Statistical Modelling 3 (2003), 15–41
Reduced-rank vector generalized linear models
Thomas W Yee
Department of Statistics, University of Auckland,
Private Bag 92019,
Auckland, New Zealand.
eMail:
yee@stat.auckland.ac.nz
Trevor J Hastie
Department of Statistics,
Stanford University,
Stanford, California, USA
Abstract:
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.
Keywords:
CATEGORICAL DATA ANALYSIS; ITERATIVELY REWEIGHTED LEAST SQUARES;
LINEAR PREDICTORS; MULTINOMIAL; LOGIT MODEL;
REDUCED RANK REGRESSION; STEREOTYPE MODEL;
VECTOR GENERALIZED LINEAR MODELS.
Downloads:
Illustrative
data and code in zipped archive
VGAM software available from
http://www.stat.auckland.ac.nz/~yee
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