On a class of change-point models in covariance structures for growth curves and repeated measurements

Abstract

Models for growth curves or repeated measurements usually consist of a polynomial trend for the mean response plus error terms. We consider a general covariance structure for the errors which includes a class of autoregressive models with ‘change- points’. Such models depend on a small number of parameters, but are of sufficient generality to be useful in practical applications, especially when enviromental or physiological changes on different times lead to nonstationary error processes. Failure to take this into account leads to inefficient estimatiors of the mean trend. The estimation procedure includes both ML and REML methods. The effect of using these methods on the efficiency of the estimation is also studied by theoretical and Monte Carlo methods.

Keywords:

• Growth Curves
• Covariance Structures
• Autoregressive Errors
• Change Point
• ML
• REML

¹On leave of absence working as Statistics and Information Scientist with World Health Organization, European Centre for the Environment and Health, Via Vincenzo Bona 67, 1-00156, Rome, Italy.

¹On leave of absence working as Statistics and Information Scientist with World Health Organization, European Centre for the Environment and Health, Via Vincenzo Bona 67, 1-00156, Rome, Italy.

Notes

¹On leave of absence working as Statistics and Information Scientist with World Health Organization, European Centre for the Environment and Health, Via Vincenzo Bona 67, 1-00156, Rome, Italy.