# Re: st: Cumulative probabilities

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: Cumulative probabilities Date Wed, 21 Oct 2009 08:02:10 -0400

```Evans Jadotte <evans.jadotte@uab.es> :
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 <evans.jadotte@uab.es> 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?
>