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.

Singular value decomposition of probability matrices: Probabilistic aspects of latent dichotomous variables

Abstract: SUMMARY This paper gives a matrix approach to determine when a statistical dependence between two manifest categorical random variables can be viewed as generated by some unobserved latent variables, in the sense that the manifest variables are conditionally independent with respect to the latent variables. By the singular value decomposition of the matrix representing deviations from statistical independence of the two manifest variables, we give a necessary and sufficient condition for existence of dichotomous latent variables, which are 'responsible' for conditional independence. We give a technique for identifying the distributions of such latent variables and also the conditional distributions of the manifest variables given the latent variables. Finally, we discuss some probabilistic aspects.

A general non-linear multilevel structural equation mixture model

Abstract: In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include nonlinear interaction and quadratic effects (e.g., Klein & Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh, Skrondal, & Pickles, 2004). We present a general nonlinear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric nonlinear structural equation models (Kelava & Nagengast, 2012; Kelava, Nagengast, & Brandt, in press) with multilevel structural equation mixture models (B. O. Muthen & Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework.

Multidimensional housing deprivation indices with application to Spain

Abstract: The main aim of this article is to define a multidimensional housing deprivation index and identify the main determining characteristics of this phenomenon, using Spain as reference. A latent variable model is used in order to overcome some of the traditional difficulties encountered in multidimensional deprivation studies. The construction of a latent structure model has allowed a set of partial housing deprivation indices to be grouped together under a single index. It has also enabled each individual to be assigned to a different class depending on the level and type of deprivation. Results show that the vector of observed variables (having hot running water, heating, a leaky roof, damp walls or floor, rot in window frames and floors and overcrowding) and the correlations among such variables can be explained by a single latent variable. There are also specific characteristics that differentiate the population affected by housing deprivation.

Alternative Specifications of Multivariate Multilevel Probit Ordinal Response Models

Abstract: Multivariate multilevel models for ordinal variables are quite complex with respect to both interpretation and estimation. The specification in terms of a multivariate latent distribution and a set of thresholds helps in the interpretation of the variance-covariance parameters. However, most existing estimation algorithms for multilevel models can be used only if the model is reparameterized as a univariate model with an additional dummy bottom level. Moreover, the univariate formulation allows the model to be cast in the framework of Generalized Linear Latent and Mixed Models (Rabe-Hesketh, Pickles, & Skrondal, 2001a), a rather general class that includes, as special cases, structural equations and factor models. This article outlines the multivariate latent distribution specification and the corresponding interpretation issues; it then shows the univariate formulation, along with some alternative parameterizations that are useful in the estimation phase. An application to student ratings data illustrate...