Showing papers on "Latent variable model published in 1979"
TL;DR: In this article, the authors present the results of the application of latent trait analyses to a series of tests that vary in factorial complexity, and determine what characteristics are estimated by the models for these tests, while at the same time determining the relationship of latent traits to traditional item analysis and factor analysis indices.
Abstract: In order to extend the use of latent trait models across the full spectrum of mental testing, the applicability of the models to multivariate data must be determined. Since all of the commonly used models assume a unidimensional test, the applicability of the procedures to obviously multidimensional tests, such as achievement tests, is questionable. This paper presents the results of the application of latent trait analyses to a series of tests that vary in factorial complexity. The purpose is to determine what characteristics are estimated by the models for these tests, while at the same time determining the relationship of latent trait parameters to traditional item analysis and factor analysis indices.
789 citations
TL;DR: In this paper, a model with dichotomous indicators of latent variables is developed, where latent variables are related to each other and to a set of exogenous variables in a system of structural relations.
Abstract: A model with dichotomous indicators of latent variables is developed. The latent variables are related to each other and to a set of exogenous variables in a system of structural relations. Identification and maximum likelihood estimation of the model are treated. A sociological application is presented in which a theoretical construct (an attitude) is related to a set of background variables. The construct is not measured directly, but is indicated by the answers to a pair of questionnaire statements.
187 citations
TL;DR: In this paper, a special class of log-linear models for analysis of these variables (viz., latent structure of latent class models) which take account of the actual distributional properties corresponding to the sampled cross-classification of the variables, the ordinal character of the variable, and the status of the observed variables as indicators of unobservable or latent variables are considered.
124 citations
TL;DR: In this article, it was shown that the parameter estimates obtained with the iterative procedure cannot lie outside the allowed interval, and this was later confirmed in a follow-up paper.
Abstract: In this note, we describe the iterative procedure introduced earlier by Goodman to calculate the maximum likelihood estimates of the parameters in latent structure analysis, and we provide here a simple and direct proof of the fact that the parameter estimates obtained with the iterative procedure cannot lie outside the allowed interval. Formann recently stated that Goodman's algorithm can yield parameter estimates that lie outside the allowed interval, and we prove in the present note that Formann's contention is incorrect.
75 citations
TL;DR: In this article, a matrix approach is used 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.
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.
34 citations
TL;DR: The authors compare results from two such latent variable models with results from the Wisconsin regression model of status attainment, showing that the gains that come from latent variable model compared to regression analyses illustrate the price an investigator pays for such gains.
16 citations
TL;DR: In this paper, large sample properties of statistics used in latent root regression analysis are investigated by examining the matrix of correlations among the predictor and response variables as the sample size becomes infinite.
Abstract: Large sample properties of statistics used in latent root regression analysis are investigated by examining the matrix of correlations among the predictor and response variables as the sample size becomes infinite. The latent roots and latent vectors of the asymptotic correlation matrix are derived for specific model configurations of interest. From the study of the asymptotic latent roots and latent vectors, a new statistic is proposed for use in detecting nonpredictive multicollinearities.
8 citations
TL;DR: In this article, the authors extend their analysis to cover the case of several latent variables and use a maximum likelihood procedure to estimate the parameters of a model in which one observes multiple indicators and multiple causes of a single latent variable.
Abstract: Joreskog/Goldberger [1975] use a maximum likelihood procedure to estimate the parameters of a model in which one observes multiple indicators and multiple causes of a single latent variable. This note extends their analysis to cover the case of several latent variables.
3 citations