Title: Hilbert regression model for complex responses
Authors: Agnese Maria Di Brisco - University of Piemonte Orientale (Italy) [presenting]
Abstract: In a standard regression model, it is generally assumed that the response is normally distributed. In case the response is a percentage or a rate, i.e., it is defined on a bounded interval, a beta-type regression model is preferable. If the response exhibits further complexities, such as bimodality, heavy tails, and outlying observations, proper regression models have to be tailored. A further source of complexity concerns the nature of the covariates, should they be high-dimensional or functional. To deal with these issues, the proposed regression model is the Hilbert flexible beta regression model. The latter is designed to cope with complex bounded responses being based on a special mixture of betas. Moreover, it accounts for Hilbert covariates, either high-dimensional or functional, with a principal component analysis strategy, whereas the estimation issues are addressed with MCMC techniques. Finally, the selection of the most significant coefficients of the expansion of the Hilbert terms is performed through Bayesian variable selection methods that take advantage of shrinkage priors. The effectiveness of the proposal is illustrated with intensive simulation studies. Results concerning a real application aimed at regressing the percentage of milk fat onto spectrometric curves are also illustrated, showing a fit behavior of the proposed model that is more satisfactory in comparison to competing approaches.