st: Cumulative probabilities

[Evans Jadotte <evans.jadotte@uab.es>]

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,

Evans  

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