Bootstrap variability measure on EBLUPs (predictions)

[lsandell]

Hi there, I am using PROC MIXED to generate predictions within a longitudinal cohort of a continuous outcome (EBLUPs). I have a few questions regarding the validity of the results generated.

1. I assume the SE, 95% CI, and p-values of my fixed effects are valid (not underestimated) since I am modeling the measured outcome (not the predicted outcome), correct?

2. If I do want to generate valid SE's for my EBLUPs, how would you suggest I set up my bootstrap in order to generate these values? Would I be bootstrapping for residuals, another measure, etc.? 

Thanks!

[SteveDenham · Accepted solution]

For part 1, my answer is yes, provided there is no model misspecification.

I see a couple ways of attacking #2.

If you have predicted values at each time point for each subject (obtained from the model fit and using the OUTP= option), you can resample those by bootstrap to get some values. To get "pure" eBLUPs, set up several dummy subjects with a missing dependent variable. The OUTP option will generate predicted values by using eBLUPs. The key here is how many dummy subjects, as these will serve as the basis for the resampling.

Another way is to use the BLUP option in PROC HPMIXED. This will require knowing the covariance parameters (which you should from your MIXED run). You use a PARMS statement with a PARMSDATA dataset and specify NOITER.

A third is to use HPLMIXED as in this example: https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_hplmixed_examples01.htm 

Let us know if any of these are of use.

SteveDenham

[lsandell]

Thank you Steve. This is very helpful. Is there a preferred method for also generating standard errors for the EBLUP values? I did use the OUTP= option in PROC MIXED to get my EBLUPs but I also wanted to report some sort of valid variance measure for each one. I noticed in the documentation that the SEs generated with this option often 'underestimate', so I was thinking I could use some sort of resampling to generate less biased SEs. Am I thinking about this correctly? Thanks!

[SteveDenham]

In most cases, a bootstrap SE will be less biased than a delta calculated SE, as the delta method essentially linearizes the Taylor expansion, so higher order terms that could account for skewness are ignored.  So, if you have a reasonable population to sample from, then it would seem that there would be less bias. However, the calculation of a mean value across the various subsamples makes the same kind of linearization. I think the key for SE's might be to work in the variance space and then calculate a pooled estimate of the SE by formula.  For anything resampling related, look through Rick Wicklin's blog:The DO Loop. Another good start would be  https://communities.sas.com/t5/Ask-the-Expert/How-Do-I-Use-the-Bootstrap-Method-in-SAS-Q-amp-A-Slide... 

SteveDenham