GAM Specifications - Quick Tab

Click the Variables button to display a standard variable selection dialog box, where you can specify 1) the dependent variable, 2) categorical predictor variables, 3) continuous predictor variables, and 4) count (weight) variable. Note that the limit on the maximum number of observations is 200,000.

Specify the two codes that identify the two groups in the dependent variable in the Code for dependent variable fields. If you are not sure about the codes that were used in the dependent variable to identify the groups, double-click on the edit field (or press the F2 key on your keyboard), and a Variable Code Window will be displayed containing all integer codes and their alphanumeric equivalents found in the grouping variable in the current data file. You can select a grouping code in this dialog (i.e., transfer it to the edit field) by double-clicking on it.

During the analysis, all dependent variable values (codes) equal to the code entered into the first edit field will be recoded to 0 (zero); all dependent variable values (codes) equal to the code entered into the second field will be recoded to 1 (one). Thus, when interpreting the predicted values, partial residuals, and related statistics, remember that these are computed with respect to this coding, e.g., in the observational statistics, the closer a predicted value is to 1, the greater is the predicted probability that the respective case belongs to the category identified by the code in the second field. Note that this option is only available if the distribution for the dependent variable is Binomial (as selected in the Distribution list on the Generalized Additive Models Startup Panel - Quick tab).

Click the Factor codes button to display the Select Codes for Categorical Independent Variables dialog box, which is used to specify the codes that were used in the respective (categorical or grouping) variables to identify to which group each case belongs. Note that this option is only available if categorical predictor variables where specified.

Click the DF of covariates button to display the Degree of Freedom Values dialog box, which is used to specify the degrees of freedom for the cubic spline smoother that will be applied to each predictor variable. The fewer degrees of freedom you specify, the smoother is the cubic spline fit to the partial residuals, and typically, the worse is the overall fit of the model. The issue of degrees of freedom for smoothers is discussed in detail in Hastie and Tibshirani (1990).

As described in the Introductory Overview, the generalized additive models approach applies a cubic spline scatterplot smoother to each predictor (the scatterplot of each predictor against the partial residuals). When estimating a single parameter value, we lose one degree of freedom, i.e., we add one degree of freedom to the overall model. It is not clear how many degrees of freedom are lost due to estimating the cubic spline smoother for each variable. Intuitively, a smoother can either be very smooth, not following the pattern of data in the scatterplot very closely, or it can be less smooth and more closely following the pattern of the data.  In the most extreme case, a simple line would be very smooth, and require us to estimate a single slope parameter, i.e., we would use one degree of freedom to fit the smoother (simple straight line); on the other hand, we could force a very "non-smooth" line to connect each actual data point, in which case we would "use-up" approximately as many degrees of freedom as there are points in the plot.