Dynamic latent trait models with mixed hidden Markov structure for mixed longitudinal outcomes

Latent variable (LV) models are increasingly being used in environmental epidemiology as a way to summarize multiple environmental exposures and thus minimize statistical concerns that arise in multiple regression. LV models may be especially useful when multivariate exposures are collected repeatedly over time. LV models can accommodate a variety of assumptions but, at the same time, present the user with many choices for model specification particularly in the case of exposure data collected repeatedly over time. For instance, the user could assume conditional independence of observed exposure biomarkers given the latent exposure and, in the case of longitudinal latent exposure variables, time invariance of the measurement model. Choosing which assumptions to relax is not always straightforward. We were motivated by a study of prenatal lead exposure and mental development, where assumptions of the measurement model for the time-changing longitudinal exposure have appreciable impact on (maximum-likelihood) inferences about the health effects of lead exposure. Although we were not particularly interested in characterizing the change of the LV itself, imposing a longitudinal LV structure on the repeated multivariate exposure measures could result in high efficiency gains for the exposure-disease association. We examine the biases of maximum likelihood estimators when assumptions about the measurement model for the longitudinal latent exposure variable are violated. We adapt existing instrumental variable estimators to the case of longitudinal exposures and propose them as an alternative to estimate the health effects of a time-changing latent predictor. We show that instrumental variable estimators remain unbiased for a wide range of data generating models and have advantages in terms of mean squared error. Copyright © 2017 John Wiley & Sons, Ltd.

Often quantities of interest in psychology cannot be observed directly. These unobservable quantities, known as latent variables, tend to be complex, often multidimensional, constructs. In many cases these constructs are categorical, such that individuals belong to mutually exclusive and exhaustive unobservable subgroups. Latent class analysis (LCA) is a statistical approach to modeling a discrete latent variable using multiple, discrete observed variables as indicators. Examples of latent class variables that appear in the psychology literature include temperament type, substance use behavior, teaching style, stages of change in the transtheoretical model, and latent classes of risk. The first section of this chapter provides a conceptual introduction to the concept of a latent class followed by a technical introduction to the mathematical model, including multiple-groups LCA and LCA with covariates. This is followed by a discussion of parameter restrictions, model selection, and goodness-of-fit. The second section demonstrates LCA using the empirical example of depression subtypes in adolescence. Five latent classes were identified based on responses to eight questionnaire items assessing depression symptoms: Non-depressed (characterized by a low probability of reporting all eight depression symptoms), sad, disliked, sad + disliked, and depressed (characterized by a high probability of reporting all eight depression symptoms). The third section presents longitudinal extensions of the model, including repeated-measures LCA and latent transition analysis (LTA). The empirical example is extended to examine change in depression subtypes over time. The final sections describe recent extensions to the latent class model and areas that merit additional research in the future. Keywords: latent class analysis; latent transition analysis; latent variable model; categorical data

In this chapter, we address distributed learning algorithms for statistical latent variable models, with a focus on topic models. Many high-dimensional datasets, such as text corpora and image databases, are too large to allow one to learn topic models on a single computer. Moreover, a growing number of applications require that inference be fast or in real time, motivating the exploration of parallel and distributed learning algorithms. We begin by reviewing topic models such as Latent Dirichlet Allocation and Hierarchical Dirichlet Processes. We discuss parallel and distributed algorithms for learning these models and show that these algorithms can achieve substantial speedups without sacrificing model quality. Next we discuss practical guidelines for running our algorithms within various parallel computing frameworks and highlight complementary speedup techniques. Finally, we generalize our distributed approach to handle Bayesian networks. Several of the results in this chapter have appeared in previous papers in the specific context of topic modeling. The goal of this chapter is to present a comprehensive overview of distributed inference algorithms and to extend the general ideas to a broader class of Bayesian networks. Latent Variable Models Latent variable models are a class of statistical models that explain observed data with latent (or hidden) variables. Topic models and hidden Markov models are two examples of such models, where the latent variables are the topic assignment variables and the hidden states, respectively. Given observed data, the goal is to perform Bayesian inference over the latent variables and use the learned model to make inferences or predictions.

ObjectiveWe aimed to explore factors affecting family health management during home quarantine as well as the effects of variations in family health management (FHM) on individuals’ health status.MethodsUsing stratified random sampling, 618 families in Wuhan as well as cities within its surrounding provinces were recruited and surveyed online. Latent class variables were extracted from four modules: disinfection, space layout, physical exercise, and food reserves. The analysis was conducted using the poLCA package in R software (v.4.1.0). Chi-squared tests, Fisher’s exact tests, and non-parametric Kruskal–Wallis tests were used to compare groups as appropriate.ResultsWe found an overall questionnaire reliability of 0.77 and a total omega of 0.92, indicating that the survey results were credible. The Bayesian information criterion and Akaike information criterion were used to identified four latent class variables, namely latent non-family health management (18.9%) and latent low, medium, and advanced FHM (30.93%, 29.49%, and 20.59%, respectively). Gender, household income level, body mass index, the presence of a nearby community hospital, and self-rated health status showed statistically significant differences with respect to latent FHM. Moreover, we found a statistically significant difference in emotional reactions when comparing latent advanced and low to mid-level latent FHM. Compared with latent non-family health managers, we detected statistically significant differences in individual energy levels between potential family health managers at latent low and medium levels. Additionally, we found statistically significant differences in individual energy levels between latent advanced and low level family health managers.ConclusionsWe found that multiple factors, including gender, household income, and body mass index, were correlated with latent FHM during home quarantine. We conclude that FHM can meaningfully improve individuals’ health. Thus, increasing social support for individuals can improve FHM as well as individuals’ health during home quarantine.

Extending the traditional discrete choice model by incorporating latent psychological factors can help to better understand the individual’s decision-making process and therefore to yield more reliable part-worth estimates and market share predictions. Several integrated choice and latent variable (ICLV) models which merge the conditional logit model with a structural equation model exist in the literature. They assume homogeneity in the part-worths and use latent variables to model the heterogeneity among the respondents. This paper starts from the mixed logit model that describes the heterogeneity in the part-worths and uses the latent variables to decrease the unexplained part of the heterogeneity. The empirical study presented here shows these ICLV models perform very well with respect to model fit and prediction.

Measurement of non-random attrition effects on mobility rates using trip diaries data

In the past years, latent variable models have played an important role in various industrial AI systems, among which quality prediction is one of the most representative applications. Inspired by the idea of deep learning, those basic latent variable models have been extended to deep forms, based on which the quality prediction performance has been significantly improved. However, different latent variable models have their own strengths and weaknesses, a model works well under one scenario might not provide satisfactory performance under another. The motivation of this article is based on the viewpoint of information fusion and ensemble learning for heterogeneous latent variable models. Particularly, a collaborative deep learning and model fusion framework is formulated for the purpose of industrial quality prediction. In the first stage of the framework, collaborative layer-by-layer feature extractions are implemented among different latent variable models, through which different patterns of latent variables are identified in different layers of the deep model. Then, in the second stage, an ensemble regression modeling strategy is proposed to fuse the quality prediction results from different latent variable models, which is based on a well-designed data description method. Two real industrial examples are used for performance evaluation of the proposed method, based on which we can observe that information fusions in terms of both collaborative layer-by-layer feature extraction and heterogeneous model ensemble have positive effects in improving prediction accuracy and stability.

Joint modeling of Anaemia and Malaria in children under five in Nigeria

The biasing effects of measurement error in path analysis models can be overcome by the use of latent variable models. In cases where path analysis is used in practice, it is often possible to use parcels as indicators of a latent variable. The purpose of the current study was to compare latent variable models in which parcels were used as indicators of the latent variables, path analysis models of the aggregated variables, and models in which reliability estimates were used to correct for measurement error in path analysis models. Results showed that point estimates of path coefficients were smallest for the path analysis models and largest for the latent variable models. It is concluded that, whenever possible, it is better to use a latent variable model in which parcels are used as indicators than a path analysis model using total scale scores.

Latent trait models have long been used in the social science literature for studying variables that can only be measured indirectly through multiple items. However, such models are also very useful in accounting for correlation in multivariate and longitudinal data, particularly when outcomes have mixed measurement scales. Bayesian methods implemented with Markov chain Monte Carlo provide a flexible framework for routine fitting of a broad class of latent variable (LV) models, including very general structural equation models. However, in considering LV models, a number of challenging issues arise, including identifiability, confounding between the mean and variance, uncertainty in different aspects of the model, and difficulty in computation. Motivated by the problem of modelling multidimensional longitudinal data, this article reviews the recent literature, provides some recommendations and highlights areas in need of additional research, focusing on methods for model uncertainty.

The high dimensionality of global gene expression profiles, where number of variables (genes) is very large compared to the number of observations (samples), presents challenges that affect generalizability and applicability of microarray analysis. Latent variable modeling offers a promising approach to deal with high-dimensional microarray data. The latent variable model is based on a few latent variables that capture most of the gene expression information. Here, we describe how to accomplish a reduction in dimension by a latent variable methodology, which can greatly reduce the number of features used to characterize microarray data. We propose a general latent variable framework for prediction of predefined classes of samples using gene expression profiles from microarray experiments. The framework consists of (i) selection of smaller number of genes that are most differentially expressed between samples, (ii) dimension reduction using hierarchical clustering, where each cluster partition is identified as latent variable, (iii) discretization of gene expression matrix, (iv) fitting the Rasch item response model for genes in each cluster partition to estimate the expression of latent variable, and (v) construction of prediction model with latent variables as covariates to study the relationship between latent variables and phenotype. Two different microarray data sets are used to illustrate a general framework of the approach. We show that the predictive performance of our method is comparable to the current best approach based on an all-gene space. The method is general and can be applied to the other high-dimensional data problems.

New approaches to cognitive work analysis through latent variable modeling in mining operations

BackgroundDomestic Violence is a threatening worldwide problem. Its consequences against women can be dramatic, as it negatively affects women’s quality of life reflected in their general wellbeing including physical, mental, emotional and sexual health, in addition to the economic cost. Both domestic violence and its cost are multidimensional constructs that cannot be directly measured.MethodologyIn this study, a latent trait model is used by applying item response theory to measure both domestic violence and its consequent cost via thirty-five observed variables. Accordingly, the study fills a gap in the literature since it is the first attempt to examine the relationship between domestic violence and its consequent cost in Egypt using latent variable modelling rather than simple descriptive statistics. Each construct is considered as a multidimensional latent variable. The overall latent trait model also estimates the relationship between domestic violence and its consequent cost. The effect of a number of socioeconomic covariates on domestic violence is examined within the model. The proposed model is fitted to data from the 2015 Egypt Economic Cost of Gender-Based Violence Survey (ECGBVS) using Mplus software.ResultsThe study shows that psychological violence is equally important in measuring domestic violence, as physical violence. The cost resulting from domestic violence relies in its measurement both on the reduced quality of life and the monetary cost endured by the violated woman and children. For socioeconomic covariates, it is shown that domestic violence is affected by women’s and husband’s age, educational level, and husband’s occupational status.ConclusionDomestic violence is measured by summarizing four forms of violence: physical, psychological, sexual and economic violence, in a single continuous latent variable measuring “Domestic Violence”. Similarly, Cost is measured by summarizing three forms of consequent cost of violence: economic cost, cost on children and cost on women’s quality of life, in another a single continuous latent variable “Cost”. Each of these dimensions is measured by a number of aspects, reflecting the multidimensional nature of the variables. The fitted latent trait model ensured the positive relationship between Domestic Violence and its consequent multidimensional cost.

<p>Joint models for longitudinal and survival data have been widely discussed in the literature. This thesis proposes a joint model using a stereotype model for the longitudinal ordinal responses and a Cox proportional hazards model for survival time. Our current joint model has a new feature since no literature has examined the joint model under the stereotype model. The stereotype model can improve the fit by adding extra score parameters, but it still has the advantage of requiring only a single parameter to describe the effect of a predictor on the item response levels. We give an example to model longitudinal ordinal data and survival data for patients being followed up after treatments. The main focus is on modeling both the quality of life data and the survival data simultaneously with a goal of understanding the association between the two processes over time. These two models are linked through a latent variable that characterizes the quality of life of an individual and is assumed to underlie the hazard rate. In other words, the latent variable serves as a shared variable in the joint model. We present the joint model in two different aspects: one based on a Bayesian approach and the other one a semiparametric approach using the EM algorithm. For the Bayesian approach, the latent variable is treated as a continuous variable and is assumed to have a multivariate normal distribution. The partial survival likelihood function is used in the survival component of the Bayesian joint model, while the full likelihood function is considered in the semiparametric joint model. In the latter approach the baseline hazard is assumed to be a step function and has no parametric form. The latent variable in the semiparametric joint model is then treated as a discrete variable. We illustrate our methodologies by analyzing data from the Staccato study, a randomized trial to compare two treatment methods, for Human Immunodeficiency Virus (HIV) infection of Thai patients on Highly Active Antiretroviral Therapy (HAART), in which the quality of life was assessed with a HIV Medical Outcome Study (MOS-HIV) questionnaire. Furthermore, we extend the study further to the case of multiple failure types in the survival component. Thus, the extension of the joint model consists of the stereotype model and the competing risks model. The Bayesian method is employed to estimate all unknown parameters in this extended joint model. The results we obtained are consistent for both the Bayesian joint model and the semiparametric joint model. Both models show that patients who had a better quality of life were associated with a lower hazard of HIV progression. Patients on continuous treatment also had a lower hazard of HIV progression compared with patients on CD4-guided interruption treatment.</p>

In this paper, a new latent variable model is proposed for the realization of 2-D single-input-single-output linear causal systems. For the general (n, m)th-order 2-D system, the latent variable model obtained here is implicit when nnem. Importantly, however, even in this case, the model is recursively computable. The advantage of the proposed realization is that the dimension of the latent variable is nm, which is much smaller than that for existing latent variable realizations, such as Fornasini-Marchesini (FM) and Roesser models. Given a particular 2-D system, an algorithm is developed for further reducing the size of the realization.