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Reliable Inference in Highly Stratified Contingency Tables: Using Latent Class Models as Density Estimators

Published online by Cambridge University Press:  04 January 2017

Drew A. Linzer*
Affiliation:
Department of Political Science, Emory University, 327 Tarbutton Hall, 1555 Dickey Drive, Atlanta, GA 30322 e-mail: dlinzer@emory.edu

Abstract

Contingency tables are among the most basic and useful techniques available for analyzing categorical data, but they produce highly imprecise estimates in small samples or for population subgroups that arise following repeated stratification. I demonstrate that preprocessing an observed set of categorical variables using a latent class model can greatly improve the quality of table-based inferences. As a density estimator, the latent class model closely approximates the underlying joint distribution of the variables of interest, which enables reliable estimation of conditional probabilities and marginal effects, even among subgroups containing fewer than 40 observations. Though here focused on applications to public opinion, the procedure has a wide range of potential uses. I illustrate the benefits of the latent class model—based approach for greatly improved accuracy in estimating and forecasting vote preferences within small demographic subgroups using survey data from the 2004 and 2008 U.S. presidential election campaigns.

Type
Regular Articles
Copyright
Copyright © The Author 2011. Published by Oxford University Press on behalf of the Society for Political Methodology 

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