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nested, unbalanced anova

5 messages · Pfeiffer, Steven, Spencer Graves, Peter Dalgaard +1 more

Peter Dalgaard
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On Jan 6, 2013, at 04:00 , Pfeiffer, Steven wrote:

            

      
      
      
    

        
As far as I can tell, this is still an orthogonal design, so just proceed as usual. You're not in real trouble unless you have plots with one of the subplots missing. The whole thing will boil down to an analysis of the within-plot differences.

Just avoid things like Type-III sums of squares (base R won't do them, but popular add-ons will) because they get it wrong when cell counts are unequal.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Spencer Graves
    

    

      
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On 1/6/2013 12:45 AM, peter dalgaard wrote:

            

      
      
      
    

        
Plot is  a random effect.  Honysuckle, trenched, and moisture are 
fixed.  You may also wish to consider using either the nlme or lme4 
packages, though they may not be needed "unless you have plots with one 
of the subplots missing", as Prof. Dalgaard indicated. Pinhiero and 
Bates (2000) Mixed-Effects Modeling in S and S-Plus (Springer) is the 
best book I know on the subject.  The nlme package contains script files 
with names like ch01.R containing R code to work all the examples in the 
book;  system.file('scripts', package='nlme') will give you the full 
path to where it is installed.  These are necessary, because the R 
implementation contains a very few subtle changes from what is in the 
book.  There is also an r-sig-mixed-models at r-project.org email list that 
may interest you.  I have not used this in years, and I would expect 
that people on this email list could help you with more current 
information on what's available.


       Hope this helps.
       Spencer Graves

  
  


  


      

    

    

      
      

        


  

        

      Peter Dalgaard
    

    

      
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On Jan 6, 2013, at 09:45 , peter dalgaard wrote:

        

            

      
      
      
    

        
That might be a bit unfair. Type-III methodology has its proponents, I'm just not one of them. Within their own logic, I'm sure Type-III SS are computed correctly. It's just that this is one of the cases where you can be misled into thinking that the design is orthogonal so Type-III and Type-II is the same. It isn't.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      John Fox
    

    

      
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Dear Peter,

Thank you for the clarification, since one (I hope) popular add-on that
computes type-II and -III tests for repeated-measures designs is the Anova()
function in the car package. 

The type-II tests are, in my opinion, preferable, because they are maximally
powerful, e.g., for main effects when the interactions to which the main
effects are marginal are zero in the population (the situation in which a
main effect test is typically of interest), but I'd argue (not here, because
it would take more space than is reasonable in an email), that the type-III
tests test reasonably interpretable hypotheses.

Steven: A forthcoming paper in the R Journal, available as a preprint at
<http://journal.r-project.org/accepted/2012-02/Fox+Friendly+Weisberg.pdf>,
explains how to use the Anova() and linearHypothesis() functions in the car
package for univariate and multivariate tests in repeated-measures designs.
The paper doesn't, however, try to clarify the distinctions among "type-I,"
"II," and "III" tests.

Best,
 John

-----------------------------------------------
John Fox
Senator McMaster Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada