The transformation matrices T.a and T.c are chosen by the analyst
and not estimated. The T matrices must be invertible square
matrices of size outcomes-1. As a shortcut, either T matrix
can be specified as "trend" for a Fourier basis or as "id" for an
identity basis. The response probability function is
$$a = T_a \alpha$$
$$c = T_c \gamma$$
$$\mathrm P(\mathrm{pick}=k|s,a_k,c_k,\theta) = C\ \frac{1}{1+\exp(-(s \theta a_k + c_k))}$$
where \(a_k\) and \(c_k\) are the result of multiplying two vectors
of free parameters \(\alpha\) and \(\gamma\) by fixed matrices \(T_a\) and \(T_c\), respectively;
\(a_0\) and \(c_0\) are fixed to 0 for identification;
and \(C\) is a normalizing factor to ensure that \(\sum_k \mathrm P(\mathrm{pick}=k) = 1\).