# Logistic regression - how do I interpret Odds ratio & how do I explain a very high OR

#### sallyr

##### New Member
Hello,

As part of my doctoral thesis I have completed a logistic regression to assess the impact of some parenting variables on recovery from a diagnosis. I have so far used teaching notes, a variety of text books and the internet to help me analyse the results. I am a clinician foremost and stats is most definitely not my strong point hence why I am asking (begging, haha) for help!

This is what I have got so far...

The model was significant, x 2 (1, n = 57) = 8.73, p < 0.01, indicating that the model was able to distinguish between participants who did and those who did not recover from their diagnoses. The Hosmer-Lemeshow Goodness of Fit Test (p = 0.76) supported the model. The model as a whole explained between 14.2% (Cox and Snell R square) and 29% (Nageklkerke R Squared) of the variance in recovery from diagnoses, and correctly classified 89.5% of cases. The role of the parenting behaviour was significant to the model (p = 0.03). The odds ratio for the parent behaviour was 1485.02 indicating that presence of the parent behaviour meant the participants were 1485% times more likely to retain their diagnosis than if the parent behaviour was not present.

So these are my questions
1) In the last sentence, have I interpreted the odds ratio into percentages correctly?
2) Why is the Odds ratio so high?! I have checked for incorrect data and although there are some missing, the rest is all correct. I have spent a bit of time researching high or's on the internet, and have found that high OR's can suggest multicollinearity, however in this case VIF and tolerance values did not suggest any problems with multicollinearity. I have asked around at Uni to see if anyone else can help but no-one seems to be able to explain it, and I cant find an answer on any previous threads.

Any advice would be very very gratefully received, and if you are able to explain it in very simple terms so there is a hope of my non-stats brain understanding it I would be even more appreciative.

#### gianmarco

##### TS Contributor
Re: Logistic regression - how do I interpret Odds ratio & how do I explain a very hig

Hello,
I think that people here would need a bit more info: for example, what's your sample size (57?), and how many predictors you have?
Secondly, you report just one OR, but what about the OR of the other predictors? Can you upload a snapshoot of your result's table?

Besides, as for classification, you may find useful not to simply report the percentage of correctly classified cases (which depends upon the chosen cut-off point on estimated probability) but using the ROC curve instead, which provides you with a measure of the discriminatory power of your model. I believe that any stat pack should provide a ROC curve facility.

Gm

#### gianmarco

##### TS Contributor
Re: Logistic regression - how do I interpret Odds ratio & how do I explain a very hig

Hello,
I am not so familiar (and happy) with SPSS output.
Nonetheless, if you look at page 4 (bottom), you can see the coefficients (B) for the two predictors. The sign of the coefficient tells you the direction of the "influence" that each predictor has on the outcome of the dependent variable. In both cases, your predictors have a negative impact.

To interpret the coefficient, usually you may reason in terms of exponentiated coefficient, which are odds ratios (Exp(B) in your table).

An odds ratio greater than 1 (say, 1.2) means that a 1-unit increase in the predictor increases the odds for the positive outcome of the dependent variable by 1.2, whereas an odds ratio of say 0.23 indicates that a 1-unit increase in the predictor decreases the odds for the positive outcome of the dependent variable by 0.23.

As for the ROC curve, I was referring to the ROC curve for the fitted model, not for the individual predictors.
Should you have access to MedCalc, I suggest to use it for logistic regression. There is a nice help documentation, and the analysis output is very neat and understandable. You could also use R, which is free, but requires to be able to feed commands 'manually'.

Hope this helps,
gm

#### sallyr

##### New Member
Re: Logistic regression - how do I interpret Odds ratio & how do I explain a very hig

Thanks GM,

Yes sample size is 57 (after missing data removed), and I have just one predictor, threat_aug, as none of the other parenting variables were found to correlate with this dependant variable (I have done another log reg with two predictors that were associated with a different dependant variable and have a query about that too but thought addressing one at a time might be best?!) The dependant variable is whether or not the participant has a diagnoses.

I have attached my outputs, and have now done an ROC curve and put this at the end although, like most stats, this is new to me!

#### sallyr

##### New Member
Re: Logistic regression - how do I interpret Odds ratio & how do I explain a very hig

Thanks GM, I really appreciate your help. I'm sorry though, the initial post I replied had the stats on for the other log reg I did (I'm getting so muddled) so whilst you were replying to that I was deleting that and replying again with the correct results.

So, using the stats I have just uploaded, has an odds ratio (Exp(B)) of 1485. So that means that 1-unit increase in threat aug increases the odds for having diagnosis by 1485? Is that plausible?

#### gianmarco

##### TS Contributor
Re: Logistic regression - how do I interpret Odds ratio & how do I explain a very hig

Hello,
I never happened to face such huge ORs. I have googled a little about large odds ratio(s) and I have found different discussions about the topic, spanning from multicollinearity issues to the scale of the predictors (e.g., mm vs km).
You may want to perform a similar web search to get an idea by yourself, and to possibly exclude one issue at the time in hope to understand what is going on with your model.

Gm