# [R-sig-ME] Computing reliability for the least squares estimates of each level1 coefficient across the set of J level-2 units

Doran, Harold HDoran at air.org
Mon Jan 29 20:12:15 CET 2018

```The formulas you need are in the SO post you put up yourself. So, lmer gives you the output you need to do it, just follow those formulas you have already posted. An object of class mer does not provide the reliability (which I question in terms of usefulness, but that's another issue)

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Blazej Mrozinski
Sent: Monday, January 29, 2018 2:03 PM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Computing reliability for the least squares estimates of each level1 coefficient across the set of J level-2 units

Good evening,
Please accept my apology for cross-posting (I've been advised to avoid it) but I can't find my answer anywhere.
4 days ago I posted my question to stackOverflow (with screenshots of formulas, that are skipped here): https://stackoverflow.com/
questions/48438755/how-to-compute-reliability-estimates-
from-lmer-lme-results.
<https://stackoverflow.com/questions/48438755/how-to-compute-reliability-estimates-from-lmer-lme-results>

I'm coming from a commercial MLM (HLM7) software and would like to (...drop it eventually) 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:
Reliability Estimates (overall or average reliability for the least squares estimates of each level 1 coefficent across the set of J level-2 units) calculated according to Equation 3.58 in Hierarchical Linear Models (2nd ed.)

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.

Is this possible with a built-in formula? Some other package function?
Or maybe someone could help me in extracting appropriate values from lmer result object and compute it "by hand" ?
Thank you very much!

Kind Regards,
Blazej Mrozinski

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