What is the interpretation of odds ratio in logit regressions? I understand that coefficients greater than 1 correspond to positive effects, whereas coeficients less than 1 are negative effects, however beyond that i am less sure.
Woudl i be right in thinking that if i have a odds ratio of 1.15, that that means a one unit increase in the iv is associated with a 1.15x increase in the dv?
Lets look at an example. Here we use example data for only women in the USA and we want to explain whether or not they join a union. The variable union is 0 when you are not in a union and 1 otherwise. The variable grade_c is current grade completed, centered at 12 (high school).
It is helpful to start with the constant (_cons): This is the baseline odds, the odds of being a union member if all explanatory variables are 0. So for someone with just high school, who is not black, has an unskilled job, and does not live in the south the odds of being a union member is $.35$, which means we expect to find $.35$ union members in that group for every non-union member.
This odds increases by a factor $1.15$ (or $(1.15-1)\times100\%=15\%$) for every year of education. The odds of being a union member for black women is almost twice the odds of being a union member of non-black women. The odds of being a union member when one has a skilled job is $29\%$ larger than the odds of being a union member when one has an unskilled job, but the odds of being a union member is when one has a white collar job is only half the odds of being a union member when one has an unskilled job. When one lives in the south the odds of being a union member is $61\%$ less than when one does not live in the south.
Logistic regression Number of obs = 1,867
LR chi2(5) = 123.18
Prob > chi2 = 0.0000
Log likelihood = -979.6908 Pseudo R2 = 0.0591
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union | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
grade_c | 1.149667 .0284497 5.64 0.000 1.095238 1.206802
|
black |
not black | 1 (base)
black | 1.960042 .2569584 5.13 0.000 1.515913 2.534292
|
occat |
white collar | .4980248 .0725356 -4.79 0.000 .3743488 .6625605
skilled | 1.292565 .1860619 1.78 0.075 .9748186 1.713882
unskilled | 1 (base)
|
south |
non-south | 1 (base)
south | .3936798 .0491845 -7.46 0.000 .3081754 .5029077
|
_cons | .3515493 .0353179 -10.41 0.000 .2887165 .4280563
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