[R-sig-ME] Variance estimate at 0 with lmer - not with lme - issue or rounding ?

[Douglas Bates]

On Fri, May 11, 2012 at 2:16 AM, nospamjehol-lists at yahoo.fr
<nospamjehol-lists at yahoo.fr> wrote:
> Hello all,
>
> I'm getting puzzled by the following:
>
> I'm fitting a simple hierarchical model with individual identity as random factor. Fitted with lmer (lme4 package) the result look like this:
>
> Formula: response ~ some fixed effects + (1 | indiv)
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  indiv     (Intercept) 0.0000   0.0000
>  Residual             1.4802   1.2166
> Number of obs: 116, groups: name, 69
>
> The variance estimate for individuals is a perfect 0 (which is always suspicious...and maybe an indication of problem in data distribution across effects)

No, an estimate of zero is not suspicious.  It is simply an indication
that the variability between individuals is not significantly larger
than what one would expect from the random variability in the
response.  (By the way, is that really the output from the model fit
because the name "name" in the last line should be "indiv".)

> I then fitted the model with lme (in nlme package) and got:
> Formula: lme(fixed=response ~ some fixed effects,random= ~ 1 | indiv)
> Random effects:
>  Formula: ~1 | indiv
>          (Intercept) Residual
> StdDev: 9.796623e-05 1.2166
> which I agree is a (very) small variance estimate but is less suspicious.

One of the internal differences between lme and lmer is that the
variance component estimates in lmer can go to zero gracefully whereas
in lme they can't because lme works on the scale of the logarithm of
the relative standard deviation.  It took a long time to figure out
how to solve the "going to zero gracefully" problem.

> I'm hitting this "issue" regularly with this dataset, as under some combination of fixed effect variables the variance estimate for individuals suddenly drops to a perfect 0.
>
> So to help me figure out if I should look for a problem in the distribution of data across variables, my question is:
>
> Is the difference in variance estimated by lmer and lme function such as the one observed here likely just caused by a rounding issue (and thus I should assume that with lmer the estimate is correct and simply 0), or is it sign of a real "problem" in my dataset?

Just a rounding issue.

> As ever, thanks for your help (here and in other posts that provide answers so we don't have to ask)
>
> Jehol
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>
>
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