# Goodness of fit for binary logistic regression

#1

What is a good test to check for goodness of fit for a binary logistic regression? I tried the hosmer-lemeshow test and obtained a p-value of 0.012 which means insignificant from the article i referred. Is it correct?
Suppose I consider a null hypothesis that the model is insgnificant, a p-value less than 0.05 will result in rejection of hypothesis(at 5%), isnt it?

#2

For Classification, as in your case is Binary, you can use ROC curve and compute AUC which ranges from 0 to 1 the higher the better, and it actually tells you how fit is your model.

#3

I have done ROC and got an AUC of 0.742â€¦but im working on a project where they demand whether the model is appropriate or not, hence goodness of fit, i.e. statistically prove the model is significant.

#4

Okay, if this is the case.
In Hypothesis testing we initially assume null hypothesis to be true
P-value < 0.05 Alternate Hypothesis is true which means significance.
P-value > 0.05 Null Hypothesis is true which means non significance.

so if your probability value lies below 0.05 then your null hypothesis gets rejected and alternate becomes true which means model is significant.
Refer this paper for more tests on goodness of fit.

Thanks

#5

Yes, i referred the same article, in all the examples they show, the model is said to be significant when the p- value is greater than 0.05. This was confusing me, because for individual predictors, it is significant when p-value is less than 0.05.