If, as you say, X3 is associated with both z and y, then X3 is potentially confounding the relationship between z and y. If this is the case, when X3 is added to the model, the odds ratio for z will change.
So I think what you are asking is how to test this confounding effect. The change in the odds ratio for z in model 1 compared to the odds ratio for z in model2. Is that right?
If so, you don't test this. It is a confounding effect, a bias. What you need to determine is whether or not the change is important.
If the odds ratio for z in model 1 was 2.00 and in model 2 it was 1.98, I would say that X3 is not exerting much of a confounding effect (assuming z is a dichotomous variable). If, however, the odds ratio for z in model 2 was 1.50, I would have evidence that X3 was an important confounder because it has resulted in, what I consider to be, a large change in the odds ratio for z.
Note, this does not apply if X3 is in the causal pathway between z and y. In this case, X3 is not a confounder but an intermediate variable and adjusting for X3 would bias your estimate of the effect of z.
______________________________________________
Kieran McCaul MPH PhD
WA Centre for Health & Ageing (M573)
University of Western Australia
Level 6, Ainslie House
48 Murray St
Perth 6000
Phone: (08) 9224-2701
Fax: (08) 9224 8009
email: [email protected]
http://myprofile.cos.com/mccaul
http://www.researcherid.com/rid/B-8751-2008
______________________________________________
If you live to be one hundred, you've got it made.
Very few people die past that age – George Burns
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of [email protected]
Sent: Friday, 12 June 2009 8:44 PM
To: [email protected]
Subject: st: question for listserve
I am trying to determine the statistical significance of the change in a
parameter estimate for a predictor variable in a logistic regression when
another predictor is added In other words, I have two models;
model 1: logit y on z x1 x2
model 2: logit y on z x1 x2 x3.
I want to check if the association between y and z is mediated in part by
x3. I have already determined that z is associated with x3 and that y is
associated with x3.
I have tried to do this with the suest command but I do not trust the
results since the two regressions are not run on independent samples.
I would be grateful for any guidance from anyone on how to perform a valid
statistical test the change in the parameter estimate for z when x3 is
added to the regression.
John T. Schousboe
University of Minnesota
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