Running the Analysis

  1. To run a Generalized Linear Models analysis, from the menus choose:

    Analyze > Generalized Linear Models > Generalized Linear Models...

    Figure 1. Generalized Linear Models Type of Model tab
    Generalized Linear Models Type of Model tab
  2. Select Custom as the type of model.
  3. Select Gamma as the response distribution.
  4. Select Power as the link function and type -1 as the exponent of the power function. This is an inverse link.
  5. Click the Response tab.
    Figure 2. Generalized Linear Models Response tab
    Generalized Linear Models Response tab
  6. On the Response tab, select Average cost of claims as the dependent variable.
  7. Select Number of claims as the scale weight variable.
  8. Click the Predictors tab.
    Figure 3. Predictors tab
    Predictors tab
  9. On the Predictors tab, select Policyholder age through Vehicle age (when variables are listed in file order) as factors.
  10. Click Options.
    Figure 4. Generalized Linear Models Options dialog
    Generalized Linear Models Options dialog
  11. In the Options dialog, select Descending as the category order for factors. This indicates that the first category of each factor will be its reference category; the effect of this selection on the model is in the interpretation of parameter estimates.
  12. Click Continue, then click the Model tab.
    Figure 5. Predictors tab
    Predictors tab
  13. On the Model tab, select holderage through vehicleage (when variables are listed in file order) as model terms.
  14. Click the Estimation tab.
    Figure 6. Estimation tab
    Estimation tab
  15. On the Estimation tab, select Pearson chi-square from the Scale Parameter Method drop-down list in the Parameter Estimation group. This is the method used by McCullagh and Nelder, so we follow it here in order to replicate their results.
  16. Click the EM Means tab.
    Figure 7. EM Means tab
    EM Means tab
  17. Select holderage (Policyholder age) as a term to display means for and select Repeated as the contrast.
  18. Select vehiclegroup (Vehicle group) as a term to display means for and select Pairwise as the contrast.
  19. Select vehicleage (Vehicle age) as a term to display means for and select Repeated as the contrast.
  20. Select Sequential Sidak as the adjustment method.
  21. Click the Save tab.
    Figure 8. Save tab
    Save tab
  22. On the Save tab, select Predicted value of linear predictor and Standardized deviance residual. These values are saved to the active dataset and can help you diagnose any problems with the model fit.
  23. Click OK.

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