# Results of logistic regression look odds

When doing a logistic regression, $$y = x_1+x_2$$, it gave an odds ratio for $$x_1$$ of $$3.1$$. When doing another logistic regression, $$y = x_1+x_2+x_3$$, it gave an odds ratio for $$x_1$$ of $$5.1$$. Does this make sense? I thought when increasing the number of adjusted variables, odds ratio for $$x_1$$ should be reduced. Any suggestions for interpreting why odds ratio for $$x_1$$ got increased after adding another covariate?

• Have a look at the paper of Norton & Dowd (2017). They explain that odds ratios really estimate $\exp(\beta/\sigma)$ where $\sigma$ is the standard deviation of the error term. That means that odds ratios from models containing different predictors can't really be compared. See also here. – COOLSerdash Dec 13 '19 at 12:51
• Thanks for the links, very helpful – mark Dec 13 '19 at 16:09
• What do you mean by the odds ratio of $x_1$? $x_1$ is a variable. Odds ratio is a value. – Acccumulation Dec 13 '19 at 20:05
• please fix your title – Glen_b Dec 14 '19 at 10:28