[R] lme: anova vs. intervals

[Douglas Bates]

"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
> 
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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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