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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?

 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 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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