[R-sig-ME] Apparent false convergence in lmer with some BIBD data

[Ben Bolker]

Douglas Bates wrote:

  [snip]

> What is happening here is that the likelihood surface is unusually
> flat so a wide range of values provide a likelihood close to that at
> the mle.  Consider the enclosed plot of the profiled deviance as a
> function of theta, this relative standard deviation parameter.
> Because this is the profiled deviance we would compare the change in
> the profiled deviance (the difference between the value shown here and
> the minimum) to a chisquared distribution with 11 degrees of freedom
> (from 9 fixed-effects parameters and two variance components).  A 95%
> joint confidence region would include all the values shown here and
> many more.  The difference between the value at theta = 0 and at the
> optimal theta is negligible.

   Silly question, but I would have thought that the relevant number of
df would be 1, counting only the parameter we are NOT allowing to vary
(i.e. we're profiling on theta), rather than the 11 that we ARE allowing
to vary?

  This wouldn't change the argument that theta=0 is nearly
indistinguishable from theta-hat approx 0.3, but the 95% confidence
region would only go out to about theta=0.8?

  Or am I just thinking about this wrong?

 Ben Bolker