3. A Goodness-of-Fit Test for the Latent Class Model When Expected Frequencies are Small

Mark Reiser · Yi-Ching Lin

43 citations0/0 files storedSociological Methodology

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Psychometric Methodologies and Testing Statistical Methods and Applications Statistical Methods and Bayesian Inference

Abstract

In this paper, a goodness-of-fit test for the latent class model is presented. The test uses only the limited information in the second-order marginal distributions from a set of k dichotomous variables, and it is intended for use when k is large and the sample size, n, is moderate or small. In that situation, a 2k contingency table formed by the full cross-classification of k variables will be sparse in the sense that a high proportion of cell frequencies will be equal to zero or 1, and the chi-square approximation for traditional goodness-of-fit statistics such as the likelihood ratio will not be valid. The second-order marginal frequencies, which correspond to the bivariate distributions, are rarely sparse even when the joint frequencies have a high proportion of zero cells. Results from Monte Carlo experiments are presented that compare the rates of Type I and Type II errors for the proposed test to the rates for traditional goodness-of-fit tests. Results show that under commonly encountered conditions, a test of fit based on the limited information in the second-order marginals has a Type II error rate that is no higher than the error rate found for full-information test statistics, and that the test statistic given in this paper does not suffer from ill effects of sparseness in the joint frequencies.

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References

2012Applications of Item Response Theory To Practical Testing Problems 1974Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models 1984The NIMH Epidemiologic Catchment Area Program 1950Measurement and prediction 1970Fitting a Response Model for n Dichotomously Scored Items 1988Full-Information Item Factor Analysis 1974The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach 1978Contributions to Factor Analysis of Dichotomous Variables

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2003Latent class model diagnostics—a review and some proposals 2002Bayesian Estimation and Model Selection in Ordered Latent Class Models for Polytomous Items 2003Latent Class Model Diagnosis from a Frequentist Point of View 2019An efficient charting scheme for multivariate categorical process with a sparse contingency table

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