Hello, I'm an undergraduate student completing my dissertation (using SPSS) so please bear with my very limited understanding of binary logistic regression.
My outcome variable = referral outcome for ADHD assessment (dichotomous: accepted or rejected)
Significant predictor variable = gender
However ExpB which I understand to be the log odds ratio, is 20.520 with confidence intervals LI= 4.139 UI= 101.731
I've been told by my supervisor that 20.520 is implausibly high - e.g., it wouldn't be right for me to report that males are at 20.520 higher odds of being accepted for ADHD assessment (which is what I've interpreted these results to mean).
I've done lots of research to try to figure out what went wrong
- there is no multicollinearity (VIF are all between 1 and 2)
- there are 106 cases so I don't think the sample size is too small?
- the other predictor variables are all on the same scale (only one other variable is sig)
- there are a 3 outliers but the data has been input correctly and I believe it's not ultimately helpful to just remove them without good reason? Also, when I tried removing them, the ExpB just got larger...
- gender is set as a nominal variable in SPSS
Have attached table for reference.
Any help would be hugely appreciated about how to interpret this number, whether it could in fact be plausible? Or if not, what I could do as a next step?
Thank you.
Such high OR are mostly implausible. It could depend on the number of cases, especially if you have 6 males and 100 females, for example, which would only leave 6 males for the analysis. This could be the reason you have such huge confidence intervals. I would recommend posting the descriptive analysis so we could have more insight into your data.
Thanks for your response.
Data includes 64 males (38 accepted, 26 rejected) and 42 females (13 accepted, 29 rejected).
Predictor variables are:
Gender
Age
Teacher rated inattention score
Parent rated inattention
Teacher rated hyperactivity
Parent rated hyperactivity
2 sig predictor variables = gender and teacher rated inattention.
One thing I've noticed is that if I remove the other significant predictor variable (teacher rated inattention), the OR for gender reduces to 4.278 (LI= 1.442, UI= 12.688) - male children generally are 3x more likely to receive assessment so this seems more plausible? I'm not suggesting I remove a significant variable but I'm struggling to understand how to interpret this.
Any help at all would be greatly appreciated and can give further specifics - just let me know what.
There are several ways to interpret your data. The reason why we 'exponentiate' the coefficient value is to facilitate the interpretation of your output.
In my class, I generally discourage students using 'odds ratio' as the 'odds' is unit-less. Another way of interpretation is 'back-transforming' your logit function to the probability scale. You can do this by dividing your coefficient by 4.
By back-transforming your logit outcome to a probability scale, your unit changes from logit to %. For instance, if you take your 'gender' variable coefficient and divide by 4, it would be 3/4 = 0.75 or 75%. Your interpretation would be something like: 'Being a male (assuming code==1 denotes for male) increases the *probability* of being admitted by 75% compared to female (code==0), adjusting for other variables.'
Another way of interpreting your result would be comparing your result with the intercept (constant). Intercept is when all your variables are set to zero. And I see that your intercept is -17, which implies that when all variables are set to zero, the chance of being admitted is very low. You may have to center or scale your age variable as age value of zero makes no sense. Consult with your supervisor regarding these approaches.
Hello Rebecca,
For your data set, the "crude" odds ratio (OR) for males vs. females is 3.27, whereas the "adjusted" OR (using the logistic output results) appears to be 20.52.
First, crude and adjusted OR values can and do differ!
Second, they should be interpreted in their respective contexts.
For your sample of 106 cases, when you take into account ("control for") the age, teacher-rated inattention, parent-rated inattention, and parent-rated hyperactivity, gender appears as an influential variable for referral outcome, with the odds of acceptance being somewhere between 4X and 101X higher for males than for females. Note that the lower end of this continuum for the estimated confidence limits is not that far removed from the crude OR.
*Is the analysis flawed? I see nothing to support that conclusion (though the caveat of "we haven't seen all the data points" should be mentioned).
*Would the estimated OR values change wildly if you were to re-estimate the model, omitting the non-sigificant variables? In my experience, that's unlikely.
*Is the result sample specific? Always a possibility.
Good luck with your work.
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