# Coefficient changes sign when adding a variable in logistic regression

In my logistic regression the sign of coefficients of a variable (location distance of an amenity) changes based on other variables (with time -ve, with travel distance +ve) in the model. When the location distance is the only variable in the model, it has +ve sign.

• Should the variable need to maintain the +ve sign no matter what other variables are added in the model?
• Does changing sign signify a multicollinearity issue? Some IVs are gaining significance while in a bivariate model, they didn't show significance and vice versa.
• Is it okay to add variables that don't have much significance (ex: travel distance has a significance of 0.33 individually, but 0.05 when added with other variables) but becomes significant in the model? thanks.
• I happens for the same reason it happens in ordinary multiple regression. See the diagram here. There will be some collinearity among the variables, but it can be quite mild. Dec 16 '13 at 20:09
• Simpson's paradox is explained here. stats.stackexchange.com/questions/78255/…
– Sycorax
Dec 16 '13 at 20:11
• You have included the tag [multivariate-regression] & state "I have input it into a multivariate regression". Do you mean that you reran the model w/ >1 predictor variable, or reran the model w/ >1 response / dependent model? Note that >1 predictor, but only 1 response variable is multiple logistic regression. Multivariate LR is when there are >1 response variable. If your situation is actually the former (which I suspect), please edit to clarify & change the tag. Jan 12 '14 at 22:50
• If your situation is multiple LR, then Simpson's Paradox is what's going on. To help understand the idea of the inclusion / exclusion of a confounding variable changing the sign of a focal variable, it may help you to read my answer here: Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression? Although that answer is focused on a different question, & written in the context of linear regression, it illustrates confounding in a way that may make it intuitively accessible. Jan 12 '14 at 22:59
• Sep 25 '14 at 21:52