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Underdispersion with anova testing methods

2 messages · Brian Ripley, Patrick Connolly

Original
Brian Ripley
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On Thu, 21 Mar 2002, Patrick Connolly wrote:

            

      
      
      
    

        
1) A poisson family does not, a quasipoisson family does. It's your
choice, but a Poisson distribution does not have a dispersion
parameter so you would be fitting a quasi-model.

2) It's not valid to look at terms in a sequential anova table like this,
as they all interact (and especially at main effects with an interaction
present).  Use drop1().

            

      
      
      
    

        
Are these small counts?  If so, the residual deviance is a badly biased
estimate of the dispersion parameter, so there might not be
under-dispersion at all.  See the V&R on-line Statistical Complements
for examples.

  
    

      
      
    

  


  


      

    

    

      


  

        

      Patrick Connolly
    

    

      
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Using anova of a glm with test = "Chisq", I get this:

Analysis of Deviance Table

Model: poisson, link: log

Response: Days

Terms added sequentially (first to last)


                Df Deviance Resid. Df Resid. Dev P(>|Chi|)
NULL                              373     370.56          
Block            3    71.05       370     299.51 2.543e-15
Variety          1    94.04       369     205.47 3.096e-22
Instar           3   126.21       366      79.26 3.553e-27
Variety:Instar   3     7.74       363      71.53      0.05


Other interactions were much less prominent.  I'm only interested in
the effect of Variety, and one would expect an effect of Instar, so I
want to be able to block on Instar and Block.

Evidently, the Chisquare test does not use an estimate of the
dispersion parameter.  Were it included, the interaction would have a
much smaller probability.  Is there a good reason why one should or
should not makes such an adjustment?  In any case, will it matter when
I'm interested only in the effect of Variety?


Alternatively, could the underdispersion come from my ignoring the
fact that the insects are measured at the four different instars and
so the independence assumption is not true.  I could not think of a way
of taking that lack of independence into account.

Suggestions welcome.

Thanks