$\text{P}\left(Y_{in}|X_{in},X{*}_n;{\text{Γ}}_{\text{i}},{\text{α}}_{\text{i}},{\beta }_i\right)$	represents the measurement component of choice given explanatory variable and latent construct;	(A.5a)
$f\left(I_{nmk}|X{*}_n;a_{mk},{\text{λ}}_{mk}\right)$	represent the measurement of the latent variable model;	(A.5b)
$f\left(X{*}_n|X_n;{\delta }_m,{\text{γ}}_m\right)$	represents the structural component of the latent variable model; and	(A.5c)
$\partial X^{*}$	the integral of X* and represents the marginal estimates from the joint probability of $Y_{in},I_{nmk},X{*}_n$.	(A.5d)