Specialized Models • Nonlinear Regression with Built-In Models • Introduction to the Nonlinear Fit Curve Personality
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Introduction to the Nonlinear Fit Curve Personality
Some models are linear in the parameters (for example, a quadratic or other polynomial); others 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 example, in the Fit Model chapter of Fitting Linear Models, there was a significant linear relationship between oxygen uptake and time spent running. For more information about Fit Model, see Fitting Linear Models. For more information about Fit Y by X, see the Basic Analysis book.
The Nonlinear platform is the place to fit models that are nonlinear in the parameters. This chapter shows the analysis of a nonlinear relationship: drug toxicity as a function of concentration. The effect of concentration on toxicity changes from low to high doses, so this relationship is nonlinear.
The following are examples of equations for linear and nonlinear functions.
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Linear function: Y=β0+β1ex
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Nonlinear function: Y=β0+β1eβ2x
The Nonlinear platform’s Fit Curve personality provides predefined models, such as polynomial, logistic, Gompertz, exponential, peak, and pharmacokinetic models. 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.
Fit Curve also enables you to build a model to create the prediction formula. Then you set upper and lower parameter limits in Nonlinear. For details, see Example of Setting Parameter Limits in Nonlinear Regression with Custom Models.