# Pairwise likelihood inference for the multivariate ordered probit model

## TL;DR

This paper derives a closed-form expression for the pairwise score vector in the multivariate ordered probit model, enhancing likelihood-based inference by improving optimization speed and standard error computation.

## Contribution

It introduces a novel closed-form expression for the pairwise score vector, facilitating faster optimization and more accurate inference in multivariate ordered probit models.

## Key findings

- Enables faster gradient-based optimization routines.
- Provides a new method to compute standard errors and confidence intervals.
- Improves likelihood-based inference accuracy.

## Abstract

This paper provides a closed form expression for the pairwise score vector for the multivariate ordered probit model. This result has several implications in likelihood-based inference. It is indeed used both to speed-up gradient based optimization routines for point estimation, and to provide a building block to compute standard errors and confidence intervals by means of the Godambe matrix.