The SPP Procedure

Fitted Model Validation That Uses Goodness-of-Fit Tests

If you want to check how likely the data are to be generated by the fitted model, you can perform a goodness-of-fit test that is based on a chi-square statistic. The model goodness-of-fit test that is displayed by the GOF option in the MODEL statement uses quadrats to compute the observed and expected counts and subsequently to perform the chi-square test. The model goodness-of-fit test is a simulation-based test that uses the fitted model to generate different realizations of the point process. For each simulated realization, the SPP procedure calculates the expected count under the model and computes the mean of this expected count over all the realizations. The mean of this expected count over all realizations is used to compute a Pearson residual as

\[ \text {Pearson residual} = \frac{O_ c-E_ c}{\sqrt {E_ c}} \]

where $O_ c$ is the observed count in each quadrat, based on the data, and $E_ c$ is the expected count under the model. Based on these observed and expected counts, a chi-square statistic is computed and a Pearson chi-square test is performed. A small p-value indicates that the data are not likely to be generated by the model.