GAM Summary Results Spreadsheets and Graphs

Click the OK button in the GAM Specifications dialog box to display a series of spreadsheets and graphs that summarize the analysis, report various diagnostic tables and graphs, and display the major results of the analysis. Below is a brief description of each computed result; for details concerning the computations and interpretation of these results, refer to Hastie and Tibshirani (1990). The interpretation of results from fitting Generalized Additive Models is complex and requires experience (note that these techniques were only developed fairly recently, and there is not a large body of literature and "experience" with these techniques); Hastie and Tibshirani (1990) provide detailed discussions on how to interpret the results from these types of analyses, and more importantly, how to use this information to evaluate the appropriateness of the solutions obtained. More recent developments in this area are discussed in detail in Schimek (2000).

Result statistics. Note that the residuals reported in the results spreadsheets and graphs are computed for the adjusted (z-transformed) dependent variable values, as shown in formula 6.3 of Hastie and Tibshirani (1990).

Iteration history. This spreadsheet summarizes the number of iterations in the inner loop, at each iteration of the outer loop, along with the final value of the deviance at each outer iteration. For additional details concerning the fitting of generalized additive models, refer to the Introductory Overview, Hastie and Tibshirani (1990), or Schimek (2000).

Summary statistics. This spreadsheet displays the summary of the results at the point of convergence. Displayed values include the final deviance, the residual degrees of freedom (see also the Introductory Overview for a discussion of the issue of degrees of freedom in generalized additive models), the number of cases, number of iterations, the estimate of the scale value (see also the description of Generalized Linear/Nonlinear Models for details), and a value of R-square computed as the relative improvement in the overall Deviance for the final model; this latter value provides an overall index of the goodness of fit of the model. For additional details, see Hastie and Tibshirani (1990).

Fit summary. This spreadsheet summarizes the result statistics for each predictor variable. The column labeled GAM coef. (coefficient) provides an index for each predictor that is the equivalent to the parameter estimate in a Generalized Additive Model. Note that for each categorical predictor with k classes, k-1 indicator variables are created, coded as 0 and 1 for each observation, depending on whether or not the respective observation does or does not belong to the respective (first, second, etc.) class. The column labeled Non-Linear p-value provides an approximate p-value for the comparison of the Generalized Additive Model with the Generalized Linear/Nonlinear Model, i.e., an indication of whether or not the added parameters (complexity) of the generalized additive model significantly improved the quality of the fit to the data. For details, see Hastie and Tibshirani (1990).

Responses vs. predicted values. This plot shows the predicted values for the (un-transformed) dependent variable plotted against the observed values.

Responses vs. residuals. This plot shows the observed dependent variable values plotted against the residuals.

Predicted values vs. residuals. This plot shows the predicted dependent variable values plotted against the residuals.

Histogram of responses. This plot shows a histogram of the observed dependent variable values.

Histogram of residuals. This plot shows a histogram of the residual values.

Normal and half-normal probability plots of residuals. These plots show the normal or half-normal probability plots of the residual values.

Observational statistics (Predicted and residual values). This spreadsheet shows the values of the dependent (response) variable, the predicted values, and the residual values. For details, see Hastie and Tibshirani (1990) or Schimek (2000).

Spline information. For each continuous predictor variable, STATISTICA will compute the cubic spline scatterplot smoother, along with the 95% confidence bands. For computational details, see Hastie and Tibshirani (1990).

Spline line and 95% confidence band. For each continuous predictor variable, a scatterplot will be shown of the original and smoothed predictor values vs. the partial residual statistics. The partial residual statistics are the residuals after removing the effects of all other covariates from the model. Hence, this graph allows you to evaluate the nature of the relationship between the respective predictor and the (transformed) response variable in the final fitted model.

Observational statistics for predictors. For each predictor variable results spreadsheets will be computed showing the original and smoothed predictor values (and 95% confidence intervals for the smoothed values) and the partial residual statistics. The partial residual statistics are the residuals after removing the effects of all other covariates from the model. Hence, this graph allows you to evaluate the nature of the relationship between the respective predictor and the response variable in the final fitted model.