Regression Diagnostics and Residual Analysismain topic
Regression Diagnostics and Residual AnalysisFollowing any modeling procedure, it is a good idea to assess the validity of your model. Logistic regression has a collection of diagnostic plots, goodness-of-fits tests, and other diagnostic measures to do this. These residuals and diagnostic statistics allow you to identify factor/covariate patterns that are either poorly fit by the model, have a strong influence upon the estimated parameters, or which have a high leverage. Minitab provides different options for each of these, as listed in the following table. Hosmer and Lemeshow [24] suggest that you interpret these diagnostics jointly to understand any potential problems with the model.
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To identify... |
Use... |
Which measures... |
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poorly fit factor/covariate patterns |
Pearson residual |
the difference between the actual and predicted observation |
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standardized Pearson residual |
the difference between the actual and predicted observation, but standardized to have s = 1 |
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deviance residual |
deviance residuals, a component of deviance chi-square |
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delta chi-square |
changes in the Pearson chi-square when the jth factor/covariate pattern is removed |
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delta deviance |
changes in the deviance when the jth factor/covariate pattern is removed |
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factor/covariate patterns with a strong influence on parameter estimates |
delta beta |
changes in the coefficients when the jth factor/covariate pattern is removed-based on Pearson residuals |
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delta beta based on standardized Pearson residuals |
changes in the coefficients when the jth factor/covariate pattern is removed-based on standardized Pearson residuals |
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factor/covariate patterns with a large leverage |
leverage (Hi) |
leverages of the jth factor/covariate pattern, a measure of how unusual predictor values are |
The graphs available in the Graphs subdialog box allow you to visualize some of these diagnostics. You can also store some of these statistics to graph if you like. See [22] for a further discussion of diagnostic plots. You can use Minitab's graph brushing capabilities to identify points. See Brushing Graphs.