Paper presented at the 26th Annual Southern African Transport Conference 9 - 12 July 2007 "The challenges of implementing policy?", CSIR International Convention Centre, Pretoria, South Africa.
ABSTRACT:Robust regression and local polynomial smoothing are applied to the inverse problem for the logistic differential equation (DE) model, in order to develop a more objective, accurate and automatable trends model. A method of inferring the time shift parameter is proposed and applied, allowing the closed form solution of the DE to be used for the prediction of ownership levels in Johannesburg.
A simulation study is employed to verify and evaluate the application of non-linear regression to the inverse problem. It is demonstrated that considerable improvements in accuracy, over the transformation to linear-form method, can be obtained. However, on application to actual data, the non-linear regression algorithm fails to converge.
The appropriateness of the methods in the case of lower asymptote and early growth phase data, and heterogeneous populations are investigated by simulation.
