[R-sig-ME] Interpretation of odd error variances in glmer

[Douglas Bates]

On Wed, Nov 18, 2009 at 11:54 AM, Brendan Halpin <brendan.halpin at ul.ie> wrote:
> I'm trying to fit a cross-classified multi-level logistic regression
> using glmer and am getting exactly zero variance on one of the grouping
> levels. I have observations on grades, nested within class within
> department on the one hand, and within student on the other.
>
> Here is an example:
>
>     Generalized linear mixed model fit by the Laplace approximation
>     Formula: gradeA ~ 1 + cao + subj1 + subj2 + subj3 + as.factor(stu_gend)
>      + ageentry + as.factor(yrs5) + as.factor(year) + modsize + meancao +
>        depfemr + (1 | deptno) + (1 | modinst) + (1 | id)
>
>         AIC    BIC logLik deviance
>      155671 155901 -77813   155627
>     Random effects:
>      Groups  Name        Variance Std.Dev.
>      id      (Intercept) 1.9624   1.4009
>      modinst (Intercept) 1.6783   1.2955
>      deptno  (Intercept) 0.0000   0.0000
>     Number of obs: 264059, groups: id, 11656; modinst, 6420; deptno, 26
>
> If I change the outcome variable, I get non-zero variance.
>
> How do I interpret this? Is it a model estimation problem?

It is quite legitimate for the ML estimates of a variance component to
be zero.  It simply means that there is not enough variability
accounted for by that term to warrant incorporating the term.

For another outcome variable there may be enough variation that can be
attributed to this factor.