[R] ANOVA and lmer

[Douglas Bates]

On Feb 7, 2008 3:43 PM, Eric Imbert <eric.imbert at univ-montp2.fr> wrote:

> I am analyzing from a very simple experiment.
> I have measured plants of two different colours (yellow and purple) in 9
> different populations.

> So, I have two different factors : a fixed effect (Colour with two
> levels) and a random one (Population with 9 levels).

> I first analyzed the data with the aov function
> LargS is the variable

> aov(formula = LargS ~ Col + Error(Col/Pop))

> Terms:
>                     Col
> Sum of Squares  3.440351
> Deg. of Freedom        1

> Estimated effects are balanced

> Stratum 2: Col:Pop

> Terms:
>                 Residuals
> Sum  of Squares   3017.112
> Deg. of Freedom        16

> Residual standard error: 13.73206

> Stratum 3: Within

> Terms:
>                 Residuals
> Sum of Squares   3347.385
> Deg. of Freedom       302

> To test for the interaction Col*Pop, I used the following F-ratio =
> (3017/16)/(3347/302) = 188. Highly significant !

> Now, let's go to the analysis performed by lmer - First I do the linear
> model without the Col*Pop interaction :
> m3=lmer(LargS ~ Col + (1 | Pop)

> And next with the interaction : m2=lmer(LargS ~ Col + (Col | Pop))

I don't think this model provides a comparison that is directly
comparable with the test you describe above.

There is a model that is intermediate to your m2 and m3 models in
terms of the number of parameters.  (Actually when I see these results
I realize that there is a bug in anova for lmer models in that the
count of the parameters 1 less than it should be.  I forgot to include
the residual variance as a parameter to be estimated.  However, this
will not affect comparisons here because it is only the differences in
the counts that matter.)

You model m2 is shown as having 5 parameters, which should be 6 (2
fixed effects, 3 variance components for the random effects, 1
residual variance estimate), while m2 is shown as having 3 parameters
(should be 4: 2 f.e. + 1 r.e. var + 1 resid var).  The model

LargS ~ Col + (1|Pop) + (1|Col:Pop)

which allows for random effects for each population and for each
Col:Pop combination, has 5 parameters (currently shown as 4).  The
random effects for Pop are independent of each other and with a
constant variance while the random effects for the Col:Pop
combinations are independent of each other and of the Pop random
effects and with another constant variance.  Thus there are 2 f.e. + 2
r.e. var + 1 resid. var.

I think it is important to plot the data first and decide which of
these models is indicated by the data.  It sounds like the structure
of your experiment is similar to the structure of the "barley" data
set in the lattice package.  Deepayan Sarkar's forthcoming book
"Lattice: Multivariate Data Visualization with R" (to be published by
Springer and due to ship next month) describes very effective ways of
plotting such data.  You can get a preview at his web site for the
book http://lmdvr.r-forge.r-project.org

> Comparing both models : anova(m2,m3) :
>
>    Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
> m3  3 1710.67 1721.97 -852.33
> m2  5 1714.59 1733.43 -852.30 0.0746      2     0.9634
>
> => Conclusion : the interaction Col*Pop is not significant !
>
> I guess I am missing something.
> Who can help ?
>
> Eric
>
>
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