STOCHASTIC GROWTH CURVE ANALYSIS

The problem of modelling growth is considered from the biological and statistical points of view leading to a list of desirable features for a class of growth models. A flexible class of growth models is proposed which has a biological basis, is theoretically tractable and is suitable for recursive fitting techniques. The class is based on empirical stochastic differential equations. Procedures are outlined for identifying the model to be fitted within the class and detecting changes of phase in the underlying growth mechanism. The models are fitted using the recursive procedure of Brown, Durbin and Evans (1975), extended by McGilchrist and Sandland (1979). The method of scoring is developed for estimation of the correlation parameters in the case of autocorrelation in the residuals and the use of the independent recursive residuals obtained from the procedure is outlined. The recursive scoring algorithm for the case of the residuals forming a first order Markov process is presented in an appendix. Several uses of the model are presented in the last section showing all the procedures applied to data on single individuals covering plant, human and animal growth.