Nonparametric and Semiparametric M-Quantile Inference for Longitudinal Data

• Activity Number: 551
• Type: Invited
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Nikos Tzavidis and Nicola Salvati and Hukum Chandra and Raymond Chambers*+
• Companies: CSSR and DSMAE and IASRI and CSSM
• Keywords: M-quantile regression ; Quantile regression ; Spline regression ; Mixed models ; Hierarchical data ; Random effects

Abstract

M-quantile regression is used to model the M-quantiles of the conditional distribution of an outcome variable given a set of covariates. An M-quantile random effects model allows one to account for data with hierarchical structure, e.g. longitudinal data, when modelling these M-quantiles. When the functional form of the relationship between the response variable and the covariates is unknown or is complicated, an approach based on use of a penalized spline approximation can offer signi?cant advantages compared with one based on a linear model. In this paper we extend the M-quantile random effects model to nonparametric regression, in the sense that the M-quantile regression functions are estimated from the data using penalised spline approximations. Maximum likelihood estimation for this model is described and then evaluated via simulation studies as well as by a real world application.