 \mathbb{R}\)</span>, then for <span class="math inline">\(k \in \{1,\ldots,K\}\)</span>, <span class="math display">\[
\text{OrderedProbit}(k~|~\eta,c) = \left\{ \begin{array}{ll} 1 -
\Phi(\eta - c_1) &amp; \text{if } k = 1, \\[4pt] \Phi(\eta - c_{k-1}) -
\Phi(\eta - c_{k})  &amp; \text{if } 1 &lt; k &lt; K, \text{and} \\[4pt]
\Phi(\eta - c_{K-1}) - 0 &amp; \text{if } k = K. \end{array} \right. \]</span> The <span class="math inline">\(k=K\)</span> case is written with the redundant subtraction of zero to 