# st: Cumulative probabilities

 From Evans Jadotte To statalist@hsphsun2.harvard.edu Subject st: Cumulative probabilities Date Tue, 20 Oct 2009 17:16:19 +0200

```Hello listers,

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