Quantile regression via vector generalized additive models.
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.
Yee
Thomas W
TW
Department of Statistics, University of Auckland, Private Bag 92019, Auckland 1001, New Zealand. statwy@stat.nus.edu.sg, t.yee@auckland.ac.nz
D000293:Adolescent; D000328:Adult; D000367:Age Factors; D015992:Body Mass Index; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D015233:Models, Statistical; D009520:New Zealand; D044382:Population Groups; D012044:Regression Analysis; D012737:Sex Factors