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st: Need help with a significance test...


From   "Jeff A." <jeff@pop.psu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Need help with a significance test...
Date   Fri, 07 Jun 2002 14:49:54 -0400

...not really a stata question per se, but this is one of the most knowledgeable stat lists that I know of (can't seem to find the answer anywhere):

I have 2 logistic regression equations each containing a dichotomous Dep.Var. that represents engaging in or not engaging in a particular behavior over the past year (the outcome in each equation is a different, but related, behavior representing a different degree of seriousness). Each equation has about 4-5 Ind.Vars that are the same for each of the 2 equations. Each equation is used to provide a predicted prevalence rate (with appropriate transformations) for different categories of individuals controlling for other characteristics. E.g.

log odds Y1 = b0 + b1x1 + b2x2 + b3x3

log odds Y2 = b00 + b11x1 + b22x2 + b33x3

(e.g., x1=gender, x2=age, x3=education - Y1 = serious behavior, Y2 = less serious behavior)


Question:
Does anyone know of an appropriate significance statistic to use if I wish to get a p value for the difference between the ratio of Y1 and Y2 for different categories of a predictor variable?

In other words, if the ratio of the predicted rates of the 2 behaviors Y1 / Y2 (or really log-odds in the example below) is greater for males than females in the sample, how can I test this ratio to determine whether the difference (rate, log-odds, whatever) is sufficiently beyond chance?

E.g., if the log-odds of behavior Y1 = .80 for males of avg. age and avg. educ
and
the log-odds of behavior Y2 = .40 for males of avg. age and avg. educ

than the log-odds of the more serious behavior (Y1) is twice that of Y2 (the less serious behavior) for males of avg. age and educ.

Then if this ratio of Y1 to Y2 is three for females of avg. age and educ., how do I test to see the predicted ratio of 2 for males is bigger than the predicted ratio of 3 for females?

(there may be a better way to run the model than Logistic regression, but Y1 and Y2 are not mutually exclusive - e.g., someone can do both).

Thanks much in advance -- (published cites to an answer are also welcome)
Jeff


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