Maximum Augmented Empirical Likelihood Estimation of Categorical Marginal Models for Large Sparse Contingency Tables

L. Andries Ark (), Wicher P. Bergsma and Letty Koopman
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L. Andries Ark: University of Amsterdam
Wicher P. Bergsma: THE London School of Economics AND POLITICAL SCIENCE
Letty Koopman: University of Amsterdam

Psychometrika, 2023, vol. 88, issue 4, No 6, 1228-1248

Abstract: Abstract Categorical marginal models (CMMs) are flexible tools for modelling dependent or clustered categorical data, when the dependencies themselves are not of interest. A major limitation of maximum likelihood (ML) estimation of CMMs is that the size of the contingency table increases exponentially with the number of variables, so even for a moderate number of variables, say between 10 and 20, ML estimation can become computationally infeasible. An alternative method, which retains the optimal asymptotic efficiency of ML, is maximum empirical likelihood (MEL) estimation. However, we show that MEL tends to break down for large, sparse contingency tables. As a solution, we propose a new method, which we call maximum augmented empirical likelihood (MAEL) estimation and which involves augmentation of the empirical likelihood support with a number of well-chosen cells. Simulation results show good finite sample performance for very large contingency tables.

Keywords: categorical marginal model; Cronbach’s alpha; large categorical data sets; marginal homogeneity; maximum empirical likelihood estimation; maximum likelihood estimation; scalability coefficients (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11336-023-09932-7

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