Longitudinal data analysis: Non-stationary error structures and antedependent models

Non-stationary covariance structures had not been analyzed in detail for longitudinal data mainly because the existing applications did not require their use. Data from the Iowa Cochlear Implant Project showed this type of structure and the problem needed to be addressed. We propose a linear model for longitudinal data in which the correlation structure includes the Box-Cox transformation of the time scale. This transformation can produce nonstationary covariance structures within subjects, with stationarity as a special case. Restricted maximum likelihood methods for parameter estimation (REML) are discussed and the method is applied to speech recognition data from the Iowa Cochlear Implant Project. The growth curve for this audiologic performance measure is shown. Possible extensions for the model are suggested. (C) 1998 John Wiley & Sons, Ltd.