear regression approach to the construction of projected lifetables

This paper implements Wilmoth’s [Computational methods for fitting and extrapolating the Lee–Carter model of mortality change, Technical report, Department of Demography, University of California, Berkeley] and Alho’s [North American Actuarial Journal 4 (2000) 91] recommendation for improving the Lee–Carter approach to the forecasting of demographic components. Specifically, the original method is embedded in a Poisson regression model, which is perfectly suited for age–sex-specific mortality rates. This model is fitted for each sex to a set of age-specific Belgian death rates. A time-varying index of mortality is forecasted in an ARIMA framework. These forecasts are used to generate projected age-specific mortality rates, life expectancies and life annuities net single premiums. Finally, a Brass-type relational model is proposed to adapt the projections to the annuitants population, allowing for estimating the cost of adverse selection in the Belgian whole life annuity market.

Multilevel Latent Class Models

The latent class (LC) models that have been developed so far assume that observations are independent. Parametric and non-parametric random-coefficient LC models are proposed here, which will make it possible to modify this assumption. For example, the models can be used for the analysis of data collected with complex sampling designs, data with a multilevel structure, and multiple-group data for more than a few groups. An adapted EM algorithm is presented that makes maximum-likelihood estimation feasible. The new model is illustrated with examples from organizational, educational, and cross-national comparative research.

Latent Class Models

A statistical model can be called a latent class (LC) or mixture model if it assumes that some of its parameters differ across unobserved subgroups, LCs, or mixture components. This rather general idea has several seemingly unrelated applications, the most important of which are clustering, scaling, density estimation, and random-effects modeling. This article describes simple LC models for clustering, restricted LC models for scaling, and mixture regression models for nonparametric random-effects modeling, as well as gives an overview of recent developments in the field of LC analysis. Moreover, attention is paid to topics such as maximum likelihood estimation, identification issues, model selection, and software.

Latent Class Factor and Cluster Models, Bi‐Plots, and Related Graphical Displays

We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independent, dichotomous latent factors, the LC factor model has the same number of distinct parameters as an LC cluster model with R+1 clusters. Analyses over several data sets suggest that LC factor models typically fit data better and provide results that are easier to interpret than the corresponding LC cluster models. We also introduce a new graphical bi-plot display for LC factor models and compare it to similar plots used in correspondence analysis and to a barycentric coordinate display for LC cluster models. New results on identification of LC models are also presented. We conclude by describing various model extensions and an approach for eliminating boundary solutions in identified and unidentified LC models, which we have implemented in a new computer program.

Measuring exposure to bullying at work: The validity and advantages of the latent class cluster approach

Abstract This paper addresses the construct and predictive validity of two methods for classifying respondents as victims of workplace bullying. Although bullying is conceived as a complex phenomenon, the dominant method used in bullying surveys, the operational classification method, only distinguishes two groups: victims versus non-victims. Hence, the complex nature of workplace bullying may not be accounted for. Therefore a latent class cluster approach is suggested to model the data, which was obtained by using the Negative Acts Questionnaire (NAQ) administered to employees in Belgium (n=6,175). Latent class modelling is a method of analysis that does not appear to have been used in occupational health psychology before. In this study, six latent classes emerged: “not bullied,” “limited work criticism,” “limited negative encounters,” “sometimes bullied,” “work related bullied,” and “victims.” The results show that compared to the traditional operational classification method, the latent class cluster approach shows higher construct and higher predictive validity with respect to self-assessments and indicators of strain and well-being at work. The consequences of these results for theory, future research, and practice are discussed.

Latent class models for classification

An overview is provided of recent developments in the use of latent class (LC) and other types of finite mixture models for classification purposes. Several extensions of existing models are presented. Two basic types of LC models for classification are defined: supervised and unsupervised structures. Their most important special cases are presented and illustrated with an empirical example.

Cultural classifications under discussion latent class analysis of highbrow and lowbrow reading

Abstract Cultural classifications, in the sense of categorisations of cultural goods and practices, are often abused in cultural stratification studies to classify people involved with these goods and practices. In this paper the issue is discussed of how to use cultural classifications without begging the question of their definition and without claiming to have at our disposal an archimedean point permitting the classification of cultural goods. Using time budget data from the 1990 Dutch Time Budget Survey (over 3000 respondents) and focussing on one cultural activity (reading in leisure time) latent class analysis - a method for finding the latent classes or categories of variables - provides an empirical basis which permits exploring an extrapolation of Peterson and Simkuss (1992) suggestion (on omnivorous and univorous musical preferences) with respect to actual reading behavior. It is shown that present-day Dutch society is composed of clearly distinguishable categories: non-readers, high readers, and low readers. Besides, there is a small group which combines apparently heterogeneous categories. (Focus on a single cultural practice must make one hesitant to label this group ‘reading omnivores’.) Subsequently, a multinomial logit model is described and used to test hypothesized causal relationships between kinds of reading behavior and a number of background (SES) and intervening variables. These variables help to account for class membership and thus make possible the explanation of differences in reading behavior.

Estimating the Association between Latent Class Membership and External Variables Using Bias-adjusted Three-step Approaches

Latent class analysis is a clustering method that is nowadays widely used in social science research. Researchers applying latent class analysis will typically not only construct a typology based on a set of observed variables but also investigate how the encountered clusters are related to other, external variables. Although it is possible to incorporate such external variables into the latent class model itself, researchers usually prefer using a three-step approach. This is the approach wherein after establishing the latent class model for clustering (step 1), one obtains predictions for the class membership scores (step 2) and subsequently uses these predicted scores to assess the relationship between class membership and other variables (step 3). Bolck, Croon, and Hagenaars (2004) showed that this approach leads to severely downward-biased estimates of the strength of the relationships studied in step 3. These authors and later also Vermunt (2010) developed methods to correct for this bias. In the current study, we extended these correction methods to situations where class membership is not predicted but used as an explanatory variable in the third step, a situation widely encountered in social science applications. A simulation study tested the performance of the proposed correction methods, and their practical use was illustrated with real data examples. The results showed that also when the latent class variable is used as a predictor of external variables, the uncorrected three-step approach leads to severely biased estimates. The proposed correction methods perform well under conditions encountered in practice.

Robustness of Stepwise Latent Class Modeling With Continuous Distal Outcomes

Recently, several bias-adjusted stepwise approaches to latent class modeling with continuous distal outcomes have been proposed in the literature and implemented in generally available software for latent class analysis. In this article, we investigate the robustness of these methods to violations of underlying model assumptions by means of a simulation study. Although each of the 4 investigated methods yields unbiased estimates of the class-specific means of distal outcomes when the underlying assumptions hold, 3 of the methods could fail to different degrees when assumptions are violated. Based on our study, we provide recommendations on which method to use under what circumstances. The differences between the various stepwise latent class approaches are illustrated by means of a real data application on outcomes related to recidivism for clusters of juvenile offenders.