Quantile Regression for Repeated Responses Measured with Error

• Activity Number: 495
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Pedro Torres-Saavedra*+ and Huixia Judy Wang and Daowen Zhang
• Companies: and North Carolina State University and North Carolina State University
• Keywords: Quantile regression ; Semi-Nonparametric Distribution ; Measurement Error

Abstract

Some problems in biostatistics involve a response variable that is difficult to measure. Muscular strength, usually quantified through the grip strength, is an example of such variables. Often several measurements of the grip strength with considerable measurement error are taken on the same subject. A research interest is to estimate the conditional quantiles of the latent response variable. Naively replacing the latent response variable by the subject-specific average of the contaminated replicates in a conventional quantile regression model could lead to serious bias in the quantile estimates. Therefore, we propose a semi-nonparametric approach to estimate the conditional quantiles of a latent response variable which allows the subject random effects to follow a flexible distribution. We apply the proposed method to a grip strength data set and compare it to the conventional approach. Using statistical theory and simulation studies, we argue that our method outperforms the conventional approach. We also demonstrate through simulation studies that the proposed method leads to consistent estimates of the conditional quantiles of a latent response variable.