Bayesian Multi-Level Quantile Regression for Longitudinal Data

• Activity Number: 647
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Chih-Chieh Chang* and Kiros Berhane
• Companies: University of Southern California and University of Southern California
• Keywords: Bayesian ; Mixed effects regression ; Quantile regression ; Longitudinal Data

Abstract

Conventional mixed effects regression focuses only on effects on the conditional mean, which may be inappropriate when the interest is in testing the effects on extremes of the outcome distribution (e.g. BMI at the 85th percentile). We propose a multilevel quantile regression model with errors following the Asymmetric Laplace Distribution with a data-driven skew parameter under a Bayesian framework. Using our approach, the estimates of parameters would be unbiased regardless of the structure of random errors. This approach allows 1)direct modeling of risk effects with higher accuracy, 2)characterizing inter-subject heterogeneity, 3)accounting for cross-level effects, and 4)modeling non-linear growth trajectories in longitudinal/multi-level data. Besides deriving analytic solutions with improved properties, we conducted simulations to show that our proposed approach consistently provided appropriate estimates at extreme percentiles even when dealing with heteroscedastic errors, and multiple random effects from various levels. We illustrate the new approach through analysis of longitudinal BMI to model determinants of overweight status based on data from the Children's Health Study.