# Does BoxCox transformation work for logistic regression?

I'm working on a case study from this MIT course. I'm practicing classification problems.

Here is the code for my model. (The dataset can be accessed from the link. I can add it to this post)

idx <- sample(seq(1, 3), size = nrow(Book), replace = TRUE, prob = c(.45, .35, .2))
train <- Book[idx == 1,]
val <- Book[idx == 2,]
test <- Book[idx == 3,]

glm.fit1 <- glm(Florence ~., family = binomial, data = train)
summary(glm.fit1)
glm.probs1 <- predict(glm.fit1, test, type='response')
glm.pred1 <- rep("0",nrow(test))
glm.pred1[glm.probs1 >.5] <- "1"


This is the confusion matrix

> table(glm.pred1,test$Florence) glm.pred1 0 1 0 787 73 1 0 1  I have tried a few subsets of predictors and they have performed poorly. I checked for linearity relationship between the logit of the outcome and each predictor variables. # Select only numeric predictors num.train <- num_vars(train) # Bind the logit and tidying the data for plot num.train <- num.train %>% mutate(logit = log(probabilities/(1-probabilities))) %>% gather(key = "predictors", value = "predictor.value", -logit) ggplot(num.train, aes(logit, predictor.value))+ geom_point(size = 0.5, alpha = 0.5) + geom_smooth(method = "loess") + theme_bw() + facet_wrap(~predictors, scales = "free_y") The correlation between my predictors and response are largely weak and the relationships appear to be mostly non-linear. How do you adjust them to fit the assumptions for logistic regression? • 1. Monotonic transformations cannot make non-monotonic relationships linear. 2. Your response is 0-1, so the logits should all be -infinity or plus infinity. If you're looking at logits of some fitted model, that's useless if the model is badly wrong. 3. Your plots seems to be flipped around; you're not trying to predict x's from the response but the other way around; how are these curves useful? – Glen_b -Reinstate Monica Jan 21 at 2:24 • How do you suggest checking for linearity between predictors and a response? – Sebastian Jan 21 at 2:32 • That would be a question of its own – Glen_b -Reinstate Monica Jan 21 at 2:37 • I misspoke. I meant to say - how do you suggest checking for linearity between the logit of the outcome and each predictor? My understanding is that is what gets assumed in logistic regression – Sebastian Jan 21 at 2:38 • The logit of the outcome is not observed (or rather, it is, but they're all$\pm\infty\$), and you can't rely on a fitted model's correctness while you're constructing a diagnostic check for its correctness. If you want to ask how to perform diagnostic checks on a logistic regression, again that's a whole new question. – Glen_b -Reinstate Monica Jan 21 at 2:41