# Ordinal Probit Functional Outcome Regression with Application to Computer-Use Behavior in Rhesus Monkeys

## TL;DR

This paper introduces the OPFOR model for ordinal functional outcomes, demonstrating its effectiveness through simulations and an application to rhesus macaques' computer-use behavior, outperforming standard models.

## Contribution

The paper develops the first ordinal probit functional outcome regression model (OPFOR) and shows its advantages over existing ordinal longitudinal methods.

## Key findings

- OPFOR performs well with various basis functions.
- OPFOR achieves near nominal coverage for credible intervals.
- In application, OPFOR provides nuanced insights into monkey behavior.

## Abstract

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, but exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (Macaca mulatta), we introduce the Ordinal Probit Functional Outcome Regression model (OPFOR). OPFOR models can be fit using one of several basis functions including penalized B-splines, wavelets, and O'Sullivan splines -- the last of which typically performs best. Simulation using a variety of underlying covariance patterns shows that the model performs reasonably well in estimation under multiple basis functions with near nominal coverage for joint credible intervals. Finally, in application, we use Bayesian model selection criteria adapted to functional outcome regression to best characterize the relation between several demographic factors of interest and the monkeys' computer use over the course of a year. In comparison with a standard ordinal longitudinal analysis, OPFOR outperforms a cumulative-link mixed-effects model in simulation and provides additional and more nuanced information on the nature of the monkeys' computer-use behavior.