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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