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Logistic Regression Using SAS®: Theory and Application by Paul D. Allison

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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
 BlacksNonblacksTotal
Death282250
Life455297
Total7374147

Let’s consider the table in more general form as

m11m12
m21m22

where mij 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 pij is the probability of falling into cell (i, j), then mij=npij.

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 ...

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