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