Aassessing Parameters Estimates in Nonlinear Regression Using Profile Plot

Nonlinear regression analysis requires iterative estimation procedures to achieve lest squares solutions. Depending on the form and parameterization of the specified expectation function and the data being considered, these techniques may result in nonlinearity of the estimation situation with respect to one or more parameters. The degree of nonlinearity for each estimated parameter can be assessed by examining profile t plots, whereas the pairwise behavior of parameter estimates is examined using profile pair sketches. The extent of nonlinearity is determined by comparing these plots to those of the corresponding linear estimation situation. These plots may also be used to develop exact likelihood intervals and inference regions for the parameters. Computational procedures to produce the required graphics are reviewed and the application is demonstrated using a two-parameter exponential function.