[R] lme: anova vs. intervals

[ripley@stats.ox.ac.uk]

On 21 Jun 2002, Douglas Bates wrote:

> "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.

Yes, and since apparently treatment `contrasts' were used, it does not
make much (any?) sense to test the three-factor coefficient whilst still
fitting the four-factor interaction.  That coefficient has a very complex
interpretation, and dropping it is not equivalent to dropping the
three-factor interaction (since that affects how the four-factor one is
coded).

Advice: the simplest interpretation is likely to come from sequential
backward elimination respecting the hierarchy of terms.

>
> (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
> > Lab: (513) 529-4262
> > FAX: (513) 529-4243
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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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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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