Latent class analysis variable selection

We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable's usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. A headlong search algorithm is used to explore the model space and select clustering variables. In simulated datasets we found that the method selected the correct clustering variables, and also led to improvements in classification performance and in accuracy of the choice of the number of classes. In two real datasets, our method discovered the same group structure with fewer variables. In a dataset from the International HapMap Project consisting of 639 single nucleotide polymorphisms (SNPs) from 210 members of different groups, our method discovered the same group structure with a much smaller number of SNP

The Use of Loglinear Models for Assessing Differential Item Functioning Across Manifest and Latent Examinee Groups

Loglinear latent class models are used to detect differential item functioning (DIF). These models are formulated in such a manner that the attribute to be assessed may be continuous, as in a Rasch model, or categorical, as in Latent Class Mastery models. Further, an item may exhibit DIF with respect to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a "real world" data set

The Role of Trust in Explaining Food Choice: Combining Choice Experiment and Attribute Best−Worst Scaling

This paper presents empirical findings from a combination of two elicitation techniques—discrete choice experiment (DCE) and best–worst scaling (BWS)—to provide information about the role of consumers’ trust in food choice decisions in the case of credence attributes. The analysis was based on a sample of 459 Taiwanese consumers and focuses on red sweet peppers. DCE data were examined using latent class analysis to investigate the importance and the utility different consumer segments attach to the production method, country of origin, and chemical residue testing. The relevance of attitudinal and trust-based items was identified by BWS using a hierarchical Bayesian mixed logit model and was aggregated to five latent components by means of principal component analysis. Applying a multinomial logit model, participants’ latent class membership (obtained from DCE data) was regressed on the identified attitudinal and trust components, as well as demographic information. Results of the DCE latent class analysis for the product attributes show that four segments may be distinguished. Linking the DCE with the attitudinal dimensions reveals that consumers’ attitude and trust significantly explain class membership and therefore, consumers’ preferences for different credence attributes. Based on our results, we derive recommendations for industry and policy

Insights into Latent Class Analysis

Latent class analysis is a popular statistical technique for estimating disease prevalence and test sensitivity and specificity. It is used when a gold standard assessment of disease is not available but results of multiple imperfect tests are. We derive analytic expressions for the parameter estimates in terms of the raw data, under the conditional independence assumption. These expressions indicate explicitly how observed two- and three-way associations between test results are used to infer disease prevalence and test operating characteristics. Although reasonable if the conditional independence model holds, the estimators have no basis when it fails. We therefore caution against using the latent class approach in practice

A comparison of two-stage segmentation methods for choice-based conjoint data: a simulation study.

Due to the increasing interest in market segmentation in modern marketing research, several methods for dealing with consumer heterogeneity and for revealing market segments have been described in the literature. In this study, the authors compare eight two-stage segmentation methods that aim to uncover consumer segments by classifying subject-specific indicator values. Four different indicators are used as a segmentation basis. The forces, which are subject-aggregated gradient values of the likelihood function, and the dfbetas, an outlier detection measure, are two indicators that express a subject’s effect on the estimation of the aggregate partworths in the conditional logit model. Although the conditional logit model is generally estimated at the aggregate level, this research obtains individual-level partworth estimates for segmentation purposes. The respondents’ raw choices are the final indicator values. The authors classify the indicators by means of cluster analysis and latent class models. The goal of the study is to compare the segmentation performance of the methods with respect to their success rate, membership recovery and segment mean parameter recovery. With regard to the individual-level estimates, the authors obtain poor segmentation results both with cluster and latent class analysis. The cluster methods based on the forces, the dfbetas and the choices yield good and similar results. Classification of the forces and the dfbetas deteriorates with the use of latent class analysis, whereas latent class modeling of the choices outperforms its cluster counterpart.Two-stage segmentation methods; Choice-based conjoint analysis; Conditional logit model; Market segmentation; Latent class analysis;

Latent tree models

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned

Dynamics and sparsity in latent threshold factor models: A study in multivariate EEG signal processing

We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated series to underlying, dynamic latent factor processes. Structured priors on model hyper-parameters are key to the efficacy of dynamic latent thresholding, and MCMC-based computation enables model fitting and analysis. A detailed case study of electroencephalographic (EEG) data from experimental psychiatry highlights the use of latent threshold extensions of time-varying vector autoregressive and factor models. This study explores a class of dynamic transfer response factor models, extending prior Bayesian modeling of multiple EEG series and highlighting the practical utility of the latent thresholding concept in multivariate, non-stationary time series analysis.Comment: 27 pages, 13 figures, link to external web site for supplementary animated figure