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Abstract:
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We propose a new method for modeling interval data. The relationship between an interval-valued response and a set of interval-valued predictors is investigated by considering a joint regression model, one for the centers (location) of response and predictors, and the other one for the radii (imprecision). Previous works on this problem either can not obtain different regression coefficients for the center and the radii, or they do not consider the dependence between them. Our model overcomes these drawbacks as both the centers and the radii of predictors are used for predicting both the center and the radius of response with the flexibility of identifying the different effects of the center and radius of a predictor on response, along with accounting for the dependence between the center and the radius. We develop a Bayesian estimation method, with an automated feature screening for selecting the most important predictors using "slab and spike" and "local-global shrinkage" priors. We assess the accuracy, precision, and predictive power of the proposed model by simulation studies and analysis of a real-life dataset comparing two standard drugs treating acute lymphocytic leukemia.
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