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Reduced-rank vector generalized linear models

Department of Statistics, University of Auckland, New Zealand, Department of Statistics and Applied Probability, National University of Singapore, Singapore, yee{at}stat.auckland.ac.nz

Trevor J Hastie

Department of Statistics, Stanford University, Stanford, CA, USA

Reduced-rank regression is a method with great potential for dimension reduction but has found few applications in applied statistics. To address this, reduced-rank regression is proposed for the class of vector generalized linear models (VGLMs), which is very large. The resulting class, which we call reduced-rank VGLMs (RR-VGLMs), enables the benefits of reduced-rank regression to be conveyed to a wide range of data types, including categorical data. RR-VGLMs are illustrated by focussing on models for categorical data, and especially the multinomial logit model. General algorithmic details are provided and software written by the first author is described. The reduced-rank multinomial logit model is illustrated with real data in two contexts: a regression analysis of workforce data and a classification problem.

Key Words: categorical data analysis • iteratively reweighted least squares • linear predictors • multinomial logit model • reduced rank regression • stereotype model • vector generalized linear models

Statistical Modelling, Vol. 3, No. 1, 15-41 (2003)
DOI: 10.1191/1471082X03st045oa


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