[R] How to estimate the residual SD for each sample separately in mixed-effects model?

[Michal Figurski]

Dear R-helpers,

I am developing a Mixed-Effects model for a study of immunoassays using 
'lme4' library. The study design is as follows: 10 samples were run 
using 7 different immunoassays, 3 times each, in duplicates. Data 
attached. I have developed the following model:

c.lme <- lmer(Result~SPL + (SPL|Assay/Run) -1, data=data)

This model has excellent predictions - the Rsquared of the predicted vs 
measured results is almost 1, with very small RMSE. However, I am not 
interested in the estimates of the mean, but in SDs from the model.

I access the SDs using b<-VarCorr(c.lme). There:
  - the 'attr(b$Assay, "stddev")' is the assay-to-assay SD component for 
each sample (SDaa)
  - the 'attr(b$Run, "stddev")' is the run-to-run component (SDrr)
  - the 'attr(b, "sc")' i.e. the residual (SDres), would be the 
within-run component, but it's a single number for all the samples.

* The problem:
  - how to estimate the 'within-run' component (SDres) for each sample 
separately, as the two other components?

* Solutions tried:
  - subtracting SDaa and SDrr from total SD - sometimes produces 
negative results
  - adding SDres to SDaa + SDrr is usually greater than total SD
  - ...

I have no idea how to do this in a formally acceptable way. Any help 
would be appreciated.

Kind regards,

-- 
Michal J. Figurski, PhD
HUP, Pathology & Laboratory Medicine
Biomarker Research Laboratory
3400 Spruce St. 7 Maloney
Philadelphia, PA 19104
tel. (215) 662-3413
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