I normally work with linear regression, but came across a need to use logistic regression. I started with glm(y ~ x1 + ..., data, family = binomial()). Almost none of my variables were showing large coefs, which is fine.

Just for kicks I ran the same model, but excluded the intercept glm(y ~ x1 + ... - 1, data, family = binomial()). In this model most of the coefs were large and significant.

My problem is that I don't have too much experience with logistic regression and I am afraid of using this model simply because I don't want to mess up the interpretation. So my question is:

  1. What is the interpretation of the exponentiated coefficients of a logistic regression model that has no intercept?
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    $\begingroup$ The proposed duplicate should address your questions 2 and 3. Regarding 1: the interpretation of (exponentiated) coefficients in logistic regressions per log odds is per coefficient, holding all other predictors constant. So this interpretation works in the exact same way with or without an intercept. Does that answer your question? $\endgroup$ – Stephan Kolassa Mar 23 '18 at 7:17
  • $\begingroup$ @StephanKolassa Your interpretation of the (log) odds ratio without an intercept is not what I think of. If it is, it must be a biased estimator because omitting an intercept "torques" the trend-line either up or down (resulting in a flatter or steeper probability curve). Yet my gut says there must be another interpretation: I believe it estimates something (else) consistently... if the OP edited the question to focus on item 1, I think it would be worth leaving open. $\endgroup$ – AdamO Mar 23 '18 at 15:01
  • $\begingroup$ @AdamO, what do you have in mind? Certainly the exponentiated coefficients are odds ratios whether the intercept is there or not. Are you thinking of suppressing the intercept w/ only categorical variables (as in: How can logistic regression have a factorial predictor and no intercept?)? $\endgroup$ – gung - Reinstate Monica Mar 23 '18 at 16:29