Minitab provides different options for each of these potential problems, as listed in the following table. Hosmer and Lemeshow^{1} indicate that you interpret these diagnostics jointly to understand any potential problems with the model.
Potential problem | Diagnostic statistic | Definition of statistic |
---|---|---|
Factor/covariate patterns that do not have an acceptable fit | Pearson residual | The difference between the actual and predicted observation |
Standardized Pearson residual | The difference between the actual and predicted observation, but standardized to have σ = 1 | |
Deviance residual | Deviance residuals, a component of deviance chi-square | |
Delta chi-square | Changes in the Pearson chi-square when the j^{th} factor/covariate pattern is removed | |
Delta deviance | Changes in the deviance when the j^{th} factor/covariate pattern is removed | |
Factor/covariate patterns that have a strong effect on the parameter estimates | Delta beta calculated with the Pearson residuals | Changes in the coefficients when the j^{th} factor/covariate pattern is removed |
Delta beta calculated with the standardized Pearson residuals | Changes in the coefficients when the j^{th} factor/covariate pattern is removed | |
Factor/covariate patterns that have a large leverage | Leverage (Hi) | Leverages of the j^{th} factor/covariate pattern, a measure of how unusual predictor values are |
Residual plots let you visualize some of these diagnostics. You can also store and plot other diagnostics. Delta chi-square and delta deviance are useful for identifying factor/covariate patterns that do not fit the model well. The delta beta statistics are useful for identifying a factor/covariate pattern with a strong effect on the parameter estimates. Typically, you plot these delta statistics against either the estimated event probability or the leverage. The estimated event probability is the probability of the event, given the data and model. Leverages are used to assess how unusual the predictor values are. You can use Minitab's graph brushing capabilities to identify points that are on a graph.