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st: estimation of SE of correlation after mixlogit


From   Nick Darson <nick.darson@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: estimation of SE of correlation after mixlogit
Date   Fri, 12 Aug 2011 19:59:31 +1000

Hi listers,

After running mixlogit, I am wondering how I exactly calculate the
standard error of the correlation.

To my understanding, I have to do this manually after obtaining the
covariance-variance components using the command "mixlcov" (please
tell me if there is an easier automatic way that I have overlooked,
such as using nlcom - I have tried this but always get error
messages).

For example, I have a multinomial model with three possible
alternatives: low, mid, high (low as the base case; mid and high are
random and allowed to be correlated).

Hence, after estimation with mixlogit and using "mixlcov", I obtain
the values for v21, v11, and v22.

This way I can easily calculate the correlation of the two variables:
rho= _b[v21] / sqrt (_b[v11] * _b[v22])

However, how do I calculate the SE of this correlation?
I found the following formula:  SE(rho) =  sqrt ( 1-rho^2 / n -2 )

However, which value do I use for "n"? In my case, I have repeated
measures (each of the 200 individuals makes 5 choices). Hence, should
I use n=200 (the number of subjects), n= 1000 (total number of
observations), or do I need to look how many cases actually have
chosen mid and high (e.g. let's say from the 1000 total choices, 200
are mid and 300 are high, hence n=500)?

Thankful for any help on this apparently simple issue.

Cheers,
Nick
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