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

["JVerkuilen (Gmail)" <jvverkuilen@gmail.com>]

On Sat, Nov 17, 2012 at 4:05 PM, Jordan Silberman
<silberman.stata@gmail.com> wrote:
>
> 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?

I don't have much to say about the other questions so I won't blather
on about them, but the notion of assuming infinite DF isn't totally
crazy. Think of using the normal distribution for a humble one sample
t test. The normal is a t with infinite DF. When n > 30 it's not too
far off and when n > 100 you aren't really benefitting from using the
t distribution anymore. Most of the benefit of using DF comes when n
is pretty small. Estimated DF are good on average (i.e., probably in a
mean squared error sense), but under other losses they may not be so
great.

I do agree that it would be quite nice if there were other estimates
available, though, if for no other reason than the potential for a
journal reviewer's panties to get in a bunch about exactly which
method was used.
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