Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys
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Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, however the 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 Regression Model or OPFRM to perform ordinal function-on-scalar regression. The OPFRM is flexibly formulated to allow for the choice of different basis functions including penalized B-splines, wavelets, and O'Sullivan splines. We demonstrate the operating characteristics of the model in simulation using a variety of underlying covariance patterns showing the model performs reasonably well in estimation under multiple basis functions. We also present and compare two approaches for conducting posterior inference showing that joint credible intervals tend to out perform point-wise credible. Finally, in application, we determine demographic factors associated with the monkeys' computer use over the course of a year and provide a brief analysis of the findings.
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