Latent class models in the social and behavioral sciences have remained structurally simple. One reason for this is that inference in statistical models can be computationally difficult. Methods for approximate inference, known as variational approximations, which have been developed in the machine learning, graphical modeling and statistical physics literatures, can be used to alleviate the computational difficulties of inference for latent variable models. The aim of the present article is to set these methods alongside some social and behavioral science literature to which they are relevant, and in particular to consider their potential for “categorical causal modeling”, using latent class analysis. We have collated a number of popular categorical-data models with latent variables and causal structure, typically incorporating a Markovian structure. The efficacy of the approximation methods has been demonstrated through simulations related to an important behavioral science model.

Traditional mediation analysis assumes that a study population is homogeneous and the mediation effect is constant over time, which may not hold in some applications. Motivated by smoking cessation data, we propose a latent class dynamic mediation model that explicitly accounts for the fact that the study population may consist of different subgroups and the mediation effect may vary over time. We use a proportional odds model to accommodate the subject heterogeneities and identify latent subgroups. Conditional on the subgroups, we employ a Bayesian hierarchical nonparametric time-varying coefficient model to capture the time-varying mediation process, while allowing each subgroup to have its individual dynamic mediation process. A simulation study shows that the proposed method has good performance in estimating the mediation effect. We illustrate the proposed methodology by applying it to analyze smoking cessation data.

This paper brings together and compares two developments in the analysis of Likert attitude scales. The first is the generalization of latent class models to ordered response categories. The second is the introduction of latent trait models with multiplicative parameter structures for the analysis of rating scales. Key similarities and differences between these two methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of “life satisfaction” data. The way in which the latent trait model defines a unit of measurement, takes into account the order of the response categories, and scales the latent classes, is discussed. While the latent class model provides better fit to these data, this is achieved at the cost of a logically inconsistent assignment of individuals to latent classes.

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identifiability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and efficient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.

We study a proportional reduction in loss (PRL) measure for the reliability of categorical data and consider the general case in which each of N judges assigns a subject to one of K categories. This measure has been shown to be equivalent to a measure proposed by Perreault and Leigh for a special case when there are two equally competent judges, and the correct category has a uniform prior distribution. We consider a general framework where the correct category is assumed to have an arbitrary prior distribution, and where classification probabilities vary by correct category, judge, and category of classification. In this setting, we consider PRL reliability measures based on two estimators of the correct category—the empirical Bayes estimator and an estimator based on the judges' consensus choice. We also discuss four important special cases of the general model and study several types of lower bounds for PRL reliability.

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizations are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.

Diagnostic models (DMs) provide researchers and practitioners with tools to classify respondents into substantively relevant classes. DMs are widely applied to binary response data; however, binary response models are not applicable to the wealth of ordinal data collected by educational, psychological, and behavioral researchers. Prior research developed confirmatory ordinal DMs that require expert knowledge to specify the underlying structure. This paper introduces an exploratory DM for ordinal data. In particular, we present an exploratory ordinal DM, which uses a cumulative probit link along with Bayesian variable selection techniques to uncover the latent structure. Furthermore, we discuss new identifiability conditions for structured multinomial mixture models with binary attributes. We provide evidence of accurate parameter recovery in a Monte Carlo simulation study across moderate to large sample sizes. We apply the model to twelve items from the public-use, Early Childhood Longitudinal Study, Kindergarten Class of 1998–1999 approaches to learning and self-description questionnaire and report evidence to support a three-attribute solution with eight classes to describe the latent structure underlying the teacher and parent ratings. In short, the developed methodology contributes to the development of ordinal DMs and broadens their applicability to address theoretical and substantive issues more generally across the social sciences.

Polycystic ovary syndrome (PCOS) is associated with a higher prevalence of sleep disturbances and obesity. Treatment of PCOS includes modifying lifestyle behaviours associated with weight management. However, poor sleep in the non-PCOS population has been associated with poorer lifestyle behaviours. The aim was to investigate whether sleep disturbance confounds or modifies the association between lifestyle factors and PCOS. This was a cross-sectional analysis from the Australian Longitudinal Study on Women’s Health cohort aged 31–36 years in 2009 were analysed (n 6067, 464 PCOS, 5603 non-PCOS). Self-reported data were collected on PCOS, anthropometry, validated modified version of the Active Australia Physical Activity survey, validated FFQ and sleep disturbances through latent class analysis. Women with PCOS had greater adverse sleep symptoms including severe tiredness (P = 0·001), difficulty sleeping (P < 0·001) and restless sleep (P < 0·001), compared with women without PCOS. Women with PCOS also had higher energy consumption (6911 (sd 2453) v. 6654 (sd 2215) kJ, P = 0·017), fibre intake (19·8 (sd 7·8) v. 18·9 (sd 6·9) g, P = 0·012) and diet quality (dietary guidelines index (DGI)) (88·1 (sd 11·6) v. 86·7 (sd 11·1), P = 0·008), lower glycaemic index (50·2 (sd 4·0) v. 50·7 (sd 3·9), P = 0·021) and increased sedentary behaviour (6·3 (sd 2·8) v. 5·9 (sd 2·8) h, P = 0·009). There was a significant interaction between PCOS and sleep disturbances for DGI (P = 0·035), therefore only for women who had adequate sleep was PCOS associated with a higher DGI. For women with poorer sleep, there was no association between PCOS and DGI. The association between PCOS and improved diet quality may only be maintained if women can obtain enough good quality sleep.