= Solution
The additive model has four free <regression coefficients>[coefficients]: an intercept, two treatment contrasts, and one outcome contrast. The interaction model adds
$$
(3-1)(2-1)=2
$$
treatment-by-outcome <interaction terms>[interaction term], making six parameters for six cells. It is saturated, so the residual degrees of freedom fall from two to zero and the <likelihood-ratio test> has
$$
\boxed{6-4=2\text{ degrees of freedom}}.
$$
The deviance reduction is $44.48$, with p-value $2.194\times10^{-10}$. The <analysis of deviance for nested generalized linear models> therefore gives overwhelming evidence against a common outcome distribution across the three groups. The observed proportions and the negative treatment--Worse interactions show that both doses reduce the chance of worsening relative to Control, with a larger reduction for LD.
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