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st: mlogit: predicted probabilities with confidence limits


From   "Dedman, Dan" <D.Dedman@ljmu.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: mlogit: predicted probabilities with confidence limits
Date   Wed, 26 Sep 2007 14:18:53 +0100

I run a multinomial logistic regression model, where the outcome variable has three levels. From this I can obtain predicted probabilities for each level of the outcome. I would like to put confidence intervals around these probabilities, but I am not sure how to do it. I can obtain confidence intervals for the linear prediction (using the -stdp- option with -predict-), but I am not sure how to incorporate this information into the equations which relate the linear prediction to the probability:

P(y=1) =         1/(1+exp(beta2*x)+exp(beta3*x))
P(y=2) = exp(beta2*x)/(1+exp(beta2*x)+exp(beta3*x))
P(y=3) = exp(beta3*x)/(1+exp(beta2*x)+exp(beta3*x))

(where beta2*x is the linear prediction for outcome level 2, etc)

I apologise if this is more of a stats question than specifically a Stata issue.

Thanks in advance.

Dan

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Daniel Dedman
Public Health Information Specialist/Analyst
North West Public Health Observatory
t: 0151 231 4552
m: 07812 192578
f: 0151 231 4515
e: d.dedman@ljmu.ac.uk
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