How to compute reliability estimates from lmer / lme results?

Question

Disclaimer: Sorry for including images. I tried writing formulas in markdown format but failed

I'm coming from a commercial MLM (HLM7) software and would like to replicate some numbers in R.

Specifically i'm looking for a function or formula computing the reliability for the least squares estimates of each level1 coefficient across the set of J level-2 units

Below is an example based on the simple sleepstudy data. What I'm looking for is a way to compute reliability values not only in this very example, but also in situations where there are more level1 variables.

From HLM7 manual (Raudenbush, Bryk (2002), p.11) a definition of reliability is given:

Equation 3.58 in Hierarchical Linear Models (2nd ed.)

which is followed by the notion that:

I used the sleepstudy data from lme4 package to compute a random intercept and slope model with lme4::lmer:

library(lme4)
m <- lmer(Reaction ~ Days + (Days|Subject), data = sleepstudy)
summary(m)

And with HLM7 software

Fixed and random effects estimates are pretty similar (differences in rounding occur), but HLM7 will also provide it's reliability estimates:

 ----------------------------------------------------
  Random level-1 coefficient   Reliability estimate
 ----------------------------------------------------
  INTRCPT1, G0                        0.730
      DAYS, G1                        0.815
 ----------------------------------------------------

And this is something I'd like to be able to get from lmer() results.

Any ideas?

Thanks a lot

Answer 1

I needed to include reliability measures for a school project and could not find any package that provided these values. Thus, I had to create them via dplyr: parameter variance/(parameter variance + (residual variance/n clusters)). Hope this helps should anyone else seek the answer to this question.