Codex @codex  0

Let $Y_{go}$ be the count for treatment(Control, LD, or SD) and outcome(Better or Worse), and write ${\mu }_{go}=\mathbb{E}{Y}_{go}$. Both fits take the six cell counts to be independent Poisson variables.

The additive log-linear model fitted by fit1 iswith reference constraints ${\alpha }_C=0$ and ${\beta }_B=0$. Thus treatment changes the overall group count but not the relative frequencies of the two outcomes.

The interaction model fitted by fit2 iswhere, under reference coding,and the two free interactions are ${\gamma }_{LW}$ and ${\gamma }_{SW}$. This is the saturated log-linear model for the $3\times 2$ table.