[R] lme: anova vs. intervals
Douglas Bates
bates at stat.wisc.edu
Fri Jun 21 15:59:18 CEST 2002
"Martin Henry H. Stevens" <HStevens at muohio.edu> writes:
> Windows 2000 (v.5.00.2195), R 1.5.1
> I have an lme object, fm0, which I examine with anova() and intervals().
> The anova output indicates one of the interaction terms is
> significant, but the intervals output shows that the single parameter
> for that term includes 0.0 in its 95% CI. I believe that the anova is
> a conditional (sequential) test; is intervals marginal or approximate?
The intervals are both marginal and approximate, although the
approximation is generally very good. The anova output is based on
the same type of test, F-tests for general linear hypotheses
conditional on the relative values of the variance components. By
default the anova output is for sequential tests.
> Which should I trust as more accurate or, alternaitvely, more
> conservative?
They are testing different hypotheses. You must decide which is the
more meaningful hypothesis.
In this case the intervals on the three-factor interaction term are
marginal intervals from a model that includes the four-factor
interaction. Most analysts would eliminate that four-factor
interaction before considering marginal tests on a three-factor
interaction.
(Caution: This answer was composed first thing on a morning when I
got up early (North American time) to watch the Germany-U.S.A. world
cup soccer match. It is entirely possible that I am writing nonsense.)
> Partial output follows.
> Thanks for the insight.
> Hank
>
> > anova(fm0)
> numDF denDF F-value p-value
> (Intercept) 1 69 6331.902 <.0001
> Fert 3 44 42.176 <.0001
> Seed 1 44 0.488 0.4886
> Litter 1 69 1.830 0.1805
> Density 1 69 68.714 <.0001
> Fert:Seed 3 44 0.061 0.9799
> Fert:Litter 3 69 0.294 0.8294
> Fert:Density 3 69 0.381 0.7667
> Seed:Litter 1 69 0.005 0.9447
> Seed:Density 1 69 0.449 0.5048
> Litter:Density 1 69 0.141 0.7087
> Fert:Seed:Litter 3 69 0.256 0.8565
> Fert:Seed:Density 3 69 4.254 0.0081
> Fert:Litter:Density 3 69 1.814 0.1527
> Seed:Litter:Density 1 69 4.083 0.0472
> Fert:Seed:Litter:Density 3 69 1.047 0.3773
>
> > intervals(fm0)$fixed
> lower est. upper
> (Intercept) 2.8880007 3.25040348 3.61280623
> ...
> Density 0.1076366 0.41670852 0.72578044
> ...
> SeedC:LitterR:Density -0.4803310 0.06412348 0.60857794
>
>
>
>
> Martin Henry H. Stevens, Assistant Professor
> 338 Pearson Hall
> Botany Department
> Miami University
> Oxford, OH 45056
>
> Office: (513) 529-4206
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>
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--
Douglas Bates bates at stat.wisc.edu
Statistics Department 608/262-2598
University of Wisconsin - Madison http://www.stat.wisc.edu/~bates/
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