MODEL response <(responseoptions)> = <PARAM(effects)> <splineeffects> </ modeloptions>;
MODEL events / trials = <PARAM(effects)> <splineeffects> </ modeloptions>;
The MODEL statement specifies the response (dependent or target) variable and the predictor (independent or explanatory) effects of the model. You can specify the response in the form of a single variable or in the form of a ratio of two variables, which are denoted events/trials. The first form applies to all distribution families; the second form applies only to summarized binomial response data. When you have binomial data, the events variable contains the number of positive responses (or events) and the trials variable contains the number of trials. The values of both events and (trials – events) must be nonnegative, and the value of trials must be positive. If you specify a single response variable that is in a CLASS statement, then the response is assumed to be binary.
You can specify parametric effects that are constructed from variables in the input data set and include the effects in the parentheses of a PARAM( ) option, which can appear multiple times. For information about constructing the model effects, see the section Specification and Parameterization of Model Effects.
You can specify splineeffects by including independent variables inside the parentheses of the SPLINE( ) option. Only continuous variables (not classification variables) can be specified in splineeffects. Each splineeffect can have at least one variable and optionally some splineoptions . You can specify any number of splineeffects. The following table shows some examples.
Table 7.3: continued
Spline Effect Specification 
Meaning 


Constructs the univariate spline with 

Constructs the univariate spline by using 

Constructs the bivariate spline by using 

Constructs the trivariate spline by using 
Both parametric effects and spline effects are optional. If none are specified, a model that contains only an intercept is fitted. If only parametric effects are present, PROC GAMPL fits a parametric generalized linear model by using the terms inside the parentheses of all PARAM( ) terms. If only spline effects are present, PROC GAMPL fits a nonparametric additive model. If both types of effects are present, PROC GAMPL fits a semiparametric model by using the parametric effects as the linear part of the model.
There are three sets of options in the MODEL statement. The responseoptions determine how the GAMPL procedure models probabilities for binary data. The splineoptions controls how each spline term forms basis expansions. The modeloptions control other aspects of model formation and inference. Table 7.4 summarizes these options.
Table 7.4: MODEL Statement Options
Option 
Description 

Response Variable Options for Binary Models 

Reverses the response categories 

Specifies the event category 

Specifies the sort order 

Specifies the reference category 

Smoothing Options for Spline Effects 

Requests detailed spline information 

Specifies the fixed degrees of freedom 

Specifies the starting value for the smoothing parameter 

Specifies the knots to be used for constructing the spline 

Specifies polynomial orders for constructing the spline 

Specifies the maximum degrees of freedom 

Specifies the maximum number of knots to be used for constructing the spline 

Specifies the upper bound for the smoothing parameter 

Specifies the lower bound for the smoothing parameter 

Specifies a fixed smoothing parameter 

Model Options 

Requests all nonmissing values of spline variables for constructing spline basis functions regardless of other model variables 

Specifies the model evaluation criterion 

Specifies the fixed dispersion parameter 

Specifies the response distribution 

Requests a finitedifference Hessian for smoothing parameter selection 

Specifies the starting value of the dispersion parameter 

Specifies the link function 

Requests normalized spline basis functions for model fitting 

Specifies the upper bound for searching the dispersion parameter 

Specifies the algorithm for selecting smoothing parameters 

Specifies the lower bound for searching the dispersion parameter 

Specifies the offset variable 

Specifies the ridge parameter 

Specifies the method for estimating the dispersion parameter 
Response variable options determine how the GAMPL procedure models probabilities for binary data.
You can specify the following responseoptions by enclosing them in parentheses after the response variable.