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

From: Anita Narwani <>
Date: Thu, 03 Jun 2010 17:48:34 -0700

Yes I understood the strangeness of removing a main effect without interactions that contain it because I did this during my efforts using model simplification. I had checked out the link you sent a couple of days ago. It was useful. So does Type II SS remove both the factor and any interactions containing it when comparing models? i.e. to test for the main effect of B you compare A + B + A:B against A?

On Thu, Jun 3, 2010 at 4:59 PM, Joris Meys <> wrote:

> Hi Anita,
> I have to correct myself too, I've been rambling a bit. Off course you
> don't delete the variable out of the interaction term when you test the main
> effect. What I said earlier didn't really make any sense.
> That testing a main effect without removing the interaction term is has a
> tricky interpretation. By removing a main effect you test full model A + B
> + A:B against the model A + A:B. If you remove the main effect "Zoop" for
> example, you basically nest Zoop within Diversity and test whether that's
> not worse than the full model. This explains it very well:
> I'd go for type II, but you're free to test any hypothesis you want.
> Cheers
> Joris
> On Thu, Jun 3, 2010 at 9:59 PM, Anita Narwani <>wrote:
>> Thanks for your response Joris.
>> I was aware of the potential for aliasing, although I thought that this
>> was only a problem when you have missing cell means. It was interesting to
>> read the vehement argument regarding the Type III sums of squares, and
>> although I knew that there were different positions on the topic, I had no
>> idea how divisive it was. Nevertheless, Type III SS are generally
>> recommended by statistical texts in ecology for my type of experimental
>> design. Interestingly, despite the aliasing, SPSS has no problems
>> calculating Type III SS for this data set. This is simply because I am
>> entering a co-variate, which causes non-orthogonality. I would be happier
>> using R and the default Type I SS, which are the same as the Type III SS
>> anyway when I omit the co-variate of Mean.richness, except that these
>> results are very sensitive to the order in which I add the variables into
>> the model when I do enter the co-variate. I understand that the order is
>> very important relates back to the scientific hypothesis, but I am equally
>> interested in the main effects of Zoop, Diversity, and the nested effect of
>> Phyto, so entering either of these variables before the other does not make
>> sense from an ecological perspective, and because the results do change, the
>> order cannot be ignored from a statistical perspective.
>> Finally, I have tried using the Type II SS and received similar warnings.
>> Do you have a recommendations?
>> Anita.
> --
> 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
> -------------------------------
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