Date:         Fri, 27 Jun 2008 09:33:53 -0400
Reply-To:     Kevin <citam.sasl@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Kevin <citam.sasl@GMAIL.COM>
Subject:      Deviance or Pearson Chi-square for dispersion

A colleague presented me with the following statistics from a Poisson
regression:

Criteria For Assessing Goodness Of Fit

Criterion                 DF           Value        Value/DF

Deviance                4482       2353.1883          0.5250
Scaled Deviance         4482       4482.0000          1.0000
Pearson Chi-Square      4482       9265.7510          2.0673
Scaled Pearson X2       4482      17648.0121          3.9375
Log Likelihood                    15452.0090


Her question was simply whether these data suggest over- or under-
dispersion.  Having recently read the online docs (an excerpt is quoted
below) but not being familiar, these data seemed contradictory.  Perplexed,
I suggested that she repeat the analysis using a negative binomial and use
an LRT to test for overdispersion and compare the AIC/BICs.

Can anyone offer insight or references?  Should the analyst lean towards
the Deviance or Pearson Chi-Square, given only these two data?

Thanks,

Kevin


From the online docs:

"If the estimate of dispersion after fitting, as measured by the deviance
or Pearson's chi-square, divided by the degrees of freedom, is not near 1,
then the data may be overdispersed if the dispersion estimate is greater
than 1 or underdispersed if the dispersion estimate is less than 1."