文档介绍：14
I I III II II II I II
POISSON REGRESSION, LOGISTIC
REGRESSION, AND LOGLINEAR
MODELS FOR RANDOM COUNTS
PETER B. IMREY
Departments of Statistics and Medical Information Science,
University of Illinois at Urbana-Champaign, Champaign, Illinois
I. PRELIMINARIES
A. Introduction
A categorical variable is observed whenever an individual, event, or other
unit is identified and placed into one of a finite collection of categories.
Gender, ethnicity, socioeconomic class, clinical diagnosis, and cause of
death are examples. Each possible category is a level of the variable that
may assume it; for example, female and male are the levels of gender.
Categorical variables may be qualitative (nominal), or quantitative (ordinal,
interval, or ratio scaled), depending on the nature of their levels. This
chapter considers statistical models for counts of independently occurring
random events, and counts at different levels of one or more categorical
es (., responses, dependent variables). Attention is focused pri-
marily on qualitative categorizations, but the reader also will find here a
basis for understanding models for quantitative categorical variables that
are described in several references.
Categorical variables also form the primary subject matter of Huberty
and Petoskey (chapter 7, this volume), where levels are employed as fixed
predictors (., independent variables) that partially explain differences
Handbook of Applied Multivariate Statistics and Mathematical Modeling
Copyright 2000 by Academic Press. All rights of reproduction in any form reserved. 391
392 PETERB. IMREY
between observations of continuous dependent random variables. Counts
appear there only as fixed sample sizes. In contrast, we consider categorical
dependent variables whose associated random counts require explanation
by other predictors. The predictors may be categorical, continuous, or both.
We assume the reader is familiar