Perhaps the simple answer is, "its just too complicated to fit into a formula."
...or you could go with what's in the manual:
https://www.jmp.com/support/help/14/restricted-maximum-likelihood-reml-model.shtml#739871
Confidence Intervals for Variance Components
The method used to calculate the confidence limits depends on whether you have selected Unbounded Variance Components in the Fit Model launch window. Note that Unbounded Variance Components is selected by default.
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If Unbounded Variance Components is selected, Wald-based confidence intervals are computed. These are valid asymptotically but note that they can be unreliable with small samples. |
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If Unbounded Variance Components is not selected, meaning that parameters have a lower boundary constraint of zero, a Satterthwaite approximation is used (Satterthwaite 1946). |
Kackar-Harville Correction
In the REML method, the standard errors of the fixed effects are estimated using estimates of the variance components. However, if variability in these estimates is not taken into account, the standard error is underestimated. To account for the increased variability, the covariance matrix of the fixed effects is adjusted using the Kackar-Harville correction (Kackar and Harville
1984 and Kenward and Roger
1997). All calculations that involve the covariance matrix of the fixed effects use this correction. These include least squares means, fixed effect tests, confidence intervals, and prediction variances. For statistical details, see
The Kackar-Harville Correction.
Norm KHC is the Frobenius (matrix) norm of the Kackar-Harville correction. In cases where the design is fairly well balanced, Norm KHC tends to be small.
JMP Systems Engineer, Health and Life Sciences (Pharma)
