= Solution
The first coefficient is the <posterior mean> log odds of choosing invertebrates rather than fish for smaller alligators at Lake Hancock. It corresponds to
$$
\boxed{\exp(-1.852)\approx0.157}
$$
for those invertebrate-to-fish odds. This is not the absolute probability of choosing the second category, because the other categories also enter the normalization.
The size coefficient adds $-1.524$ to the invertebrate-to-fish log odds on changing to the larger class, holding lake fixed. Its common-across-lakes <odds ratio> is
$$
\boxed{\exp(-1.524)\approx0.218,}
$$
about a 78 percent reduction in the relative odds. Exponentiating a <posterior mean> log odds is a geometric summary, not the arithmetic <posterior mean> of the odds.
There are $(K-1)p=4\cdot5=20$ free category coefficients plus $I=8$ group intercepts, giving \b[28 free parameters in the fitted Poisson model]. The <effective parameter count in DIC>, $26.8$, is close to 28 and slightly smaller, consistent with some regularization or incomplete information. Comparing it with 20 would omit the nuisance intercepts. A direct conditional multinomial fit has 20 coefficients but a different observational likelihood, since it conditions on the totals.
Back to article page
