Regression Parameters as Outcomes: Simple vs. Sophisticated Analyses

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Reid D. Landes*+
• Companies: University of Arkansas for Medical Sciences
• Keywords: bias ; mean square error ; coverage probability ; heterogeneity of variance ; random coefficients regression ; hierarchical model

Abstract

Sometimes a regression parameter for an individual is the outcome of interest. Heterogeneity in the precision with which the individuals' parameters are estimated complicates the ultimate goal of estimating population-level parameters with two usual methods: (1) the simple arithmetic mean of individually estimated regression parameters and (2) random coefficients regression (RCR). We propose weights for each method to account for the heterogeneity problem. The methods are illustrated with a behavioral economic problem. Monte Carlo simulation allows us to compare statistical properties of the four estimators for small, moderate and large sample sizes. Estimators from RCR methods have better mean square error than arithmetic mean estimators, but bias in RCR estimates can reduce actual coverage probabilities below nominal levels. We provide recommendations on which method to use and when.