Pragmatic model transformations for analyzing bounded and positive responses

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 m...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2023-02, Vol.419, p.114682, Article 114682
Main Authors: Tourani-Farani, Fahimeh, Kazemi, Iraj
Format: Article
Language:English
Subjects:
Beta regression
IRLS-type algorithm
Log-symmetric
Simplex regression
Symmetric distributions
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114682