# Thread: Logistic Regression - How to interpret a Exp(b)= 0

1. ## Logistic Regression - How to interpret a Exp(b)= 0

Hi all,
I'm working on a project and keep getting caught up with how to interpret my results. I've found lots of info on how to interpret significant results, but am having a hard time with how to interpret nonsig results.

For example, with the following output:

I feel clear on how to interp the odds ratio (I think!). For example:
Controlling for dept, status, and home female faculty are .111 times less likely than male faculty members to report satisfaction.

But am not sure what to do when the Exp(b) is 0.0. Do I just write "Controlling for dept, status, and sex Visiting faculty members are 0 times more likely than HU faculty members to report satisfaction"? Could it really be that simple?

Thanks so much for any input you can provide!

PS - Is that monstrously high odds ratios for STATUS a cause for concern? Or it just is what it is?

2. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Some points might be helpful. If I were you I would not report the details of a non-significant result such as its odds ratio (Exp(b)), in the first place. I see none of your variables are even close to significance level. So I suggest not discussing them or talking about their odds ratios, because the report is unreliable in the first place.

But apart from that, extremely low or high ORs might be considered dangerous findings. They are implying existence of some artifacts in your model. Almost all your ORs are strangely extreme. So you should first make sure your model is a healthy one.

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jessireebob (05-01-2013)

4. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Also a odds ratio of 0 does not make sense. It would mean that the log odds of one level of an IV divided by the log odds of another is zero and that seems impossible. A odds ratio (Exp (0)) is one not zero when there is no signficant difference between levels of an IV.

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jessireebob (05-01-2013)

6. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by noetsi
A odds ratio (Exp (0)) is one not zero when there is no signficant difference between levels of an IV.
yeah but that's not what they're asking about. They're asking about the case when Exp(b) = 0. Of course that can't actually be true because Exp(x) > 0 for all real values of x. But computationally we can get values where a machine can't distinguish between 0 and the value you're trying to compute.

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jessireebob (05-01-2013)

8. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Thanks. This is very useful. I'm reporting an entirely nonsignificant model bc it's for a project - so I need to show that I've taken a preapproved datatset and using a preapproved test have gone through the process for stepwise regression. I can't change the parameters, so instead need to report the findings as they are and indicate that I understand how poor a fit this is.

For my project I worried that I shouldn't leave out an interp of OR (even though its relatively useless here) in an effort to show that I understand its meaning. In my report, I have prefaced it with: "Because the predictors are all nonsignificant, I would advise against using the odds ratio to interpret odds, and would instead recommend seeking a more appropriate test. As an exercise, however, below are the interpretations of the predictors' odds ratios for Model 2."

I didn't think an OR of 0 made sense. It feels like it doesn't really mean anything, but I wasn't clear on why... Thanks for helping me understand.

And thanks very much for your time and consideration!

9. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

I guess my point Dason is that an odds ratio near 0 would be very unlikely to be insignficant. For you to get an Odds Ratio such as say .000001 means that the denominator has to be huge - and that means in turn that there has to be significant differences between the odds of being at a given level of the DV for different levels of the IV.

One way to think about this is that if you have an Odds Ratio of .0001 and you reverse the 0 and 1 coding of the DV (which is entirely artificial) you would end up with an odds ratio of 10,000 which is incomprehensibly high (nearly impossible). While that could be insignficant I suppose its not very likely.

But I understand your point

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jessireebob (05-01-2013)

11. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by jessireebob
Thanks. This is very useful. I'm reporting an entirely nonsignificant model bc it's for a project - so I need to show that I've taken a preapproved datatset and using a preapproved test have gone through the process for stepwise regression. I can't change the parameters, so instead need to report the findings as they are and indicate that I understand how poor a fit this is.

For my project I worried that I shouldn't leave out an interp of OR (even though its relatively useless here) in an effort to show that I understand its meaning. In my report, I have prefaced it with: "Because the predictors are all nonsignificant, I would advise against using the odds ratio to interpret odds, and would instead recommend seeking a more appropriate test. As an exercise, however, below are the interpretations of the predictors' odds ratios for Model 2."

I didn't think an OR of 0 made sense. It feels like it doesn't really mean anything, but I wasn't clear on why... Thanks for helping me understand.

And thanks very much for your time and consideration!
I would 1) specifically mention the p values when commenting on signficance rather than the Odds Ratios themself and 2) comment on whether the model itself is signficant (for logistic regression this is done through the signficance of the -2LL or similar test).

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jessireebob (05-01-2013)

13. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by jessireebob
For my project I worried that I shouldn't leave out an interp of OR (even though its relatively useless here) in an effort to show that I understand its meaning. In my report, I have prefaced it with: "Because the predictors are all nonsignificant, I would advise against using the odds ratio to interpret odds, and would instead recommend seeking a more appropriate test. As an exercise, however, below are the interpretations of the predictors' odds ratios for Model 2."
This sounds like a useful note. But I think you can (as some good suggestion perhaps) accentuate the low power of your analysis due to small sample size for example. You are suggesting the reader to use better tests, but the test you are using is actually one of the best tests. You should instead suggest them to use your results as a pilot study to direct further studies with larger samples. After all, unlike all other variables that show very large P values, your main predictor is showing a P value about 1.5. Therefore, it shows that you are on a good way, and by collecting a reasonably large sample, it is possible to have a significant P value for it.

I didn't think an OR of 0 made sense. It feels like it doesn't really mean anything, but I wasn't clear on why... Thanks for helping me understand.
It is not actually zero. Double click your table in SPSS to activate it. Then double click on the cell which is showing 0.000. It will now disclose the real value. It would be something like this 0.000002482 (which is rounded to 0.000 by SPSS).

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hlsmith (05-01-2013), jessireebob (05-01-2013)

15. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by noetsi
I would 1) specifically mention the p values when commenting on signficance rather than the Odds Ratios themself and 2) comment on whether the model itself is signficant (for logistic regression this is done through the signficance of the -2LL or similar test).
Thanks noetsi. I am doing just that - I've selected this model (w 4 nonsig predictors) bc of the H-L and -2LL values, which indicate that as opposed to some of the nested models with fewer nonsig predictor (even one with a sig predictors), this model is best overall. I'll say something indicating that the predictors don't contribute to the model individually, but do collectively.

16. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by victorxstc
This sounds like a useful note. But I think you can (as some good suggestion perhaps) accentuate the low power of your analysis due to small sample size for example. You are suggesting the reader to use better tests, but the test you are using is actually one of the best tests. You should instead suggest them to use your results as a pilot study to direct further studies with larger samples. After all, unlike all other variables that show very large P values, your main predictor is showing a P value about 1.5. Therefore, it shows that you are on a good way, and by collecting a reasonably large sample, it is possible to have a significant P value for it.
Thanks victorxstc, this is a great point. I'll be sure to address the limitation of having such a small sample size.

I also just thought to do a correlation matrix (which I probably should have done to begin with) and I see that there is multicollinearity (though all under r>.9). This would effect logistic regression too, correct?

17. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Rather than do a collinearity analysis (which looks only at bivariate relations) you should do VIF because multicolinearity can be between sets of variables and not show up in bivariate analysis. And addition if you have categorical IV Pearson's R may do a poor job because the data is not interval.

Most software will not do a VIF test in logistic regression. Just rerun the same model in linear regression and use only the VIF value from that to test for multicolinearity. Values above 10 for a variable are problematic (although there is no agreement exactly what level is a serious problem this is the most common one).

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jessireebob (05-01-2013)

19. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by jessireebob
Thanks victorxstc, this is a great point. I'll be sure to address the limitation of having such a small sample size.

I also just thought to do a correlation matrix (which I probably should have done to begin with) and I see that there is multicollinearity (though all under r>.9). This would effect logistic regression too, correct?
I am glad you brought up this. When I mentioned a healthy model, I meant a model with minimum multicollinearity. Actually strangely large ORs can be virtually only a case of artifact usually caused by multicollinearity. So you should definitely check correlation matrices and VIFs. If your correlation matrix shows a couple of variables with correlations over 0.4 (not under 0.9), you should suspect multicollinearity. But as I have learned from noetsi, VIFs are the most accepted method for confirming it (although these methods usually accord with each other - you have some variables with correlations > 0.4, you have VIFs > 10 usually).

So once you treated your multicollinearity case, it is time to interpret your results. But before that, any interpretation might be misleading and should be avoided.

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jessireebob (05-01-2013)

21. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

Originally Posted by noetsi
I guess my point Dason is that an odds ratio near 0 would be very unlikely to be insignficant. For you to get an Odds Ratio such as say .000001 means that the denominator has to be huge - and that means in turn that there has to be significant differences between the odds of being at a given level of the DV for different levels of the IV.
It's funny that you bring that up in this thread since if you look at the actual table provided by jessireebob we do get a lot of odds ratios that are *very* close to 0 and yet we don't have a single significant parameter estimate

22. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

And since nobody mentioned it yet I'll point out that these issues you're experiencing can be a result of complete (or near-complete) seperation of the response based on the input. For instance if all of the 0s are in Home(0) and all of the 1s are in Home(1) then that can cause issues. This is harder to check when you have more predictors but the idea is essentially the same.

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hlsmith (05-01-2013), jessireebob (05-01-2013)

24. ## Re: Logistic Regression - How to interpret a Exp(b)= 0

I understand this is just a project, so I won't get too involved in the model's shortcomings. You should report as mentioned in post #9 and in the interpretation of it use some of Vic's limitations. Lastly you can calculate the actual OR by hand as well based on the beta coefficients (e.g., exp(-37.528) =5.032649e-17). Lastly, I am typically a proponate of presenting the following:

OR 0.00000000000000005(95% CI: ??,??;p-value: 0.999) this would incorporate all three components. Even though these number seem ridiculous. My calculator told me that the LCI was 0 and the UCI was infinity, but you use a calculator or program displaying enough places, you can get the actual numbers.

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jessireebob (05-01-2013)

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