Pragmatic model transformations for analyzing bounded and positive responses

Abstract

Extensions of modeling continuously bounded and positive responses in regression contexts are often prominent. Most regression techniques incorporate a response transformation to improve underlying model fittings. A further challenge is, however, demanding to promise the transformation success. It motivated us to introduce a novel modeling strategy using the generalized Johnson system of transformations. We propose joint regression modeling of the median and precision parameters by exploiting various invertible transformations and link functions. It offers a convenient alternative to several regression models, including the normal, the popular Beta for bounded, and the log-symmetric for positive responses. Other attractive features include the iteratively reweighted-least-squares algorithm (IRLS) development to facilitate computational aspects and robust residual diagnostics to detect outlying points. Monte Carlo simulations and analysis of three real-life data sets illustrate the usefulness of our modeling strategy.