Issue with controlling confound in multinomial regression analysis; different results when removing kids on meds I examined the influence of ADHD on abnormal bodyweight in a very large, national sample of children. In my multinomial regressions, I controlled for several specific confounds, which have been shown to be associated with both ADHD and bodyweight in previous studies. One of these confounds was ADHD medication. Although it was significantly associated with underweight (and not obesity; both relative to normal weight), the results I got were different when I reran my analyses after excluding children on both ADHD medications and "other" medications. When I was statistically controlling for medication use, ADHD meds increase odds of underweight, and "other" meds decreased odds of underweight (neither impacted obesity), and the relationship between ADHD and underweight was significant in the model. However, when I removed kids on these meds, the association of underweight and ADHD became non-significant (very, not even "marginally" for those who like shades of grey).
Are there particular problems that can arise when trying to control for other variables in multinomial regression, and which may have led to this situation? Clearly, the model "controlled for" medication use, since both types of medications were significantly associated with the outcome (odds of being underweight vs. normal weight), but it seems like it did not completely account for the impact of medication use in the relationship between ADHD and abnormal bodyweight.
 A: A couple preliminary points:
1) You are speaking much too causally. You may find relationships (or not) but in a study like this, you cannot show causation. Sometimes you use "associated" which is fine, but "impacted", "increase" etc aren't justified. (Probably this is just typing quickly)
2) Why multinomial regression? You seem to have binned kids into "underweight", "obese" and neither. Binning causes problems. See http://biostat.mc.vanderbilt.edu/wiki/Main/CatContinuous
Now, your question:
In full model:


*

*ADHD meds associated with underweight, controlling for ADHD. Essentially, this means that ADHD kids who took meds weighed less than similar ADHD kids who did not take meds. Similarly, non-ADHD kids who took meds weighed less than similar kids who did not take them.  So. You may have colinearity issues (how many non-ADHD kids take ADHD meds? I don't know). 

*ADHD associated with underweight, controlling for med. So, kids with ADHD who took meds weighed less than non-ADHD kids who took meds (colinearity?). And ADHD kids who did not take meds weighed less than nonADHD kids who did not take meds. 
However, without the kids on meds: ADHD not associated with underweight.
This could be a version of Simpson's paradox.
There could be an interaction between ADHD meds and ADHD. One way to look at this would be to make 4 groups:
ADHD kids no drugs
ADHD kids drugs
non-ADHD kids no drugs
non-ADHD kids drugs
(You might want to delete the kids in the last group, if there are few of them; or you might want to try to figure out why those kids are taking the drugs).
