Under the random utility interpretation, an individual with utility (U_{i j}=) (u_{i}left(V_{i j}+epsilon_{i j} ight)), where (j)

Under the random utility interpretation, an individual with utility \(U_{i j}=\) \(u_{i}\left(V_{i j}+\epsilon_{i j}\right)\), where \(j\) may be 1 or 2 , selects category corresponding to \(j=1\) with probability

\[\begin{aligned}\pi_{i} & =\operatorname{Pr}\left(y_{i}=1\right)=\operatorname{Pr}\left(U_{i 2}