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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._