$\text{P}\left(Y_{in}|X_{in},X{*}_n;{\text{Γ}}_i,{\alpha }_i,{\beta }_i\right)$	represents the measurement component of choice given explanatory variable and latent construct;
$f\left(I_{nmk}|X{*}_n;a_{mk},{\text{λ}}_{mk}\right)$	represents the measurement of the latent variable model;
$f\left(X{*}_n|X_n;{\delta }_m,{\gamma }_m\right)$	represents the structural component of the latent variable model; and
$\partial X*$	the integral of X* and represents the marginal estimates from the joint probability of Yin, Inmk, X*n.