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Title: Quantile regression via vector generalized additive models
Authors: Yee, T.W. 
Keywords: Age-reference centile analysis
Gaussian quadrature
LMS quantile regression
Penalized likelihood
S language
Vector generalized additive models
Vector generalized linear models
Vector splines
Yeo-Johnson transformation
Issue Date: 30-Jul-2004
Citation: Yee, T.W. (2004-07-30). Quantile regression via vector generalized additive models. Statistics in Medicine 23 (14) : 2295-2315. ScholarBank@NUS Repository.
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 method is illustrated by way of a large cross-sectional data set from a New Zealand working population. Copyright © 2004 John Wiley & Sons, Ltd.
Source Title: Statistics in Medicine
ISSN: 02776715
DOI: 10.1002/sim.1822
Appears in Collections:Staff Publications

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