[R] Conservative "ANOVA tables" in lmer

[Dimitris Rizopoulos]

----- Original Message ----- 
From: "Manuel Morales" <Manuel.A.Morales at williams.edu>
To: <A.Robinson at ms.unimelb.edu.au>
Cc: "Douglas Bates" <bates at stat.wisc.edu>; "Manuel Morales" 
<Manuel.A.Morales at williams.edu>; <r-help at stat.math.ethz.ch>
Sent: Wednesday, September 13, 2006 1:04 PM
Subject: Re: [R] Conservative "ANOVA tables" in lmer


> On Wed, 2006-09-13 at 08:04 +1000, Andrew Robinson wrote:
>> On Tue, September 12, 2006 7:34 am, Manuel Morales wrote:
>> > On Mon, 2006-09-11 at 11:43 -0500, Douglas Bates wrote:
>> >> Having made that offer I think I will now withdraw it.  Peter's
>> >> example has convinced me that this is the wrong thing to do.
>> >>
>> >> I am encouraged by the fact that the results from mcmcsamp 
>> >> correspond
>> >> closely to the correct theoretical results in the case that 
>> >> Peter
>> >> described.  I appreciate that some users will find it difficult 
>> >> to
>> >> work with a MCMC sample (or to convince editors to accept 
>> >> results
>> >> based on such a sample) but I think that these results indicate 
>> >> that
>> >> it is better to go after the marginal distribution of the fixed
>> >> effects estimates (which is what is being approximated by the 
>> >> MCMC
>> >> sample - up to Bayesian/frequentist philosophical differences) 
>> >> than to
>> >> use the conditional distribution and somehow try to adjust the
>> >> reference distribution.
>> >
>> > Am I right that the MCMC sample can not be used, however, to 
>> > evaluate
>> > the significance of parameter groups. For example, to assess the
>> > significance of a three-level factor? Are there better 
>> > alternatives than
>> > simply adjusting the CI for the number of factor levels
>> > (1-alpha/levels).
>>
>> I wonder whether the likelihood ratio test would be suitable here? 
>> That
>> seems to be supported.  It just takes a little longer.
>>
>> > require(lme4)
>> > data(sleepstudy)
>> > fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
>> > fm2 <- lmer(Reaction ~ Days + I(Days^2) + (Days|Subject), 
>> > sleepstudy)
>> > anova(fm1, fm2)
>>
>> So, a brief overview of the popular inferential needs and solutions 
>> would
>> then be:
>>
>> 1) Test the statistical significance of one or more fixed or random
>> effects - fit a model with and a model without the terms, and use 
>> the LRT.
>
> I believe that the LRT is anti-conservative for fixed effects, as
> described in Pinheiro and Bates companion book to NLME.
>

You have this effect if you're using REML, for ML I don't think there 
is any problem to use LRT between nested models with different 
fixed-effects structure.

Best,
Dimitris


>> 2) Obtain confidence intervals for one or more fixed or random 
>> effects -
>> use mcmcsamp
>>
>> Did I miss anything important? - What else would people like to do?
>>
>> Cheers
>>
>> Andrew
>>
>> Andrew Robinson
>> Senior Lecturer in Statistics                       Tel: 
>> +61-3-8344-9763
>> Department of Mathematics and Statistics            Fax: +61-3-8344 
>> 4599
>> University of Melbourne, VIC 3010 Australia
>> Email: a.robinson at ms.unimelb.edu.au    Website: 
>> http://www.ms.unimelb.edu.au
>>
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>
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