An EM Algorithm Fitting First-Order Conditional Autoregressive Models to Longitudinal Data

Abstract

An EM algorithm fits a state-space formulation of the longitudinal regression model in which a continuous response depends on the lagged response and both time-dependent and time-independent covariates. The baseline response depends only on covariates. The model handles both missing data and Gaussian measurement error on both response and continuous covariates. The E step uses the Kalman filter and associated filtering algorithms to update the unknown true response and predictor series for the observed data. The M step uses standard closed-form Gaussian results. Standard errors come from the supplemented EM (SEM) algorithm. The model accurately fits 6 years of pulmonary function measurements on 158 children with many missing observations.

Key Words:

• Fixed-interval smoothing algorithm
• Kalman filter
• Measurement error
• Pulmonary function
• SEM algorithm
• State-space model