Hi Jeremy,

Both seem basically acceptable to me, but I prefer the latter, that is, the plural form.

Let's say we have some data with clusters j = 1,2,...,N and our model is: y_ij = b_0 + a_0j + e_ij. If someone talks about the variance of the "random effect" (singular), I take this to mean that they are talking about var(a_0j). So I guess the singular usage here comes from the fact that "a_0j" constitutes one and only one term in the written model equation. Fair enough.

But I prefer to think of it as: we have N random effects -- a different value of a_0 for each cluster -- and we can speak about the variance of these N values. Of course that the "variance of the random effects" in the model output will not literally equal the sample variance of the observed a_0js. But in any case we are talking about the variance of some quantity of things of which there are presumably more than one.

My two cents,
Jake

Date: Mon, 22 Jul 2013 22:00:38 -0700
From: helixed2@yahoo.com
To: r-sig-mixed-models@r-project.org
Subject: [R-sig-ME] Semantics question regarding "random effect" vs. "random	effects"

Imagine a basic two-level (varying intercept) mixed-effects model, such as test scores for students clustered in classrooms.  Packages like lme4 provide an estimate of the higher-level variance.
 
When reporting that higher-level variance, I have seen authors mention both:
 
1. the variance of the "random effect"
 
or alternatively:
 
2. the variance of the "random effects"
 
I know which seems right to me, but I'd be curious to hear opinions on the proper way to write up commentary on the higher-level variance.
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