= Solution
The printed formula expands to the main effects of school type, acceptance and college, together with school-type-by-college and acceptance-by-college interactions. It contains neither a school-type-by-acceptance interaction nor the corresponding three-way interaction. Its <Poisson regression> model is therefore
$$
\log\mu_{abj}=\gamma_j+\alpha_{aj}+\beta_{bj}.
$$
For every college the mean table has <odds ratio>
$$
\boxed{\frac{\mu_{11j}\mu_{22j}}{\mu_{12j}\mu_{21j}}=1.}
$$
Thus it tests <conditional independence> of school type and acceptance given college, while permitting both margins to vary freely across colleges. It does not merely assert a common, possibly nonzero association.
The <maximum likelihood estimation> score equations match every school-type-by-college and acceptance-by-college margin. Solving them gives the <stratified two-by-two conditional independence model>'s fitted counts
$$
\boxed{\widehat\mu_{abj}=\frac{n_{a+j}n_{+bj}}{n_{++j}}.}
$$
Indeed these counts factor by row and column and have exactly the observed margins. For nondegenerate tables there are three free mean parameters per college: one total and two independent margin proportions. There are $100$ cells and $75$ parameters, hence \b[25 residual degrees of freedom]. The residual <deviance> is
$$
G^2=2\sum_{a,b,j}n_{abj}\log\frac{n_{abj}}{\widehat\mu_{abj}},
$$
with zero-count contributions interpreted as zero. The Poisson linear terms cancel because the fitted totals equal the observed totals. Under the null and suitable large-count regularity, compare $G^2$ with $\chi^2_{25}$. Sparse cells, structural zeros or degenerate margins require a different calibration, such as an appropriate conditional test or simulated reference distribution.
A large residual <deviance> is evidence of school-type/acceptance association in at least some colleges. A small one indicates compatibility with conditional independence, not proof of identical admission processes or absence of selection on qualifications. Residuals and individual college contrasts locate departures. Adding the school-type-by-acceptance term gives a common <odds ratio>, one extra parameter and 24 residual degrees of freedom. Adding the full three-way term permits each college's association and saturates the tables. The first comparison tests a common association; the second checks whether a common association is adequate. No frequencies are supplied here to evaluate these tests numerically.
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