= Edge log-ratios in a Bradley-Terry comparison tree
{title2=$\eta_{ij}=\log(\theta_i/\theta_j)$}
Orient the edges of a comparison <tree> and set $\eta_{ij}=\log\theta_i-\log\theta_j$. After anchoring one vertex strength, these edge quantities are unconstrained coordinates. The <Bradley-Terry model> probability is the <logistic function> of $\eta_{ij}$, and its binomial <log-likelihood> contribution is $m[p\eta_{ij}-\log(1+e^{\eta_{ij}})]$. Differentiating gives the fitted odds $p/(1-p)$.
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