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Individual confidence intervals for mixed models

Hi team, 

My customer would have to have the equations behind individual confidence intervals (conditional or not) for mixed models calculated by JMP.
I didn't find any references in the documentation.
Would it be possible to have the details I can share with her?

Thank a lot,

Florence

Re: Individual confidence intervals for mixed models

Florence,

I used this paper for the marginal prediction intervals (ie individual CIs). https://doi.org/10.1002/sim.8386
That paper points out that JMP previously used the incorrect degrees of freedom for its PIs in SLS-REML. I fixed SLS-REML and implemented marginal PIs in Mixed.

Conditional PIs were not implemented in Mixed, because I'm not certain what that means (a conditional estimate is already a prediction, BLUP, so what's a prediction of a prediction??). It was left as is in SLS-REML. I don't know what formula was used. They are probably "reasonable", but perhaps not completely correct.

I hope that helps!
-Elizabeth

Re: Individual confidence intervals for mixed models

@eclaassen   I'm puzzled now.    In the PROC MIXED doc for MODEL / OUTP= is a general equation for prediction variance.   Could that be used to construct JMP Conditional PIs?

Re: Individual confidence intervals for mixed models

Russ,
PROC MIXED does not do prediction intervals (ie for a new observation). OUTP gives BLUPs (just the usual conditional predictions with intervals). OUTPM gives marginal predictions with intervals. Neither of these are the prediction intervals discussed in the paper and now implemented in SLS-REML or our Mixed. The paper is discussing a marginal prediction interval - a new observation with no associated block information. I don't know what a conditional prediction interval would even be - a new observation including new block? Doubly predicting what exactly? SLS-REML has an option for conditional prediction intervals, that is predicting beyond just a BLUP. Is it mathematically correct in the standard error and dfs? I don't know, and I doubt it given that the marginal Indiv CIs had the wrong DFs, though the standard error was mostly correct before my fix a couple releases ago.

PROC MIXED OUTP == JMP Conditional Predictions (and intervals), the usual BLUPs
PROC MIXED OUTPM == JMP Marginal Predictions (and intervals)

There's massive confusion due to "prediction" being used in different ways. JMP labels prediction intervals as Indiv CIs, which includes a Conditional Indiv CI in SLS-REML. But we think of conditional means estimates as predictions thanks to BLUP. So what's a prediction interval of a conditional prediction?

Re: Individual confidence intervals for mixed models

AFAIK the OUTP prediction limits are computed as the point prediction +/- a df-adjusted critical value x prediction standard error.   A new observation would entail adding a new realization of a zero-mean independent random residual error and the prediction variance would be increased additively, so it seems the limits could just be widened accordingly.     

The setup is amenable to simulation to check that the limits are performing as advertised for both the BLUPs and predictions of new observations.

I think the individual prediction case is often important and computing these limits would be valuable for customers.    The terminology is confusing but we should be able to figure out something reasonable.