Logistic Regression Using SAS®: Theory and Application

10.2. A Loglinear Model for a 2 × 2 Table

Let’s start with the 2 × 2 table we analyzed in Chapter 4 (reproduced here as Table 10.1), which shows sentence by race for 147 death penalty cases. How can we represent this by a loglinear model?

Table 10.1. Death Sentence by Race of Defendant

	Blacks	Nonblacks	Total
Death	28	22	50
Life	45	52	97
Total	73	74	147

Let’s consider the table in more general form as

m11	m12
m21	m22

where m_ij is the expected number of cases falling into row i and column j. What I mean by this is that if n is the sample size and p_ij is the probability of falling into cell (i, j), then m_ij=np_ij.

There are a couple of different but equivalent ways of writing a loglinear model for these four frequency counts. The way I’m going to do it is consistent ...