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Ivan Ukhov (talk | contribs) |
m corrected the likelihood |
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With similar computations, the conditional likelihood of a strata of size <math>m</math>, with the <math>k</math> first observations being the cases, is
:<math>
\mathbb{P}(Y_{ij}=1\text{ for }j\leq k,Y_{ij}=0\text{ for } k<j\leq m|X_{i1},...,X_{im},\sum_{j=1}^m Y_{ij}=k)=\frac{\exp(\sum_{j=1}^k \boldsymbol{\beta}^\top X_{ij})}{\sum_{J\in \mathcal{C} _{k}^{m}} \exp(\sum_{j\in J}
</math>
where <math>\mathcal{C} _{k}^{m}</math> is the set of all subsets of size <math>k</math> of the set <math>\{1,...,m\}</math>.
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