[R-sig-ME] ML or REML for LR tests

[Ken Beath]

On 11/09/2008, at 5:01 AM, Austin Frank wrote:

> First off, thanks to all who have responded to the series of  
> questions I
> asked!
>
> On Fri, Aug 29 2008, Ken Beath wrote:
>
>> On 29/08/2008, at 2:47 PM, Austin Frank wrote:
>>
>>> 3) Is it the case that LR tests between REML models with different
>>> random effects are meaningful?  Does this apply to both nested and
>>> non-nested models?
>>>
>>
>> Maybe, but only for nested (see Q2). Supposedly it works better than
>> ML. The significance tests wont be correct but if there is a huge
>> significance level then there is probably a random effect. Simulation
>> seems a better idea.
>
> Ken was the only one to address this particular point, and I want to
> make sure I've got it straight.  Are REML-based likelihood-ratio tests
> (presumably not performed with anova.mer, as that sets REML=FALSE on  
> the
> call to logLik) an acceptable method for testing nested models with
> different random effects specifications?
>

This is discussed in Pinheiro and Bates. It is not statistically  
correct, so probably isn't a good idea for a publication. I recommend  
reading the sections in Verbeke and Molenberghs book on Linear Mixed  
Models. I have used AIC.

The easiest way to avoid choices is to decide that certain parameters  
must be modelled by random effects based on medical, biological etc  
considerations.

Ken


> As a point of reference, the anova() method is called on two lmer  
> models
> that differ only in their random effects in the manuscript by Baayen,
> Davidson, and Bates at
> http://www.ualberta.ca/~baayen/publications/baayenDavidsonBates.pdf  
> (pp
> 12-15).  The discussion of that analysis makes no mention of the
> difference between REML and ML fits.  Is this because, as discussed
> recently, the REML and ML estimates are so close that there is no
> practical difference in which quantity is used for this test?
>
>
> Thanks again!
> /au
>
> -- 
> Austin Frank
> http://aufrank.net
> GPG Public Key (D7398C2F): http://aufrank.net/personal.asc
>
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