Inverse Estimation with Random Coefficient Models and Its Implementation in R

• Activity Number: 645
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Brandon Greenwell*+ and Christine Schubert Kabban
• Companies: AFIT and Air Force Institute of Technology
• Keywords: Calibration ; Random coefficient model ; Bootstrap ; investr ; Calibration ; Linear mixed-effects model

Abstract

Inverse estimation is a classical and well known problem in regression. In simple terms, it involves the use of an observed value of the response to make inference on the corresponding unknown value of the explanatory variable. In this talk, we consider inverse estimation with random coefficient models. First, we briefly discuss point estimation and confidence intervals for the unknown predictor value. Then, we propose an alternative method based on a parametric bootstrap. The parametric bootstrap method is preferable because it takes into account the variability of the estimated variance components. The proposed bootstrap algorithm can be viewed as a parametric version of that proposed in Jones and Rocke (1999) extended to random coefficient models. We illustrate these methods on real data using the R packages investr and lme4.