The Effect of Reparameterisation on the Behaviour of Nonlinear Estimates - Mohamed Ramli, Norazan (2000)
This thesis discussed nonlinear modeling and measures o f nonlinear behaviour. A set of data, representing the average weight of dried to bacco leaves (in Several nonlinear models were used to fit the data, however only the Gompertz and the Logistic models were found to be suitable. The estimates of the para meters were calculated by using the Gauss-Ne wton algorithm in SPLUS Programming Language. A good estimator was the one which had the proper ties closed to the behaviour of a ilnear estimate . The non ilnear behaviour of the estimates was assessed using two different approaches, namely the analytical and the empirical approaches. These approaches were employed so that they could complement the existence of any laggings. The study showed that the analytical approach of curvature measures of Bates and Watts could measure the average nonlinearity but could not determine the parameters that cause d the nonlinear behaviour. Mean while, the bias formula of Box could only give the percentage of the extent to which the parameter estimates may exceed or fall short of the true parameter value, but could not be used to compare different parameterizations. An advantage of using direct measure of skewness of Hougaard was that it was scale-in dependent and could be used to measure nonlinearity in different parameterizations. The empirical approach of simulation studies had successfully revealed the full extent of the nonlinear behaviour of the estimates an d at the same time, suggested useful reparameterizations. Reparameterization was used in order to remove or reduce the nonlinear behaviour of the parameter estimates. The study showed that the nonlinear behaviour of the parameter estimates was successfully reduced after reparameterization. The Logistic model in a reparameterized model function was found to best fit the data as it has the lo therefore the closest-to-linear behaviour.