st: Re: Degrees of freedom for xtmixed

["Joseph Coveney" <stajc2@gmail.com>]

Jordan Silberman wrote:

The following URL summarizes the simple formulas used to compute
degrees of freedom in the HLM 7.0 software:
http://www.ssicentral.com/hlm/help7/faq/FAQ_Degrees_of_freedom_in_HLM_models.pdf

Is there any reason why one can't use these formulas to assign df
values to the fixed effects
estimated by xtmixed? I realize that this approach might be
conservative, which is fine for my purposes.

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Are they conservative?  For some reason, I had always believed that these kinds of simple degrees-of-freedom formulas tended to yield anti-conservative p-value estimates for fixed-effects contrasts.

While we're waiting for, say, Kenward-Roger approximations, can't we simulate under the null to get an estimate of the quantile of the test statistic with reasonable precision?  How far astray would we be led using the observed values of the variance components (REML) as first-pass estimates in the simulation?  (And if it's worrisome, aren't there formulas that you can use to compute the worst-case bound for downward bias in these estimates for both REML and MLE, at least for common models?)  

With the small samples where this whole matter arises, and with Stata MP, -xtmixed- shouldn't be so prohibitively slow as to rule out Monte Carlo simulation to get a handle on the distribution of the test statistic under the null hypothesis for a given fixed-effects contrast, as long as you're not interested in something way out in the tails of the distribution.  Is there something that makes this approach impractical or invalid?

Joseph Coveney


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