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Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Henk Kelderman
Henk Kelderman*
Affiliation:
University of Twente
*
Requests for reprints should be sent to Henk Kelderman, Department of Education, University of Twente, PO Box 217, 7500 AE Enschede, THE NETHERLANDS.
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Abstract

In this paper algorithms are described for obtaining the maximum likelihood estimates of the parameters in loglinear models. Modified versions of the iterative proportional fitting and Newton-Raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table. This is desirable if the contingency table becomes too large to store. Special attention is given to loglinear IRT models that are used for the analysis of educational and psychological test data. To calculate the necessary expected sufficient statistics and other marginal sums of the table, a method is described that avoids summing large numbers of elementary cell frequencies by writing them out in terms of multiplicative model parameters and applying the distributive law of multiplication over summation. These algorithms are used in the computer program LOGIMO. The modified algorithms are illustrated with simulated data.

Keywords

iterative proportional fittingNewton-RaphsonLOGIMOmultinornial distributionmarginal tables
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 3 , September 1992 , pp. 437 - 450
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

The author thanks Wim J. van der Linden, Gideon J. Mellenberh and Namburi S. Raju for their valuable comments and suggestions.

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