Quantile regression via vector generalized additive models

Statistics in Medicine
Thomas W Yee

Abstract

One of the most popular methods for quantile regression is the LMS method of Cole and Green. The method naturally falls within a penalized likelihood framework, and consequently allows for considerable flexible because all three parameters may be modelled by cubic smoothing splines. The model is also very understandable: for a given value of the covariate, the LMS method applies a Box-Cox transformation to the response in order to transform it to standard normality; to obtain the quantiles, an inverse Box-Cox transformation is applied to the quantiles of the standard normal distribution. The purposes of this article are three-fold. Firstly, LMS quantile regression is presented within the framework of the class of vector generalized additive models. This confers a number of advantages such as a unifying theory and estimation process. Secondly, a new LMS method based on the Yeo-Johnson transformation is proposed, which has the advantage that the response is not restricted to be positive. Lastly, this paper describes a software implementation of three LMS quantile regression methods in the S language. This includes the LMS-Yeo-Johnson method, which is estimated efficiently by a new numerical integration scheme. The LMS-Yeo-Johnson...Continue Reading

Citations

Aug 21, 2013·Reproductive Biomedicine Online·Amir WiserTogas Tulandi
Jul 7, 2016·NeuroImage·R GuerreroUNKNOWN Alzheimer's Disease Neuroimaging Initiative (ADNI)
Apr 21, 2016·PloS One·Alexander Schmidt-RichbergUNKNOWN Alzheimer’s Disease Neuroimaging Initiative
Oct 20, 2018·Journal of Clinical Medicine·Chia-Hui ChangVin-Cent Wu
Jan 1, 2009·Electronic Journal of Statistics·David RuppertRaymond J Carroll

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