Generalized Method of Moments Optimal Instrument Theory Applied to Generalized Linear Mixed Models Under Informative Sampling

• Activity Number: 70
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Mariana Saenz*
• Companies: Georgia Southern University
• Keywords: Generalized Linear Mixed Models ; Generalized Method of Moments ; Informative Sampling

Abstract

This paper derives the fixed-effects Generalized Method of Moments (GMM) estimator in Generalized Linear Mixed Models (GLMM) models in the presence of informative sampling. Optimal instrument GMM theory is used to find the consistent and asymptotically normal estimator of the fixed-effects in GLMM models in the presence of informative sampling. A simulation for a Logistic regression with a random effect is conducted to evaluate the fixed-effect estimator in the presence of informative sampling. In the simulation, four additional estimators were calculated to evaluate the fixed-effect GMM estimator proposed. The four estimators used for comparison were the classical weighted estimator, an unweighted estimator, and two different scaled weighting estimators. Simulation results show that the fixed-effects GMM estimators are consistent in the presence of informative sampling. However, the tradeoff in obtaining consistent estimators results in greater variance for the fixed-effects GMM estimators.