title: Flexible link functions in nonparametric binary regression with Gaussian process priors.
abstract: In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function.
authors.affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.
authors.forename: Dan
authors.initials: D
authors.lastname: Li
authors.affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.. xia.wang@uc.edu.
authors.forename: Xia
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Statistics and Data Sciences, University of Texas at Austin, Austin, Texas 78712, U.S.A.
authors.forename: Lizhen
authors.initials: L
authors.lastname: Lin
authors.affiliation: Department of Statistics, University of Connecticut, Storrs, Connecticut 06269, U.S.A.
authors.forename: Dipak K
authors.initials: DK
authors.lastname: Dey
mesh_terms: D000818:Animals; D055008:Anthracosis / Q000175:diagnosis / Q000209:etiology; D003032:Coal Mining / Q000706:statistics & numerical data; D003198:Computer Simulation / Q000706:statistics & numerical data; D046690:Deep Brain Stimulation / Q000706:statistics & numerical data; D005221:Fatigue / Q000628:therapy; D000882:Haplorhini; D006801:Humans; D015233:Models, Statistical; D016011:Normal Distribution; D011237:Predictive Value of Tests; D012044:Regression Analysis; D018709:Statistics, Nonparametric
keywords: Flexibility; Gaussian process; Generalized extreme value distribution; Latent variable; Markov chain Monte Carlo; Posterior consistency