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

m_{11} | m_{12} |

m_{21} | m_{22} |

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 ...

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