Confidence interval limits for REML ANOVA random effects

[#1]

I am trying to understand how the confidence interval limits for the variance estimates of the random effects REML output is calculated.

In the JMP help it is stated that:

•	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).

I am interested in the bounded intervals. However, it is not clear how the Satterthwaite approximation is implemented.

In the example in "Investment Castings.jmp" from the Sample Data Library i can reproduce the confidence interval limits using a proper number of degrees of freedom (see attached file). I need 8*(4-1) = 24 for Residual, which I can understand. But how are the degrees of freedom for the Casting and Total obtained? And where in the REML report can I find them?

[#2]

Can noone answer this?

[#3]

First, in general, SAS often does not provide details about implementation because that information is proprietary.

I do not know the answer to your question. All I found is the same documentation as you. I recommend contacting JMP Technical Support (support@jmp.com) to see if they can provide the detail you want.

[#4]

thank you Mark

I will try this.

I really hope this is not proprietary. If I cannot understand how a conifdence interval is calculated, I cannot undersatnd exactly how to interpret it.

[#5 · Accepted solution]

Support gave the solution. The degrees of freeedom is calculated as:

2 * (:Var Component / :Std Error) ^ 2