Model validation and diagnostics
In the previous chapter, we saw the utility of residual techniques. A similar technique is also required for the logistic regression model and we will develop these methods for the logistic regression model in this section.
Residual plots for the GLM
In the case of linear regression model, we had explored the role of residuals for the purpose of model validation. In the context of logistic regression, actually GLM, we have five different types of residuals for the same purpose:
- Response residual: The difference between the actual values and the fitted values is the response residual, that is,
, and in particular it is 
if yi = 1 and 
for yi = 0.
Deviance residual: For an observation i, the deviance residual is the signed square root of the contribution of the observation to the sum of the model deviance. That is, it is given by:
Where the sign is positive if 
, and negative otherwise, and 
is the predicted probability of success.
Pearson residual: The Pearson...
