R help - Mar 2002 - Underdispersion with anova testing methods

On Thu, 21 Mar 2002, Patrick Connolly wrote:
> 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?
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().
> 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.
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.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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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


-- 
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   ___      Patrick Connolly
 {~._.~}    HortResearch             Great minds discuss ideas;
 _( Y )_    Mt Albert                Average minds discuss events; 
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            Ph: +64-9 815 4200 x 7188
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