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Generalized Bilinear Models

Published online by Cambridge University Press:  01 January 2025

Vartan Choulakian
Vartan Choulakian*
Affiliation:
Universite de Moncton, Moncton, N.B.
*
Requests for reprints should be sent to Vartan Choulakian, Department de mathematiques, Universite de Moncton, Moncton, New Brunswick, CANADA EIA 3E9.
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Abstract

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family of models that includes many existing models, as well as suggest other potentially useful ones. This approach both unifies and extends models for two-way arrays, including the ability to treat response and explanatory variables differently in the models, and the incorporation of external information about the variables directly into the analysis. A unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature. A three-step procedure is proposed to analyze data sets by generalized bilinear models. Two data sets of different nature are analyzed.

Keywords

exponential familyquasi-likelihoodNewton's methodFisher scoringlogitresponse variableexplanatory variableexternal information
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 2 , June 1996 , pp. 271 - 283
Copyright
Copyright © 1996 The Psychometric Society

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Footnotes

The author is very grateful to Shizuhiko Nishisato, the associate editor and the referees for their valuable comments, which resulted in a completely improved version of an earlier manuscript.

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