Modeling and Multivariate Methods - SAS

Chapter 9 Performing Nonlinear Regression 243
Introduction to the Nonlinear Platform
Introduction to the Nonlinear Platform
The Nonlinear platform fits models that are nonlinear in the parameters. The Fit Curve personality of the
platform has a variety of predefined models, such as polynomial, logistic, Gompertz, exponential, peak, and
pharmacokinetic models.
You can also fit custom nonlinear models by specifying the model formula and parameters to be estimated.
The models can be fit using the default least squares loss function or a custom loss function. The platform
minimizes the sum of the loss function across the observations.
Specifying a grouping variable lets you estimate separate model parameters for each level of the grouping
variable. The fitted models and estimated parameters can be compared across the levels of the grouping
variable.
The Nonlinear platform is a good choice for models that are nonlinear in the parameters. Some models are
linear in the parameters (for example, a quadratic or other polynomial) or can be transformed to be such
(for example, when you use a log transformation of x). The Fit Model or Fit Y by X platforms are more
appropriate in these situations. For more information about these platforms, see the Basic Analysis and
Graphing book.
Example of Nonlinear Fitting
You have data on toxicity levels of a drug. You want to build a model for toxicity as a function of the
concentration of the drug. There are four formulations of the drug to compare. Follow the steps below:
1. Open the Bioassay.jmp sample data table.
2. Select Analyze > Modeling > Nonlinear.
3. Assign Toxicity to the Y, Response role.
4. Assign log Conc to the X, Predictor Formula role.
5. Assign Formulation to the Group role.
6. Click OK.
7. Select Sigmoid Curves > Logistic Curves > Fit Logistic 4P from the Fit Curve red triangle menu.
A portion of the report is shown in Figure 9.2.