An Introduction to Categorical Data Analysis || Loglinear Models for Contingency Tables

✍ Scribed by Agresti, Alan

• Publisher: John Wiley & Sons, Inc.
• Year: 2007
• Tongue: English
• Weight: 455 KB
• Edition: 2
• Category: Article
• ISBN: 0471226181
• DOI: 10.1002/9780470114759.ch7

✦ Synopsis

Section 3.3.1 introduced loglinear models as generalized linear models (GLMs) for count data. One use of them is modeling cell counts in contingency tables. The models specify how the size of a cell count depends on the levels of the categorical variables for that cell. They help to describe association patterns among a set of categorical response variables.

Section 7.1 introduces loglinear models. Section 7.2 discusses statistical inference for model parameters and model checking. When one variable is a binary response variable, logistic models for that response are equivalent to certain loglinear models. Section 7.3 presents the connection. We shall see that loglinear models are mainly of use when at least two variables in a contingency table are response variables. Section 7.4 introduces graphical representations that portray a model's association patterns and indicate when conditional odds ratios are identical to marginal odds ratios. The loglinear models of Sections 7.1-7.4 treat all variables as nominal. Section 7.5 presents a loglinear model that describes association between ordinal variables.

7.1 LOGLINEAR MODELS FOR TWO-WAY AND THREE-WAY TABLES

Consider an I × J contingency table that cross-classifies n subjects. When the responses are statistically independent, the joint cell probabilities {π ij } are determined by the row and column marginal totals,