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


From   "Airey, David C" <david.airey@vanderbilt.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design
Date   Mon, 9 May 2011 08:24:44 -0500

.

> I get the impression that the NOBOUND option of PROC MIXED is used more often
> than not for diagnostic purposes for a nonpositive-definite G matrix, so it
> might not be so much a difference between statisticians.
> 
> Joseph Coveney

You are right; I looked into the JMP 9 documentation (page 105, ch.5, 
Modeling and Multivariate Methods) and it says:

"Though variances are always positive, it is possible to have a 
situation where the unbiased estimate of the variance is negative. 
This happens in experiments when an effect is very weak, and by chance 
the resulting data causes the estimate to be negative. This usually 
happens when there are few levels of a random effect that correspond 
to a variance component.

JMP can produce negative estimates for both REML and EMS. For REML,
there are two checkboxes in the model launch window: Unbounded Variance
Components and Estimate Only Variance Components. Unchecking the box
beside Unbounded Variance Components constrains the estimate to be
non-negative. We recommend that you do not uncheck this if you are
interested in fixed effects. Constraining the variance estimates leads
to bias in the tests for the fixed effects. If, however, you are only
interested in variance components, and you do not want to see negative
variance components, then checking the box beside Estimate Only Variance
Components is appropriate.

If you remain uncomfortable about negative estimates of variances,
please consider that the random effects model is statistically
equivalent to the model where the variance components are really
covariances across errors within a whole plot. It is not hard to think
of situations in which the covariance estimate can be negative, either
by random happenstance, or by a real process in which deviations in some
observations in one direction would lead to deviations in the other
direction in other observations. When random effects are modeled this
way, the covariance structure is called compound symmetry.

So, consider negative variance estimates as useful information. If the
negative value is small, it can be considered happenstance in the case
of a small true variance. If the negative value is larger (the variance
ratio can get as big as 0.5), it is a troubleshooting sign that the rows
are not as independent as you had assumed, and some process worth
investigating is happening within blocks."



-Dave
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