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st: simulated data for logistic regression... remedial algebra help?


From   "Daniel Waxman" <dan@amplecat.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: simulated data for logistic regression... remedial algebra help?
Date   Sat, 17 Nov 2007 18:44:26 -0500

I am trying to create a series of simulated data sets for use in logistic
regression with the following properties:

Mortality (outcome) remains constant.   There is a single dichotomous
independent variable whose odds ratio (coefficient) and proportion of
positives can vary between the sets.  It all comes down to solving for the
intercept (`b0'), given the following relationships:

probability_negative=invlogit(`b0’)
probability_positive=invlogit(log(`odds’)+`b0’)
`proportion_positive’*probability_positive+(1-`proportion_positive’)*probabi
lity_negative=`mortality’

Sad to admit, but I am bumping up against the limitations of my algebra
skills.   
I'd imagine this is trivial for many of you...


i.e.:

************** 

clear
set obs 1000
local odds=2
local proportion_positive= .10
local mortality = .05

gen test=uniform()<`proportion_positive’

/*

************solve for `b0' here************

*/

gen probability_negative=invlogit(`b0’)
gen probability_positive=invlogit(log(`odds’)+`b0’)

gen died=uniform() < cond(test==0,probability_negative,probability_positive)

logistic died test

************************

Thanks.

Dan


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