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Predictive and Specialized Modeling > Nonlinear Regression
Publication date: 07/24/2024

Nonlinear Regression

Fit Custom Nonlinear Models to Your Data

The Nonlinear platform is a good choice for models that are nonlinear in the parameters. This chapter focuses on custom nonlinear models, which include a model formula and parameters to be estimated. Use the default least squares loss function or a custom loss function to fit models. The platform minimizes the sum of the loss function across the observations.

Figure 15.1 Example of a Custom Nonlinear Fit 

Example of a Custom Nonlinear Fit

The Nonlinear platform also provides predefined models, such as polynomial, logistic, Gompertz, exponential, peak, and pharmacokinetic models. See “Fit Curve”.

Note: 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 “Model Specification” in Fitting Linear Models and “Introduction to Fit Y by X” in Basic Analysis.

Contents

Example of the Nonlinear Platform

Launch the Nonlinear Platform

The Nonlinear Fit Report

Nonlinear Platform Options

Create a Formula Using the Model Library

Customize the Nonlinear Model Library

Additional Examples of the Nonlinear Platform

Example of Maximum Likelihood
Example of a Probit Model with Binomial Errors
Example of a Poisson Loss Function
Example of Setting Parameter Limits
Example of Analyzing Left-Censored Data
Example of Fitting a Weibull Loss Function
Example of Fitting Simple Survival Distributions

Statistical Details for the Nonlinear Platform

Statistical Details for Profile Likelihood Confidence Limits
Statistical Details for Custom Loss Functions
Statistical Details on Derivatives
Statistical Details on Effective Nonlinear Modeling
Want more information? Have questions? Get answers in the JMP User Community (community.jmp.com).