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.

Rasch models in latent classes: An integration of two approaches to item analysis

Abstract: A model is proposed that combines the theoret ical strength of the Rasch model with the heuristic power of latent class analysis. It assumes that the Rasch model holds for all persons within a latent class, but it allows for different sets of item parameters between the latent classes. An estima tion algorithm is outlined that gives conditional maximum likelihood estimates of item parameters for each class. No a priori assumption about the item order in the latent classes or the class sizes is required. Application of the model is illustrated, both for simulated data and for real data.

Higher-order latent trait models for cognitive diagnosis.

Abstract: Higher-order latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis This approach results in a parsimonious model for the joint distribution of a high-dimensional attribute vector that is natural in many situations when specific cognitive information is sought but a less informative item response model would be a reasonable alternative This approach stems from viewing the attributes as the specific knowledge required for examination performance, and modeling these attributes as arising from a broadly-defined latent trait resembling theϑ of item response models In this way a relatively simple model for the joint distribution of the attributes results, which is based on a plausible model for the relationship between general aptitude and specific knowledge Markov chain Monte Carlo algorithms for parameter estimation are given for selected response distributions, and simulation results are presented to examine the performance of the algorithm as well as the sensitivity of classification to model misspecification An analysis of fraction subtraction data is provided as an example

An Introduction to Latent Variable Models

Abstract: 1 General introduction.- 1.1 Introduction.- 1.2 Latent variables and latent variable models.- 1.3 The role of models.- 1.4 The general latent model.- 1.5 A simple latent variable model.- 1.6 Estimation and goodness-of-fit.- 1.7 Path diagrams.- 1.8 Summary.- 2 Factor analysis.- 2.1 Introduction.- 2.2 Explanatory and confirmatory factor analysis.- 2.3 The factor analysis model.- 2.4 Identifiability of the factor analysis model.- 2.5 Estimating the parameters in the factor analysis model.- 2.6 Goodness-of-fit tests.- 2.7 Rotation of factors.- 2.8 Numerical examples.- 2.9 Confirmatory factor analysis.- 2.10 Summary.- 3 The LISREL model.- 3.1 Introduction.- 3.2 The LISREL model.- 3.3 Identification.- 3.4 Estimating the parameters in the LISREL model.- 3.5 Instrumental variables.- 3.6 Numerical examples.- 3.7 Assessing goodness-of-fit.- 3.8 Multigroup analysis.- 3.9 Summary.- 4 Latent variable models for categorical data.- 4.1 Introduction.- 4.2 Factor analysis of binary variables.- 4.3 Latent structure models.- 4.4 Summary.- 5 Some final comments.- 5.1 Introduction.- 5.2 Assessing the fit of latent variable models by cross-validation procedures.- 5.3 Latent variables - fact or fiction?.- 5.4 Summary.- Appendix A Estimating the parameters in latent variable models a brief account of computational procedures.- Appendix B Computer programs for latent variable models.- Exercises.- References.

On‐line expectation–maximization algorithm for latent data models

Abstract: In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.

A Probabilistic Interpretation of Canonical Correlation Analysis

Abstract: We give a probabilistic interpretation of canonical correlation (CCA) analysis as a latent variable model for two Gaussian random vectors. Our interpretation is similar to the probabilistic interpretation of principal component analysis (Tipping and Bishop, 1999, Roweis, 1998). In addition, we cast Fisher linear discriminant analysis (LDA) within the CCA framework.