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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?
Alex
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    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? – Stephan Kolassa Mar 23 '18 at 07:17
  • @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. – AdamO Mar 23 '18 at 15:01
  • @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?](https://stats.stackexchange.com/q/130643/7290))? – gung - Reinstate Monica Mar 23 '18 at 16:29

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