Re: [R] Nested ANOVA with covariate using Type III sums of squares

From: Joris Meys <jorismeys_at_gmail.com>
Date: Thu, 03 Jun 2010 03:00:57 +0200

That's what one would expect with type III sum of squares. You have Phyto twice in your model, but only as a nested factor. To compare the full model with a model without diversity of zoop, you have either the combination diversity/phyto, zoop/phyto or phyto twice in the formula. That's aliasing.

Depending on how you stand on type III sum of squares, you could call that a "bug". Personally, I'd just not use them.

https://stat.ethz.ch/pipermail/r-help/2001-October/015984.html

Cheers
Joris

On Thu, Jun 3, 2010 at 2:13 AM, Anita Narwani <anitanarwani_at_gmail.com>wrote:

> Hello,
>
> I have been trying to get an ANOVA table for a linear model containing a
> single nested factor, two fixed factors and a covariate:
>
> carbonmean<-lm(C.Mean~ Mean.richness + Diversity + Zoop + Diversity/Phyto
> +
> Zoop*Diversity/Phyto)
>
>
>
> where, *Mean.richness* is a covariate*, Zoop* is a categorical variable
> (the
> species), *Diversity* is a categorical variable (Low or High), and
> *Phyto*(community composition) is also categorical but is nested
> within the level
> of *Diversity*. Quinn & Keough's statistics text recommends using Type III
> SS for a nested ANOVA with a covariate.
>
> I get the following output using the Type I SS ANOVA:
>
>
>
> Analysis of Variance Table
> Response: C.Mean
> Df Sum Sq
> Mean
> Sq F value Pr(>F)
> Mean.richness 1 56385326 56385326
> 23.5855 3.239e-05 ***
> Diversity 1 14476593
> 14476593
> 6.0554 0.019634 *
> Zoop 1 13002135
> 13002135
> 5.4387 0.026365 *
> Diversity:Phyto 6 126089387 21014898
> 8.7904 1.257e-05 ***
> Diversity:Zoop 1 263036
> 263036
> 0.1100 0.742347
> Diversity:Zoop:Phyto 6 61710145 10285024
> 4.3021
> 0.002879 **
> Residuals 31 74110911
> 2390675
>
> I have tried using both the drop1() command and the Anova() command in the
> car package.
>
> When I use the Anova command I get the following error message:
>
> >Anova(carbonmean,type="III")
>
> “Error in linear.hypothesis.lm(mod, hyp.matrix, summary.model = sumry,: One
> or more terms aliased in model.”
>
>
>
> I am not sure why this is aliased. There are no missing cells, and the
> cells
> are balanced (aside from for the covariate). Each Phyto by Zoop cross is
> replicated 3 times, and there are four Phyto levels within each level of
> Diversity. When I remove the nested factor (Phyto), I am able to get the
> Type III SS output.
>
>
>
> Then when I use drop1(carbonmean,.~.,Test=”F”) I get the following output:
>
> > drop1(carbonmean,.~.,Test="F")
>
> Single term deletions
>
>
>
> Model:
>
> C.Mean ~ Mean.richness + Diversity + Zoop + Diversity/Phyto + Zoop *
> Diversity/Phyto
>
> Df Sum of Sq
> RSS AIC
>
> <none> 74110911 718
>
> Mean.richness 1 49790403 123901314
> 741
>
> Diversity 0 0
> 74110911 718
>
> Zoop 0 0
> 74110911 718
>
> Diversity:Phyto 6 118553466 192664376
> 752
>
> Diversity:Zoop 0 -1.49e-08 74110911
> 718
>
> Diversity:Zoop:Phyto 6 61710145 135821055
> 735
>
>
>
> There are zero degrees of freedom for Diversity, Zoop and their
> interaction,
> and zero sums of sq for Diversity and Zoop. This cannot be correct, however
> when I do the model simplification by dropping terms from the models
> manually and comparing them using anova(), I get virtually the same
> results.
>
>
>
> I would appreciate any suggestions for things to try or pointers as to what
> I may be doing incorrectly.
>
>
>
> Thank you.
>
> Anita Narwani.
>
> [[alternative HTML version deleted]]
>
>
> ______________________________________________
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> PLEASE do read the posting guide
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>
>

-- 
Joris Meys
Statistical Consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

Coupure Links 653
B-9000 Gent

tel : +32 9 264 59 87
Joris.Meys_at_Ugent.be
-------------------------------
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