PARAMETER ESTIMATION FOR LOW‐ORDER AUTO‐REGRESSIVE MODELS WITH MISSING VALUES

Abstract

Summary Longitudinal data analysis in epidemiological settings is complicated by large multiplicities of short time series and the occurrence of missing observations. To handle such difficulties Rosner & Muñoz (1988) developed a weighted non‐linear least squares algorithm for estimating parameters for first‐order autoregressive (AR1) processes with time‐varying covariates. This method proved efficient when compared to complete case procedures. Here that work is extended by (1) introducing a different estimation procedure based on the EM algorithm, and (2) formulating estimation techniques for second‐order autoregressive models. The second development is important because some of the intended areas of application (adult pulmonary function decline, childhood blood pressure) have autocorrelation functions which decay more slowly than the geometric rate imposed by an AR1 model. Simulation studies are used to compare the three methodologies (non‐linear, EM based and complete case) with respect to bias, efficiency and coverage both in the presence and in the absence of time‐varying covariates. Differing degrees and mechanisms of missingness are examined. Preliminary results indicate the non‐linear approach to be the method of choice: it has high efficiency and is easily implemented. An illustrative example concerning pulmonary function decline in the Netherlands is analyzed using this method.