Multivariate Ordered Discrete Response Models with Lattice Structures

TL;DR

This paper develops a comprehensive framework for modeling multivariate ordered discrete responses with lattice structures, incorporating both semiparametric and parametric approaches, and provides identification conditions, estimation methods, and simulation results.

Contribution

It introduces a novel modeling approach for multivariate ordered responses with lattice structures, including identification conditions and estimation techniques for both semiparametric and parametric cases.

Findings

Identification conditions for model parameters and thresholds

Estimation methods demonstrated through simulations

Separate identification of regression and correlation parameters in bivariate probit

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.