Get formula for "Mean Confidence Interval" from Fit Model for mixed effect model

Tina

Hi all,

when fitting a model (fixed effects model) for the results of a designed experiment by Standard Least Squares, I have the opportunity to not only save the Prediction Formula as a column to the data table, but also the Mean Confidence Limit Formula. When fitting a mixed effects model (REML), however, I could save the Mean Confidence Interval to the data table, but not the formula.

Is anyone aware of the formula that is used in case of a random effects model? How does it make sense that the Mean Confidence Interval can be calculated and saved but the formula itself is not available?

 

Best,

Tina

Byron_JMP

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.

•	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.

•	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.