= Stratified two-by-two conditional independence model
{title2=$\widehat\mu_{abj}=n_{a+j}n_{+bj}/n_{++j}$}
For independent Poisson cell counts in stratified two-by-two <contingency tables>, the model $\log\mu_{abj}=\gamma_j+\alpha_{aj}+\beta_{bj}$ allows both margins to vary by stratum but excludes within-stratum association. Its fitted means are the displayed products of margins, because the <Poisson regression> score equations match those margins. Every stratum's <odds ratio> is one. With positive nondegenerate margins, $J$ strata give $3J$ parameters and $J$ residual degrees of freedom. A common association adds one parameter; stratum-specific associations saturate the tables.
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