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.
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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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Choulakian, V. Generalized bilinear models. Psychometrika 61, 271–283 (1996). https://doi.org/10.1007/BF02294339
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DOI: https://doi.org/10.1007/BF02294339