Evans Jadotte <[email protected]> :
What's z in (z-xb-...) below? If you are calculating an estimate of e
in the numerator, and dividing by the estimate of the SD of e, then
you are calculating the Z score of the idiosyncratic error, and
Phi(Z). What is this for? Can you provide refs for what "some books
suggest" ?
On Tue, Oct 20, 2009 at 11:16 AM, Evans Jadotte <[email protected]> wrote:
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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