Quantile Regression Extended to Mixed Models

• Activity Number: 73
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Michelle Quinlan*+ and Walt Stroup
• Companies: University of Nebraska-Lincoln and University of Nebraska-Lincoln
• Keywords: quantile regression ; random effects

Abstract

Quantile regression involves modeling with the goal of examining how covariates influence a quantile of the response distribution, without any distributional assumptions. The relationship between explanatory variables and a quantile of the response is allowed to change depending on the quantile of interest, unlike regression on the mean. Quantile regression solutions minimize an asymmetrically weighted sum of absolute errors. While theory for quantile regression with fixed effects has been developed, there is no analogous methodological framework for quantile regression with random effects. Theory and methodology for mixed model quantile regression is discussed along with the rationale for modeling quantiles of the distribution when effects are treated as random. Applications are discussed, including using quantile regression with random batch effects to estimate shelf life.