An Introduction to Latent Class and Latent Transition Analysis

It is known that how individuals perceive the situation result in choices. However, it is unknown, how drivers process the information of vehicle malfunctions based on the situation at hand. In this study, we only considered drivers' actions in cases where vehicles had some forms of malfunction at the time of the crash. Also due to endogeneity bias, or aggregation of the error term, we did not include the vehicle malfunction directly in our model. In addition, we used the latent variable (LV) for class allocation. Although the latent class model considering latent variable (LCLV) is not comparable with other considered models, by means of log likelihood, the results expanded our understanding regarding the indirect impact of an indicator of vehicle malfunction by means of latent variable on drivers' actions. Due to inclusion of latent variables in both, the indicator and the choice models, the relationship between those two models could be revealed based on the impacts of the latent variables. It was found that, for instance, the latent variable, which decreases the likelihood of driving vehicles with brake defect, at the same time increases taking driver action of speeding. Or female drivers are less likely to be involved in speeding driving actions before crashes due to various vehicles malfunctions. Driving under the influence of drug or alcohol or being under emotional conditions were some of the factors impacting various drivers actions. This is the earliest study implemented the technique in the context of traffic safety.

Flexible methods that relax restrictive conditional independence assumptions of latent classanalysis (LCA) are described. Dichotomous and ordered category manifest variables are viewed asdiscretized latent continuous variables. The latent continuous variables are assumed to have a mixtureofmultivariate-normals distribution. Within a latent class, conditional dependence is modeled as the mutual association of all or some latent continuous variables with a continuous latent trait (or in special cases, multiple latent traits). The relaxation of conditional independence assumptions allows LCA to better model natural taxa. Comparisons of specific restricted and unrestricted models permit statistical tests of specific aspects of latent taxonic structure. Latent class, latent trait, and latent distribution analysis can be viewed as special cases of the mixed latent trait model. The relationship between the multivariate probit mixture model proposed here and Rost’s mixed Rasch (1990, 1991) model is discussed. Two studies illustrate different uses of the proposed model.

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone.

Data on stage of change was collected between 1997–1999 on 4125 adolescent nonsmokers and smokers from central England who completed two versions of the stage of change algorithm for smoking acquisition and cessation. The fit of the latent variable defined by the spiral of change to adolescents' responses to the staging questions was examined using latent class analysis. Whether a model of sequential transition across stages fitted the observed transitions was tested with latent transition analysis (LTA). There was reasonable support for the staging algorithm but no evidence of sequential stage transition. The research was funded by Cancer Research UK.

Background: Over the last two decades, latent class analysis (LCA) has been extensively used to statistically identify phenotypes of childhood wheeze; however, less has been discussed on the external factors affecting the outcomes of LCA models in phenotype identification research. Objective: To understand the potential cause of variability in the number/types of wheeze phenotypes identified by means of LCA and to assess the performance of these models under different conditions. Methods: Here, we examined the effects of several data characteristics (sample size, data collection age and intervals), and model dimensionality (number of latent classes) on the classification of wheeze phenotypes by means of latent class and transition analysis. We also identified critical and redundant data collection points in discriminating phenotypes of wheeze using two different variable selection methods, stepwise-backward elimination, and genetic algorithm. Results: Small sample sizes suggested fewer wheeze sub-groups as they were underpowered to detect less frequently observed wheeze phenotypes. There was a strong interplay between sample size, number of data collection points and the optimal number of wheeze phenotypes extracted. A variable selection algorithm applied to LCA resulted in the exclusion of 6 redundant/non-informative time points (Month 6, Month 30, Month 69, Month 91, Month 140 and Month 198) as they contained very little discriminative and/or extra information about the wheeze classes. Conclusions: Input data characteristics and model complexity were found to be very influential on the classification of wheeze phenotypes and prevalence of each class in the population.

This article describes several latent variable approaches that can support rigorous quantitative inquiry in music education. I provide a definition of latent variables, list several advantages associated with their use for the measurement of constructs, and review three types of latent variables featuring utility for music education scholars: factor models, item response models, and latent class (mixture) models. Each type of model is illustrated with exemplar studies from music education literature. In addition, I report the results of a systematic analysis of latent variables’ use in published music education research. Over the past decade, latent variables were used in only 14.29% of the quantitative research reports in two prominent journals: the Bulletin of the Council for Research in Music Education and the Journal of Research in Music Education. The majority of these latent variable applications (80.56%) were factor models; however, there are myriad additional possibilities. While not appropriate for every study, latent variable models have as-yet unrealized potential to improve the richness and rigor in nearly all areas of music education research.

Changes in the comorbidity patterns of negative emotional symptoms and Internet addiction over time among the first-year senior high school students: A one-year longitudinal study

The authors illustrate how to perform maximum-likelihood estimation in latent class (LC) analysis when there are sampling weights. The methods are natural extensions of the approaches proposed by Clogg and Eliason (1987) and Magidson (1987) for dealing with sampling weights in the log-linear analysis of frequency tables. For the log-linear form of the LC model, the approach corresponds to a special case of Haberman's (1979) log-linear LC model with cell weights. This approach can also be applied to the probability formulation of the LC model with cell weights, which can accommodate many indicators. The authors propose an efficient estimation-maximization algorithm for estimating the parameters for this formulation. A small simulation study shows that the probability estimates obtained by this approach compare favorably to other weighting approaches. Several empirical examples are provided to illustrate various possible weighting methods in LC analysis.

Purpose Our objectives were to (a) identify oral and pharyngeal physiologic swallowing impairment severity classes based on latent class analyses (LCAs) of the Modified Barium Swallow Impairment Profile (MBSImP) swallow task scores and (b) quantify the probability of severity class membership given composite MBSImP oral total (OT) and pharyngeal total (PT) scores. Method MBSImP scores were collected from a patient database of 319 consecutive modified barium swallow studies. Because of missing swallow task scores, LCA was performed using 25 multiply imputed data sets. Results LCA revealed a three-class structure for both oral and pharyngeal models. We identified OT and PT score intervals to assign subjects to oral and pharyngeal impairment latent severity classes, respectively, with high probability (probability of class membership ≥ 0.9 given OT or PT scores within specified ranges) and high confidence (95% credible interval [CI] widths ≤ 0.24 for all total scores within specified ranges). OT scores ranging from 0 to 10 and from 14 to 18 yielded assignments in Oral Latent Classes 1 and 2, respectively, while OT = 22 was assigned to Oral Latent Class 3. PT scores ranging from 0 to 13 and from 18 to 24 yielded assignments in Pharyngeal Latent Classes 1 and 2, respectively, while PT = 26 was assigned to Pharyngeal Latent Class 3. Conclusions LCA of MBSImP task-level data revealed significant underlying oral and pharyngeal ordinal class structures representing increasingly severe gradations of physiologic swallow impairment. Clinically meaningful OT and PT score ranges were derived facilitating latent class assignment. Supplemental Material https://doi.org/10.23641/asha.12315677.

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.

Recurrent wheezing or asthma is a common problem in children that has increased considerably in prevalence in the past few decades. The causes and underlying mechanisms are poorly understood and it is thought that a numb er of distinct diseases causing similar symptoms are involved. Due to the lack of a biologically founded classification system, children are classified according to their observed disease related features (symptoms, signs, measurements) into phenotypes. The objectives of this PhD project were a) to develop tools for analysing phenotypic variation of a disease, and b) to examine phenotypic variability of wheezing among children by applying these tools to existing epidemiological data. A combination of graphical methods (multivariate co rrespondence analysis) and statistical models (latent variables models) was used. In a first phase, a model for discrete variability (latent class model) was applied to data on symptoms and measurements from an epidemiological study to identify distinct phenotypes of wheezing. In a second phase, the modelling framework was expanded to include continuous variability (e.g. along a severity gradient) and combinations of discrete and continuo us variability (factor models and factor mixture models). The third phase focused on validating the methods using simulation studies. The main body of this thesis consists of 5 articles (3 published, 1 submitted and 1 to be submitted) including applications, methodological contributions and a review. The main findings and contributions were: 1) The application of a latent class model to epidemiological data (symptoms and physiological measurements) yielded plausible pheno types of wheezing with distinguishing characteristics that have previously been used as phenotype defining characteristics. 2) A method was proposed for including responses to conditional questions (e.g. questions on severity or triggers of wheezing are asked only to children with wheeze) in multivariate modelling.ii 3) A panel of clinicians was set up to agree on a plausible model for wheezing diseases. The model can be used to generate datasets for testing the modelling approach. 4) A critical review of methods for defining and validating phenotypes of wheeze in children was conducted. 5) The simulation studies showed that a parsimonious parameterisation of the models is required to identify the true underlying structure of the data. The developed approach can deal with some challenges of real-life cohort data such as variables of mixed mode (continuous and categorical), missing data and conditional questions. If carefully applied, the approach can be used to identify whether the underlying phenotypic variation is discrete (classes), continuous (factors) or a combination of these. These methods could help improve precision of research into causes and mechanisms and contribute to the development of a new classification of wheezing disorders in children and other diseases which are difficult to classify.

Abstract. Latent class analysis has been recently proposed for the multiple imputation (MI) of missing categorical data, using either a standard frequentist approach or a nonparametric Bayesian model called Dirichlet process mixture of multinomial distributions (DPMM). The main advantage of using a latent class model for multiple imputation is that it is very flexible in the sense that it can capture complex relationships in the data given that the number of latent classes is large enough. However, the two existing approaches also have certain disadvantages. The frequentist approach is computationally demanding because it requires estimating many LC models: first models with different number of classes should be estimated to determine the required number of classes and subsequently the selected model is reestimated for multiple bootstrap samples to take into account parameter uncertainty during the imputation stage. Whereas the Bayesian Dirichlet process models perform the model selection and the handling of the parameter uncertainty automatically, the disadvantage of this method is that it tends to use a too small number of clusters during the Gibbs sampling, leading to an underfitting model yielding invalid imputations. In this paper, we propose an alternative approach which combined the strengths of the two existing approaches; that is, we use the Bayesian standard latent class model as an imputation model. We show how model selection can be performed prior to the imputation step using a single run of the Gibbs sampler and, moreover, show how underfitting is prevented by using large values for the hyperparameters of the mixture weights. The results of two simulation studies and one real-data study indicate that with a proper setting of the prior distributions, the Bayesian latent class model yields valid imputations and outperforms competing methods.

Chapter 33 - Graphical Display of Latent Budget Analysis and Latent Class Analysis, with Special Reference to Correspondence Analysis

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.

Missing data and especially dropouts frequently arise in longitudinal data. Maximum likelihood estimates are consistent when data are missing at random (MAR) but, as this assumption is not checkable, pattern mixture models (PMM) have been developed to deal with informative dropout. More recently, latent class models (LCM) have been proposed as a way to relax PMM assumptions. The aim of this paper is to compare PMM and LCM in order to tackle informative dropout in a longitudinal study of cognitive ageing measured by several psychometric tests. Using a multivariate longitudinal model with a latent process, a sensitivity analysis was performed to compare estimates under the MAR assumption, from a PMM and from two LCM. In the PMM, dropout patterns are included as covariates in the multivariate longitudinal model. In the simple LCM, they are predictors of the class membership probabilities while, in the joint LCM, the dropout time is jointly modeled using a proportional hazard model depending on latent classes. We show that parameter interpretation is different in the two kinds of models and thus can lead to different estimated values. PMM parameters are adjusted on the dropout patterns while LCM parameters are adjusted on the latent classes. This difference is highlighted in our data set because the latent classes exhibit much more heterogeneity than dropout patterns. We suggest several complementary analyses to investigate the characteristics of latent classes in order to understand the meaning of the parameters when using LCM to deal with informative dropout.