Autoregressive growth curves and Kalman filtering

Abstract

The first part of this paper describes how a Kalman filter can be used to construct maximum likelihood (ML) estimates of autoregressive (AR) and polynomial parameters in polynomial growth curves with AR-1 errors and irregularly-spaced data. The second part introduces a disturbed highest derivative polynomial (DHDP) as a model for growth curves. This model does not depend on regression coefficients. Variances of the highest derivative disturbance and the observation error are estimated (by ML) using a Kalman filter. The estimated DHDP growth curve is obtained by optimally smoothing the output of the filter. Equally spaced data is not required. The DHDP model and analysis are developed for an individual and extended to a population growth curve using data from many individuals with covariates.