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Modeling Strategies 7
Perhaps the most common response function modeled for categorical data is the logit. If you have
a dichotomous response and represent the proportion of those subjects with an event (versus no
event) outcome as p, then the logit can be written
log
p
1 p
Logistic regression is a modeling strategy that relates the logit to a set of explanatory variables
with a linear model. One of its benefits is that estimates of odds ratios, important measures of
association, can be obtained from the parameter estimates. Maximum likelihood estimation is used
to provide those estimates.
Chapter 8, “Logistic Regression I: Dichotomous Response,” discusses logistic regression for
a dichotomous outcome variable. Chapter 9, “Logistic Regression II: Polytomous Response,”
discusses logistic regression for the situation where there are more than two outcomes for the
response variable. Logits called generalized logits can be analyzed when the outcomes are nominal.
And logits called cumulative logits can be analyzed when the outcomes are ordinal. Chapter
10, “Conditional Logistic Regression,” describes a specialized form of logistic regression that is
appropriate when the data are highly stratified or arise from matched case-control studies. These
chapters describe the use of exact conditional logistic regression for those situations where you
have limited or sparse data, and the asymptotic requirements for the usual maximum likelihood
approach are not met.
Poisson regression is a modeling strategy that is suitable for discrete counts, and it is discussed in
Chapter 12, “Poisson Regression and Related Loglinear Models.” Most often the log of the count
is used as the response function.
Some application areas have features that led to the development of special statistical techniques.
One of these areas for categorical data is bioassay analysis. Bioassay is the process of determining
the potency or strength of a reagent or stimuli based on the response it elicits in biological
organisms. Logistic regression is a technique often applied in bioassay analysis, where its
parameters take on specific meaning. Chapter 11, “Quantal Bioassay Analysis,” discusses the use
of categorical data methods for quantal bioassay. Another special application area for categorical
data analysis is the analysis of grouped survival data. Chapter 13, “Categorized Time-to-Event
Data,” discusses some features of survival analysis that are pertinent to grouped survival data,
including how to model them with the piecewise exponential model.
In logistic regression, the objective is to predict a response outcome from a set of explanatory
variables. However, sometimes you simply want to describe the structure of association in a set of
variables for which there are no obvious outcome or predictor variables. This occurs frequently for
sociological studies. The loglinear model is a traditional modeling strategy for categorical data and
is appropriate for describing the association in such a set of variables. It is closely related to logistic
regression, and the parameters in a loglinear model are also estimated with maximum likelihood
estimation. Chapter 12, “Poisson Regression and Related Loglinear Models,” includes a discussion
of the loglinear model, including a typical application.
Besides the logit and log counts, other useful response functions that can be modeled include
proportions, means, and measures of association. Weighted least squares estimation is a method of
analyzing such response functions, based on large sample theory. These methods are appropriate
when you have sufficient sample size and when you have a randomly selected sample, either
Stokes, Maura E., Charles S. Davis, and Gary G. Koch. Categorical Data Analysis Using SAS®, Third Edition. Copyright © 2012,
SAS Institute Inc., Cary, North Carolina, USA. ALL RIGHTS RESERVED. For additional SAS resources, visit support.sas.com/bookstore.