The difference between with or without intercept model in logistic regression

Question

I like to understand the difference between with or without intercept model in logistic regression

Is there any difference between them except that with the intercept the coefficients regard the log(odds ratio) relative to the baseline group and without the intercept they regard the log(odds)? from what I have seen the coefficients are the same in both cases but the significance is not always the same and don't understand why is that.. in addition, in which cases will it be correct to use a model with no intercept?

This is my model: glm(NeverReturn ~ factor(Network) * TotalPrice , family = binomial) and I'm not sure about leave the intercept out or not because at the "real word" the total price cant be under 50 any way,but then the probability will be 1 not 0 so I'm confused.

Answer 1

It will almost never be meaningful to use the no intercept model in logistic regression. The intercept parameter $\beta_0$ is modelling the marginal distribution of the response $Y$, so using $\beta_0=0$ is tantamont to assuming that $P(Y=1)=0.5$, marginally. Do you really know that? If that is untrue, you cannot trust any inference from the no intercept model.