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Title: Bayesian hierarchical functional regression model for ordinal responses with flexible link functions Authors:  Jangwon Lee - Korea University (Korea, South) [presenting]
Taeryon Choi - Korea University (Korea, South)
Abstract: In the field of functional regression research, the study of ordinal functional response has many limitations compared to other types of functional responses. We propose a Bayesian hierarchical functional regression model with flexible link functions. To derive a posterior sampling scheme, we use a latent variable that is categorized by the cut-off points. The latent variable is modeled by a Bayesian functional mixed effect model based on the spectral representation of Gaussian processes. We assume a hierarchical structure on the spectral coefficient to deal with a global mean curve, group curves, and subject-specific curves. In ordinal regression, probit or logit are commonly used in a link function. But these link functions correct the skewness of response probability. To overcome this limitation, we adopt various types of link functions, such as complementary-log-log, generalized extreme value, and symmetric power link functions. Also, we consider a shape restriction on the nonparametric terms, such as monotone increasing and monotone decreasing, to better predict the probability of a response. We illustrate simulation examples and real applications to air quality index (AQI) data.