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st: Cumulative probabilities

From   Evans Jadotte <>
Subject   st: Cumulative probabilities
Date   Tue, 20 Oct 2009 17:16:19 +0200

Hello listers,

Sorry for sending this message again but I realized some characters did not appear too well.

I am estimating cumulative probabilities of the following function:

Yijk = b0 +b1Xijk + eijk + u.jk + u..k

where u.jk and u..k are two random intercepts with variance Sigma^2 (u.jk) and Sigma^2 (u..k). The variance of my raw residuals is Sigma^2 (eijk). The cumulative probabilities I want to calculate are of the form:

Phi((z-xb-uhat.jk - uhat../k/)/sqrt(?))

where Phi denotes the standard normal cumulative density. My question is: should the square root, sqrt, in the denominator contain just the variance of the raw residuals, i.e. Sigma^2 (eijk), as some books suggest? Or should it bear, according to my logic, the total variance of the model, which would be the sum Sigma^2 (e ijk) + Sigma^2 (u.jk) + Sigma^2 (u..k)? And finally, what would be the statistics rationale for using the former instead of the latter formula?

Thanks in advance,

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