= Empty groups in a binomial homogeneity test
For independent $R_i\sim\operatorname{Bin}(n_i,p_i)$, a group with $n_i=0$ necessarily has $R_i=0$ and contributes <likelihood> one. Its <probability> parameter is unidentifiable and supplies no restriction to test. If $k$ groups have positive sample sizes, the unrestricted model has $k$ <probability> parameters and the common-probability model has one; the asymptotic homogeneity test therefore has $k-1$ degrees of freedom. Zero expected-count rows must be removed rather than divided by in the Pearson statistic.
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