The GAM Procedure
- Overview
- Getting Started
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Syntax
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DetailsMissing ValuesNonparametric RegressionAdditive Models and Generalized Additive ModelsForms of Additive ModelsEstimates from PROC GAMBackfitting and Local Scoring AlgorithmsSmoothersSelection of Smoothing ParametersConfidence Intervals for SmoothersDistribution Family and Canonical LinkDispersion ParameterComputational ResourcesODS Table NamesODS Graphics
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Examples
- References
PROC GAM provides the capability to fit both nonparametric and semiparametric models. So that you can better understand the underlying trend of any given factor, PROC GAM separates the linear trend from any general nonparametric trend during the fitting as well as in the final report. This makes it easy to determine whether the significance of a smoothing variable is associated with a simple linear trend or a more complicated pattern.
For example, suppose you want to fit a semiparametric model as
![\[ y = \alpha _0 + \alpha _1z + f_1(x_1)+f_2(x_2) \]](images/statug_gam0033.png){kind=small}
The GAM estimate for this model is
![\[ y = \widehat{\alpha _0} + \widehat{\alpha _1}z + \widehat{\beta _1} x_1 + \widehat{\beta _2} x_2 + \widehat{s_1}(x_1)+ \widehat{s_2}(x_2) \]](images/statug_gam0034.png){kind=small}
where 
and 
are linear-adjusted nonparametric estimates of the 
and 
effects. The p-values for 
are reported in the parameter estimates table. 
and 
are the estimates labeled Linear(x1) and Linear(x2) in the table. The p-values for and are reported in the analysis of deviance table.
Only , , and 
are output to the output data set, with the corresponding variable names P_x1, P_x2, and P_y. For Gaussian data, the complete marginal prediction for variable x1 is:
![\[ \widehat{\beta _1} x_1+\mathrm{P\_ }{x_1} \]](images/statug_gam0043.png){kind=small}
If the additive component plots are requested by the ADDITIVE suboption, the additive component for variable x2 is computed as:
![\[ \widehat{\beta _2} (x_2-\bar{x}_2)+\mathrm{P\_ }{x_2} \]](images/statug_gam0044.png){kind=small}
where 
is the mean for variable x2.