[R-sig-ME] valid estimates using lme4?

[Douglas Bates]

On Fri, Oct 28, 2011 at 10:15 AM, Geoff Brookshire
<broog731 at newschool.edu> wrote:
> This seems to only work if you have a single random effect. You say
> that Laplace approximation:
>> may not always work satisfactorily for binary data (for binomial data with
>> more than one trials it would be a bit better)
>
> Since any model with crossed random effects will have multiple trials,
> is it alright that this doesn't work for multiple random effects?

Exactly.  That is why I mentioned "very specific models" in my earlier
reply.  The integral to evaluate the likelihood or log-likelihood is a
multi-dimensional integral over the entire random-effects vector.  It
is only practical to use quadrature methods when the integral can be
expressed as the product of low-dimensional integrals.  Otherwise the
number of quadrature points increases exponentially with the dimension
of the random effects.  Models with crossed random effects can't be
decomposed in this way.  Of course, that is not an issue for SAS (I
don't know about SPSS or STATA) because they don't fit such models.

>
> Thanks,
> Geoff
>
> On Fri, Oct 28, 2011 at 10:26 AM, Dimitris Rizopoulos
> <d.rizopoulos at erasmusmc.nl> wrote:
>> I think the reviewer refers to the fact that the Laplace approximation is
>> equivalent to using the *adaptive* Gauss-Hermite rule with one quadrature
>> point.
>>
>> I feel that he/she is right in pointing out that the Laplace approximation
>> may not always work satisfactorily for binary data (for binomial data with
>> more than one trials it would be a bit better), and it would be therefore
>> prudent to validate your results by fitting the models with the adaptive
>> Gauss-Hermite rule but with more than one quadrature points. For this check
>> argument 'nAGQ' of glmer().
>>
>>
>> I hope it helps.
>>
>> Best,
>> Dimitris
>>
>>
>> On 10/28/2011 4:04 PM, Vernooij, J.C.M. (Hans) wrote:
>>>
>>> Dear list members,
>>>
>>> For a concept article we used package lme4 for a logistic regression. A
>>> reviewer doubts about the validity of the outcomes:
>>> "I strongly urge you to compare the outcomes of lme4 in R with a validated
>>> statistical package (SAS, STATA, SPSS) as lme4 is known not to be the best,
>>> especially when the Laplace approximation is being used as the default is
>>> only one (!) integration point". (quoted)
>>>
>>> How to repond to this? In http://glmm.wikidot.com/faq the Laplace
>>> estimation is said to be less accurate than Gaus-Hermite quadrature or MCMC
>>> methods but is the difference in estimates such that the results are not
>>> valid? Should we validate the results by running different packages ?
>>> Undoubtly we will find differences so what results to report?
>>> What answer might convince the reviewer?
>>>
>>> Thanks,
>>> Hans
>>>
>>>        [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>> --
>> Dimitris Rizopoulos
>> Assistant Professor
>> Department of Biostatistics
>> Erasmus University Medical Center
>>
>> Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
>> Tel: +31/(0)10/7043478
>> Fax: +31/(0)10/7043014
>> Web: http://www.erasmusmc.nl/biostatistiek/
>>
>> _______________________________________________
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>>
>
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