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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