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Abstract:
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Functional predictors, such as EEG or fMRI, with a bounded response have become increasingly common in recent mental health studies. We propose a novel Bayesian quantile regression using a single-index of covariates and associated monotone link function. Compared to existing methods, our proposed method offers some clear practical advantages: a non-decreasing relationship of a clinically interpretable index with the pre-specified quantile of the bounded response, accommodation of unknown non-linear effects and interaction effects of predictors, and an objective data-driven identification of a biomarker for dysphoria (called reward positivity) derived from the functional predictor. Our proposed method outperforms competitors based on unrestricted single-index models and is therefore the more practical choice for analysis. We examine the properties of our method through a simulation study and a Bayesian analysis of a study of adolescent dysphoria (a bounded response) and a functional neural covariate.
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