Fitting Alternative Models

One problem with the "overdispersed" Poisson regression is that there is no formal way to test it versus the "standard" Poisson regression. However, one suggested formal test to determine whether there is overdispersion is to perform a likelihood ratio test between a "standard" Poisson regression and a negative binomial regression with all other settings equal. If there is no overdispersion in the Poisson regression, then the statistic −2×(log-likelihood for Poisson model − log-likelihood for negative binomial model) should have a mixture distribution with half its probability mass at 0 and the rest in a chi-square distribution with 1 degree of freedom.

  1. To fit the "standard" Poisson regression, recall the Generalized Linear Models dialogs and click the Estimation tab.
    Figure 1. Estimation tab
    Estimation tab
  2. On the Estimation tab, select Fixed value from the Scale Parameter Method drop-down list in the Parameter Estimation group. Leave the default value of 1.
  3. Click the Save tab.
    Figure 2. Save tab
    Save tab
  4. On the Save tab, deselect Predicted value of linear predictor and Standardized deviance residual.
  5. Click OK.
  6. To fit the negative binomial regression, recall the Generalized Linear Models dialogs and click the Type of Model tab.
    Figure 3. Type of Model tab
    Type of Model tab
  7. On the Type of Model tab, select Negative binomial with log link as the type of model. This specifies a negative binomial (with a value of 1 for the ancillary parameter) distribution with a log link function
  8. Click OK.

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