[R-sig-eco] Proper Contrasts for an Ordered ANOVA

[Nicholas Lewin-Koh]

Hi Joseph,
I think you are making things a bit more complicated than they need to
be.
You have 4 levels of instar as treatment and 2 presumably (-)correlated
responses
algae and zooplankton. You can assume you know something about the
spacing of levels
and try and fit a linear or quadratic contrast. Or you can fit the model
with
categorical levels and test the hypothesis that I4>I3>I2>I1 for algae
and the reverse 
for zooplankton. This is probably what you want, even though there is a
small loss of power, you make fewer assumptions. Contrast matrices can
be hard to set up in R if you are not familiar 
with linear models and how R calculates contrasts. I would suggest using
the contrast package 
to set up the contrast matrix and multcomp to do the tests. 

Nicholas 


> Date: Wed, 07 Apr 2010 14:08:28 -0400
> From: Joseph Simonis <jls468 at cornell.edu>
> To: r-sig-ecology at r-project.org
> Subject: [R-sig-eco] Proper Contrasts for an Ordered ANOVA
> Message-ID: <4BBCCA1C.5080105 at cornell.edu>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> Hi Everyone,
> 
>      I'm analyzing some data from an experiment and could use a quick 
> bit of clarification (and perhaps advice?) on ANOVA contrasts.
> 
>      Briefly, the experiment was testing the 'top down effects' of 
> predation by an aquatic insect on a freshwater food chain: insect eats 
> zooplankton, zooplankton eat algae.  But the insect has a few different 
> instars, and laboratory experiments I've done show that, not 
> surprisingly, later instars are "stronger" predators (consume more 
> zooplankton).  So, I wanted to see if the change in predation capability 
> with instar would translate into a change in the strength of the trophic 
> cascade.
> 
>      To answer the question, I set up an experiment with four treatment 
> levels: no insects (trmnt 1), young juveniles (2), old juveniles (3), 
> and adults (4).  And the specific question, in relation to the 
> experiment is, does zooplankton density decrease and algae density 
> increase going from treatment 1 -> 4.
> 
>      So, the treatments (and my question) are ordinal, but aren't 
> numeric or technically 'evenly spaced'.  And so I'm wondering if 
> polynomial contrasts are valid or not in this case, and then what it 
> means for the interpretation of the coefficients.  It seems like (from 
> Pinheiro and Bates, pg 46) that the fact that the treatment is ordered 
> means I should do polynomial, and then from Venables and Ripley (pg 156; 
> ed 3) that the non-evenly spaced and non-numeric part means I can't 
> interpret the coefficients in the model as coefficients in a polynomial 
> regression, which makes sense to me.  The treatment here is just ordered 
> factors.
> 
>      So then, how do I interpret the coefficients generated for the 
> polynomial contrast?  Is it mostly just in terms of the sign, rather 
> than the actual numerical value?  Again, I'm really most interested in 
> the trend (decreasing vs. increasing), so that gets me the qualitative 
> answer I want, but I wasn't sure if there was anything more I could pull 
> out of the estimates for the coefficients.
> 
>      And, feel free to let me know if there's a better way to set up the 
> contrasts for the question I have--I imagine Helmert contrasts provide 
> another way to do this?  (And a posting or two by Dalgaard on some 
> websites made me think it might be a better way to deal with ordinal 
> treatments?)  But I'm not quite sure I have my head wrapped around 
> exactly what Helmert contrasts would mean, either...
> 
>      Thanks in advance!
> 
> --Joe
> 
> -- 
> Joseph L. Simonis
> 
> Ph.D. Candidate
> Cornell University
> Department of Ecology&  Evolutionary Biology
> E447 Corson Hall
> Ithaca, NY 14853 USA
> 
> E-mail:  jls468 at cornell.edu
> 
> 
>