[R-sig-ME] random effects specification
Reinhold Kliegl
reinhold.kliegl at gmail.com
Tue Apr 8 21:47:04 CEST 2008
On Tue, Apr 8, 2008 at 8:13 PM, Sebastian P. Luque <spluque at gmail.com> wrote:
> On Tue, 8 Apr 2008 19:31:08 +0200,
> "Reinhold Kliegl" <reinhold.kliegl at gmail.com> wrote:
>
> [...]
> > If you learn how to combine estimates, you can derive the pattern of
> > means directly from your first analyses.
>
> You mean using approaches as those used in estimable() from the gmodels
> package? If so, is that equivalent to doing a separate analysis for
> each level of community with mixed models? I think it isn't for fixed
> effects only models.
>
> tapply(dta$n, list(dta$treatment, dta$community), mean)
A B
a 18.78058 18.74912
b 19.11358 18.38756
c 18.79208 18.73067
d 19.10998 18.40533
> (n.lmer1)
...
Fixed effects:
Estimate Std. Error t value
(Intercept) 18.78058 0.01784 1052.7
communityB -0.03146 0.02523 -1.2
treatmentb 0.33300 0.02523 13.2
treatmentc 0.01150 0.02523 0.5
treatmentd 0.32939 0.02523 13.1
communityB:treatmentb -0.69456 0.03568 -19.5
communityB:treatmentc -0.02995 0.03568 -0.8
communityB:treatmentd -0.67318 0.03568 -18.9
You can reconstruct the table of means from the coefficients:
A B
a : intercept intercept + communityB
b: intercept + treatmentb intercept + treatmentb +
communityB + communityB:treatmentb
c: intercept + treatmentc intercept + treatmentc +
communityB + communityB:treatmentc
d: intercept + treatmentd intercept + treatmentd +
communityB + communityB:treatmentd
This is a consequence of the default treatment contrasts associated
with factors as attributes.
> contrasts(dta$treatment)
b c d
a 0 0 0
b 1 0 0
c 0 1 0
d 0 0 1
> contrasts(dta$community)
B
A 0
B 1
You can change the default, that is specify your own contrasts as
factor attributes most flexibly via C (see ?C). lmer uses the factor
attribute (like, e.g., lm and other programs) and provides test
statistics for each of the contrasts (and their products).
Best
Reinhold
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