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Re: st: Mixed model degrees of freedom and Stata presentation


From   Jordan Silberman <silberman.stata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Mixed model degrees of freedom and Stata presentation
Date   Mon, 19 Nov 2012 17:55:39 -0500

Thank you Yulia for the very helpful response. Jordan

On Mon, Nov 19, 2012 at 2:20 PM,  <ymarchenko@stata.com> wrote:
> Jordan Silberman <silberman.stata@gmail.com> asked a few questions about
> small-sample adjustments for multilevel models.  Let me address some of them:
>
>> ...
>>
>> So, a few questions:
>>
>> 1. Are there plans to provide more extensive options for df estimation (eg,
>> Kenward-Roger, Satterthwaite, etc.) with xtmixed/xtmelogit in the future?
>> This feature would be extremely helpful, even if just one estimation method
>> is provided.
>
> The implementation of small-sample adjustments using Satterthwaite and
> Kenward-Roger approximations is very high on our development list, but we do
> not anticipate it being added in the nearest future.
>
>
>> 2. I have read that Stata statisticians believe there's no defensible way to
>> estimate df for mixed models. Can anyone explain why this is so, preferably
>> in language a non-statistician can understand?
>
> There is no theoretical justification for the proposed adjustments when they
> are applied to unbalanced designs and general mixed models.  This is why they
> were not added to Stata initially.
>
> You may find the following talk by Phil Ender useful:
>
>   www.stata.com/meeting/chicago11/materials/chi11_ender.pdf
>
> You may also find interesting the response from Douglas Bates, the author of
> R's "lmer" package, who feels even stronger about this issue than us:
>
>   https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html
>
> Even so, we are very sympathetic to those who have very small samples and who
> are loath to rely on large-sample properties that produce demonstrably
> anticonservative tests and confidence intervals.  In some cases, a
> small-sample approximation and its associated assumptions may be preferred to
> the large sample statistics with asymptotically provable distributions.
>
>
>> 3. The solution to this problem offered in Stata is to assume infinite
>> degrees of freedom. It seems to me, from a statistically naive perspective,
>> that it is literally mathematically impossible to use a less defensible
>> solution. It's not possible to provide a df estimate that is further from
>> the true df value than infinite. But I suspect that there's more to it than
>> this.  Can anyone explain why assuming that df = infinite is more defensible
>> than other df estimation methods, even though other methods are
>> mathematically guaranteed to provide more accurate df estimates?
>
> The inference currently provided by Stata for mixed models requires large
> samples and should not be used with small samples.  We agree that this is
> restrictive for small samples in practice and are looking into adding the
> commonly used degrees-of-freedom adjustments for linear mixed models.
>
>
> -- Yulia
> ymarchenko@stata.com
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