Estimation in State-Space Models with Exogenous Covariates and Missing Data

• Activity Number: 672
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Arlene Naranjo*+ and Mildred M. Maldonado-Molina and Kelli A. Komro and A. Alexandre Trindade and George Casella
• Companies: University of Florida and University of Florida and University of Florida and Texas Tech University and University of Florida
• Keywords: Kalman filter ; EM algorithm ; panel data ; dynamic linear model ; alcohol abuse

Abstract

A state-space model is proposed for multivariate data collected over time on multiple subjects. The classical model is adjusted to allow missing values in both responses and covariates, handled by a second state-space model nested inside the first. Relevant Kalman recursions are derived and expressions are given for the MLEs of model parameters derived via an EM algorithm. Simulation studies show that the exogenous variables are superfluous in the complete data case but add considerable information in the presence of missing data. The resulting EM algorithm becomes computationally intractable but a modification of the M-step leads to a process shown to be an ECM algorithm. The new procedure appears relatively robust to moderate missingness although some variance parameters are overestimated. The methodology is applied to data from the Project Northland Chicago alcohol prevention study.