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Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design


From   Jared Saletin <jsaletin@berkeley.edu>
To   "Joseph Coveney" <jcoveney@bigplanet.com>
Subject   Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design
Date   Fri, 6 May 2011 10:15:52 -0700

This is great, thank you Joesph,

Is that model considered invalid then, with negative components? Should the xtmixed output not be used? Or just accept that its a slightly different model from the one ANOVA is able to fit?

On May 6, 2011, at 2:49 AM, Joseph Coveney wrote:

> 
> Jared Saletin wrote:
> 
> Thanks for the help again Phil and David.
> 
> David: The R^2 for the ANOVA model is 0.97, adjusted to 0.91, so it seems to
> fitting the data well, AIC is about 418.97.
> 
> Phil: I flagged the -xtmixed- command with the -var- option, and the residual MS
> is now identical between the two models, the remaining random effects do not
> match the MS's from the -anova-sta model (and the cons SE remains empty).
> 
> Is there a better parameterization to use then this one, since you noted there
> are 3 error terms in the -anova- (s#a s#b and residual) and 4 random effects in
> the -xtmixed- model (s: _cons, s: R.a, s: R.b, residual).
> 
> I checked this parameterization against the example dataset:
> http://www.ats.ucla.edu/stat/stata/examples/kirk/rbf33
> 
> In the latter case all effects are estimated and the F-ratios do indeed match
> the -anova-, and again the MS does does match for the residual, but not for the
> other effects (though in this case all effects are estimated properly), probably
> accounting for the correct F-ratios.
> 
> It would seem that David's point about the data may be the most likely, and that
> for whatever reason the current dataset is causing xtmixed to fail?
> 
> --------------------------------------------------------------------------------
> 
> Except for the residual, mean squares for random effects in ANOVA are functions
> of the variance components, but they aren't the same as the variance components.
> So, the values for variances for s, a and b from -xtmixed- won't be the same as
> the corresponding mean squares in -anova-.
> 
> By setting the mean squares from your ANOVA table against their expectations and
> solving for the variance components, I get the following:
> 
> MS_e = 0.00273899 = sigma2_e
> MS_s#a = 0.012825848 = sigma2_e + 2 * sigma2_s#a
> MS_s#b = 0.014614037 = sigma2_e + 3 * sigma2_s#b
> MS_s = 0.02026831 = sigma2_e + 6 * sigma2_s + 2 * sigma2_s#a + 3 * sigma2_s#b
> 
> sigma2_s#a = (0.012825848 - 0.00273899) / 2 = 0.00504343
> sigma2_s#b = (0.014614037 - 0.00273899) / 3 = 0.00395835
> sigma2_s = (0.02026831 - 0.01008686 - 0.01187505) / 6 = -0.00028227
> 
> You can see that -anova-'s estimate for the variance of s is negative.
> Least-squares (ANOVA) allows negative variance components, but -xtmixed-
> doesn't.
> 
> So the model fit by -xtmixed- is slightly different from the one fit by -anova-
> in this case.  That's why the F statistics aren't the same.
> 
> Joseph Coveney
> 
> 


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