I'm running a categorical data analysis with a two-way design of  
nominal by ordinal structure like the Political Ideology Example  
(Table 9.5) in Agresti's book Categorical Data Analysis. The nominal  
variable is Method while the ordinal variable is Quality (Bad,  
Moderate, Good, Excellent). I rank/quantify Quality with another  
variable QualityR (1, 2, 3, 4), and run the following:

fm <- glm(Count ~  Quality + Method * QualityR, family=poisson, MyData)

I'm pretty happy with the significance testing of the main effects  
and contrasts. However after examining the following deviances, I'm  
concerned about the Poisson fitting of the data:

=============
     Null deviance: 426.36  on 35  degrees of freedom
Residual deviance: 171.71  on 16  degrees of freedom
AIC: 369.78

Number of Fisher Scoring iterations: 6
=============

If I interpret the deviances correctly, it seems the Poisson fitting  
only explains (426.36-171.71)/426.36 ~ 60% of the total variability  
in the data. Also with a residual deviance of 171.71  on 16  degrees  
of freedom, the p value is 3.83738e-28. So does it indicate Poisson  
is not a good model for the data? If not, how can I improve the  
fitting? Change the ranking numbers or switch to a different model?  
Sorry this seems more like a statistical question than R-related.

Thanks,
Gang





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