What can be done about assumption violations in logistic regression? I am working on a logistic regression solution, and I'm experiencing some issues with assumptions according to the diagnostic graphs.For linear regression, I am familiar with addressing similar problems with tranforming the response variable (log, sqrt, etc.) however these solutions wouldn't work for factor variables. What can be done in the case of:

*

*violation of normality

*heteroscedasticity

*non-linearity

The model was generated from a training-set with 292 observations. I am considering removing 1 or 2 of the observations considering graph4, however I am not sure what to do for the other issues.




 A: *

*There is no assumption of normality in logistic regression.  Linear regression is often motivated as a Gaussian GLM (since solving a least squares problem is the same as assuming the likelihood for the model is normal), and this is where the normality assumption of the residuals comes from.  In contrast, logistic regression makes the assumption that the likelihood is binomial

$$ \operatorname{logit}(p_i) = x^T_i\beta $$
$$ y_i \sim \operatorname{Binomial}(p_i; n_i) $$
As a consequence, looking at the difference between observation and prediction is not as informative (especially if the outcome is a 1/0) and you're better off looking at deviance residuals (which require grouping of continuous covariates) or other types of residuals listed in Frank Harrell's Regression modelling strategies.


*Heteroskedasticity is actually an assumption of logistic regression.  Since the variance of a binomial random variable is $np(1-p)$ and $p$ is a function of $x$, then the conditional variance changes as a function of $x$ (hence is not constant; is heteroskedastic).


*You might want to use splines.
