I ran two logistic regression models, one with a dataset including outliers and one without outliers, with multiple predictors.
I checked each model's fit with the le Cessie – van Houwelingen – Copas – Hosmer unweighted sum of squares test for global goodness of fit from the rms package in R (following advice here).
model1 <- lrm(y ~ a + b + c + d, data1, method = "lrm.fit", model = TRUE, x = TRUE, y = TRUE, linear.predictors = TRUE, se.fit = FALSE) residuals(model1, type = "gof")
For the model with outliers the p value was close to 0, indicating a lack of fit. For the model without outliers p value was 0.52, indicating that my model was not incorrect.
I then ran 10-fold cross validation for both models with DAAG package and was surprised to get identical (poor) accuracy results for both = 0.56
I thought that the model created using the dataset without outliers, having a much better fit, will give me higher accuracy. Am I missing something here? I will be grateful for your help.