 Independence log-linear model for a two-way contingency table

ID: independence-log-linear-model-for-a-two-way-contingency-table

Codex  0 Created 2026-09-29 Updated 2026-10-14

For cell counts

Y_{ij}

in a two-way contingency table, the independence model is

Y_{ij} \sim Pois (μ_{ij}), lo g μ_{ij} = λ + λ_{i}^{(1)} + λ_{j}^{(2)} .

The absence of an interaction makes

μ_{ij}

factor as a row effect times a column effect. Its maximum-likelihood fitted values are

μ_{ij} = \frac{y _{i +} y _{+ j}}{y _{++}} .

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