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st: Is a chibar2 analogue warranted for mixed-model ANOVA?
Stata reports a "chibar2(01)" test statistic after -xtmixed- for the
likelihood ratio test of whether variance components are greater than zero.
I'm testing variance components after mixed-model ANOVA of a balanced
dataset. Variance component estimates are allowed to fall below zero with
ANOVA. Should I nevertheless be halving the p-value analogously to what is
done for the chibar2 test statistic for individual variance components?
There are two considerations, which are listed below. They might or might
not affect the answer above, but I'd appreciate any comments on them,
anyway. For background, the dataset is from a gauge-study-like design, but
with three random factors (one nested within another and both crossed with a
third) and two fixed effects, crossed. With all of the interactions, this
has given rise to involved expected mean squares and quasi-F ratios.
(1) I'm proposing not to pool error terms contingent upon test outcomes
(test-and-drop)--the saturated model will be retained throughout. This
follows advice that I recall reading years ago in Leland Wilkinson's users'
manual for Systat.
(2) I'm also calculating coefficients of intraclass correlation and
proposing letting the estimates lie where they fall, that is, not
automatically declaring negative-valued parameter estimates to be zero.
See, J. L. Fleiss, _The Design and Analysis of Clinical Experiments_ (New
York: John Wiley, 1986), p. 300.
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