Multivariate Ordered Discrete Response Models with Lattice Structures

Abstract: We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using functionally independent decision thresholds. In a semiparametric framework, we model latent processes as sums of covariate indices and unobserved errors, deriving conditions for identifying parameters, thresholds, and the joint cumulative distribution function of errors. For the parametric bivariate probit case, we separately derive identification of regression parameters and thresholds, and the correlation parameter, with the latter requiring additional covariate conditions. We outline estimation approaches for semiparametric and parametric models and present simulations illustrating the performance of estimators for lattice models.