[R] lme: anova vs. intervals

Martin Henry H. Stevens HStevens at muohio.edu
Fri Jun 21 19:51:53 CEST 2002


Dear Drs. Bates and Ripley,
Thank you kindly for your replies. After reading your replies, I have 
chosen to use intervals() with appropriate hierarchical structure.
All the best,
Hank

  At 12:07 PM 6/21/2002, ripley at stats.ox.ac.uk wrote:
>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
> > > http://www.muohio.edu/~botcwis/bot/henry.html
> > >
> > > 
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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

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
http://www.muohio.edu/~botcwis/bot/henry.html

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