Getting Started | SAS/STAT 9.1 Users Guide Volume 2 only

The following example illustrates the use of the GAM procedure to explore in a nonparametric way how two factors affect a response. The data come from a study (Sockett et al. 1987) of the factors affecting patterns of insulin-dependent diabetes mellitus in children. The objective is to investigate the dependence of the level of serum C-peptide on various other factors in order to understand the patterns of residual insulin secretion. The response measurement is the logarithm of C-peptide concentration (pmol/ml) at diagnosis, and the predictor measurements are age and base deficit (a measure of acidity):

  title 'Patterns of Diabetes;   data diabetes;   input Age BaseDeficit CPeptide @@;   logCP = log(CPeptide);   datalines;   5.2   8.1  4.8   8.8   16.1  4.1  10.5   0.9  5.2   10.6   7.8  5.5  10.4   29.0  5.0   1.8   19.2  3.4   12.7   18.9  3.4  15.6   10.6  4.9   5.8   2.8  5.6   1.9   25.0  3.7   2.2   3.1  3.9   4.8   7.8  4.5   7.9   13.9  4.8   5.2   4.5  4.9   0.9   11.6  3.0   11.8   2.1  4.6   7.9   2.0  4.8  11.5   9.0  5.5   10.6   11.2  4.5   8.5   0.2  5.3  11.1   6.1  4.7   12.8   1.0  6.6  11.3   3.6  5.1   1.0   8.2  3.9   14.5   0.5  5.7  11.9   2.0  5.1   8.1   1.6  5.2   13.8   11.9  3.7  15.5   0.7  4.9   9.8   1.2  4.8   11.0   14.3  4.4  12.4   0.8  5.2  11.1   16.8  5.1   5.1   5.1  4.6   4.8   9.5  3.9   4.2   17.0  5.1   6.9   3.3  5.1  13.2   0.7  6.0   9.9   3.3  4.9   12.5   13.6  4.1  13.2   1.9  4.6   8.9   10.0  4.9   10.8   13.5  5.1   ;   run;

The following statements perform the desired analysis. The PROC GAM statement invokes the procedure and specifies the diabetes data set as input. The MODEL statement specifies logCP as the response variable and requests that univariate smoothing splines with the default of 4 degrees of freedom be used to model the effect of Age and BaseDeficit .

  title 'Patterns of Diabetes';   proc gam data=diabetes;   model logCP = spline(Age) spline(BaseDeficit);   run;

The results are shown in Figure 30.1 and Figure 30.2.

  Patterns of Diabetes   The GAM Procedure   Dependent Variable: logCP   Smoothing Model Component(s): spline(Age) spline(BaseDeficit)   Summary of Input Data Set   Number of Observations                  43   Number of Missing Observations           0   Distribution                      Gaussian   Link Function                     Identity   Iteration Summary and Fit Statistics   Final Number of Backfitting Iterations                    5   Final Backfitting Criterion                    5.542745E-10   The Deviance of the Final Estimate             0.4180791724

Figure 30.1: Summary Statistics

  Patterns of Diabetes   The GAM Procedure   Dependent Variable: logCP   Smoothing Model Component(s): spline(Age) spline(BaseDeficit)   Regression Model Analysis   Parameter Estimates   Parameter       Standard   Parameter                 Estimate          Error    t Value    Pr > t   Intercept                  1.48141        0.05120      28.93      <.0001   Linear(Age)                0.01437        0.00437       3.28      0.0024   Linear(BaseDeficit)        0.00807        0.00247       3.27      0.0025   Smoothing Model Analysis   Fit Summary for Smoothing Components   Num   Smoothing                                      Unique   Component                 Parameter              DF             GCV         Obs   Spline(Age)                0.995582        3.000000        0.011675          37   Spline(BaseDeficit)        0.995299        3.000000        0.012437          39   Smoothing Model Analysis   Analysis of Deviance   Sum of   Source                          DF         Squares    Chi-Square    Pr > ChiSq   Spline(Age)                3.00000        0.150761       12.2605        0.0065   Spline(BaseDeficit)        3.00000        0.081273        6.6095        0.0854

Figure 30.2: Analysis of Model

Figure 30.1 shows two tables. The first table summarizes the input data set and the distributional family used for the model, and the second one summarizes the convergence criterion for backfitting.

Figure 30.2 displays summary statistics for the model. It consists of three tables. The first is the Parameter Estimates table for the parametric part of the model. It indicates that the linear trends for both Age and BaseDeficit are highly significant. The second table is the summary of smoothing components of the nonparametric part of the model. By default, each smoothing component has approximately 4 degrees of freedom (DF). For univariate spline components, one DF is taken up by the (parametric) linear part of the model, so the remaining approximate DF is 3, and the main point of this table is to present the smoothing parameter values that yield this DF for each component. Finally, the third table shows the Analysis of Deviance table for the nonparametric component of the model.

In order to explore the overall shape of the relationship between each factor and the response, use the experimental graphics features of PROC GAM to plot the partial predictions .

  ods html;   ods graphics on;   proc gam data=diabetes;   model logCP = spline(Age) spline(BaseDeficit);   run;   ods graphics off;   ods html close;

These graphical displays are requested by specifying the experimental ODS GRAPHICS statement. For general information about ODS graphics, see Chapter 15, Statistical Graphics Using ODS. For specific information about the graphics available in the GAM procedure, see the section ODS Graphics on page 1581.

Figure 30.3: Partial Predictions for each Predictor (Experimental)

Both plots show a strong quadratic pattern, with a possible indication of higher-order behavior. Further investigation is required to determine whether these patterns are real or not.