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

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 t...

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Bibliographic Details
Published in:Psychometrika 2023-12, Vol.88 (4), p.1228-1248
Main Authors: van der Ark, L. Andries, Bergsma, Wicher P., Koopman, Letty
Format: Article
Language:English
Subjects:
Assessment
Behavioral Science and Psychology
Computer Simulation
Contingency tables
Educational evaluation
Educational tests & measurements
Efficiency
Humanities
Hypotheses
Law
Likelihood Functions
Probability distribution
Psychology
Psychometrics
Quantitative psychology
Statistical analysis
Statistical Theory and Methods
Statistics for Social Sciences
Structural equation modeling
Testing and Evaluation
Theory and Methods
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Summary: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.
ISSN:0033-3123
1860-0980
1860-0980
DOI:10.1007/s11336-023-09932-7