Topic
Latent variable model
About: Latent variable model is a research topic. Over the lifetime, 3589 publications have been published within this topic receiving 235061 citations.
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TL;DR: A new score distribution is introduced for the Rasch mixture model to be independent of the ability distribution and thus restricts the mixture to be sensitive to latent structure in the item difficulties only.
Abstract: Rasch mixture models can be a useful tool when checking the assumption of measurement invariance for a single Rasch model. They provide advantages compared to manifest differential item functioning (DIF) tests when the DIF groups are only weakly correlated with the manifest covariates available. Unlike in single Rasch models, estimation of Rasch mixture models is sensitive to the specification of the ability distribution even when the conditional maximum likelihood approach is used. It is demonstrated in a simulation study how differences in ability can influence the latent classes of a Rasch mixture model. If the aim is only DIF detection, it is not of interest to uncover such ability differences as one is only interested in a latent group structure regarding the item difficulties. To avoid any confounding effect of ability differences (or impact), a new score distribution for the Rasch mixture model is introduced here. It ensures the estimation of the Rasch mixture model to be independent of the ability distribution and thus restricts the mixture to be sensitive to latent structure in the item difficulties only. Its usefulness is demonstrated in a simulation study, and its application is illustrated in a study of verbal aggression.
52 citations
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TL;DR: This article offers an illustrative explanation of why a bootstrapping approach to structural equation modeling must choose to fix an indicator path rather than the latent variable variance in order for the empirical standard errors to be gensrated properly.
Abstract: In traditional applications of latent variable models, each exogenous latent variable must either have its variance parameter fixed or a loading path to a measured indicator variable fixed (either customarily to 1) Without doing so the measurement model will suffer from underidentification, thereby yielding no unique solution when estimating the parameters of interest The choice of whether to fix the variance or the loading is somewhat arbitrary, guided primarily by the researcher's need for inference regarding particular parameters within the model Under conditions of multivariate nonnormal data, the method by which one makes identified the measurement of exogenous latent variables may not be as arbitrary Specifically, as addressed briefly by Arbuckle (1997), when one is utilizing a bootstrapping approach for generating empirical standard errors for parameters of interest, the researcher must choose to fix an indicator path rather than the latent variable variance in order for the empirical standard errors to be gensrated properly This article offers an illustrative explanation of why such an approach is necessary Given the increased attention toward bootstrapping techniques within structural equation modeling, our hope is that a greater awareness and understanding of this unique situation will be facilitated
52 citations
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TL;DR: This paper provides a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables.
Abstract: Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular these two models have the same dimension. The nested Markov model is therefore the best possible description of the latent variable model that avoids consideration of inequalities, which are extremely complicated in general. A consequence of this is that the constraint finding algorithm of Tian and Pearl (UAI 2002, pp519-527) is complete for finding equality constraints.
Latent variable models suffer from difficulties of unidentifiable parameters and non-regular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.
51 citations
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TL;DR: In this paper, the authors demonstrate the close relationship between two classes of dynamic models in psychological research: latent change score models and continuous time models, and demonstrate how the two methods are mathematically and conceptually related.
Abstract: The primary goal of this article is to demonstrate the close relationship between 2 classes of dynamic models in psychological research: latent change score models and continuous time models. The secondary goal is to point out some differences. We begin with a brief review of both approaches, before demonstrating how the 2 methods are mathematically and conceptually related. It will be shown that most commonly used latent change score models are related to continuous time models by the difference equation approximation to the differential equation. One way in which the 2 approaches differ is the treatment of time. Whereas there are theoretical and practical restrictions regarding observation time points and intervals in latent change score models, no such limitations exist in continuous time models. We illustrate our arguments with three simulated data sets using a univariate and bivariate model with equal and unequal time intervals. As a by-product of this comparison, we discuss the use of phantom and de...
51 citations
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TL;DR: The proposed model has a 92.9% accuracy rate in predicting customer types, is less impacted by prior probabilities, and has a significantly low Type I errors in comparison with the other five approaches.
Abstract: A Bayesian latent variable model with classification and regression tree approach is built to overcome three challenges encountered by a bank in credit-granting process. These three challenges include (1) the bank wants to predict the future performance of an applicant accurately; (2) given current information about cardholders' credit usage and repayment behavior, financial institutions would like to determine the optimal credit limit and APR for an applicant; and (3) the bank would like to improve its efficiency by automating the process of credit-granting decisions. Data from a leading bank in Taiwan is used to illustrate the combined approach. The data set consists of each credit card holder's credit usage and repayment data, demographic information, and credit report. Empirical study shows that the demographic variables used in most credit scoring models have little explanatory ability with regard to a cardholder's credit usage and repayment behavior. A cardholder's credit history provides the most important information in credit scoring. The continuous latent customer quality from the Bayesian latent variable model allows considerable latitude for producing finer rules for credit granting decisions. Compared to the performance of discriminant analysis, logistic regression, neural network, multivariate adaptive regression splines (MARS) and support vector machine (SVM), the proposed model has a 92.9% accuracy rate in predicting customer types, is less impacted by prior probabilities, and has a significantly low Type I errors in comparison with the other five approaches.
51 citations