Chapter 50: The NLIN Procedure

Overview

The NLIN procedure produces least squares or weighted least squares estimates of the parameters of a nonlinear model. Nonlinear models are more difficult to specify and estimate than linear models. Instead of simply listing regressor variables , you must write the regression expression, declare parameter names , and supply initial parameter values. Some models are difficult to fit, and there is no guarantee that the procedure can fit the model successfully.

For each nonlinear model to be analyzed , you must specify the model (using a single dependent variable) and the names and starting values of the parameters to be estimated.

Using PROC NLIN, you can also

• confine the estimation procedure to a certain range of values of the parameters by imposing bounds on the estimates

• produce new SAS data sets containing predicted values, residuals, parameter estimates and SSE at each iteration, the covariance matrix of parameter estimates, and other statistics

• define your own objective function to be minimized

Estimation of a nonlinear model is an iterative process. To begin this process the NLIN procedure first examines the starting value specifications of the parameters. If a grid of values is specified, PROC NLIN evaluates the residual sum of squares at each combination of parameter values to determine the set of parameter values producing the lowest residual sum of squares. These parameter values are used for the initial step of the iteration.

Then PROC NLIN uses one of these five iterative methods :

• steepest-descent or gradient method

• Newton method

• modified Gauss-Newton method

• Marquardt method

These methods use derivatives or approximations to derivatives of the SSE with respect to the parameters to guide the search for the parameters producing the smallest SSE.

You can use the NLIN procedure for segmented models (see Example 50.1) or robust regression (see Example 50.2). You can also use it to compute maximum- likelihood estimates for certain models (refer to Jennrich and Moore 1975; Charnes, Frome, and Yu 1976).