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

[Douglas Bates]

On Thu, Oct 29, 2009 at 3:52 PM, Ben Bolker <bolker at ufl.edu> wrote:
> 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?

It depends on whether you want a confidence interval for this
parameter, which is an unusual parameter chosen for computational
convenience and not something that generally would be of interest, or
the projection of a joint confidence region, which is what I had in
mind.  I will admit that my statement was poorly phrased and easily
misinterpreted.
>  Or am I just thinking about this wrong?
>
>  Ben Bolker
>
>