A partial prediction (component) plot shows you the shape of the association between the predictor and the response. If a SPLINE smoother is applied to a predictor, there are separate linear and nonlinear components added to the model. For more information, see this note. In the GAM documentation, the plots in the "Getting Started" section example and in the example titled "Generalized Additive Model with Binary Data" in the Examples section (kyphosis data) show quadratic associations of the predictors with the response. In the kyphosis example this leads to a final model, fit using PROC GENMOD, which includes quadratic effects for the predictors.

For a spline-smoothed predictor, X, you can generate a plot of the predictor's nonlinear effect only or a plot of its combined linear and nonlinear effects. The nonlinear effect plot is a plot of the predictor's partial prediction variable (P_X) in the OUTPUT statement's OUT= data set against the original variable (X). The combined effect adds the linear effect to the nonlinear effect:

     Pcombined_X = Linear(X)*X + P_X;

where Linear(X) is the parameter estimate associated with X that is displayed in the "Regression Model Analysis - Parameter Estimates" table. The combined plot is created by plotting Pcombined_X against X. These plots can be created using the PLOTS= option in the PROC GAM statement. The option PLOTS=COMPONENTS produces the plot of the nonlinear effect. The option PLOTS=COMPONENTS(ADDITIVE) produces the plot of the combined linear and nonlinear effects. However, for the additive component plot, an additional amount (Linear(X)*mean(X)) is subtracted from Pcombined_X to help center the plot. See "Estimates from PROC GAM" in the Details section of the GAM documentation.

If a spline-smoothed predictor has only a linear association, then the nonlinear curve will be a flat line (indicating no nonlinear association with the response) and the combined curve will be a straight line (indicating only a linear association). If the predictor has some nonlinear association with the response, then the nonlinear portion of it is captured in the plot of P_X.

Additional discussion and another example can be found in this article.

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