I modeled the count data with Poisson regression and the Pearson chi square divided by the degrees of freedom was 0.25 suggesting under-dispersion , what can I do , is it possible to deal with this using spss or not, if possible can someone tell me how or refer to a reference.
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- $\begingroup$ What where you counting? It might help to know, as that might help to identify some reason for the underdispersion. One example: Counts of territorial birds often show underdispersion, as happened in my daughters masters thesis in ecology ... $\endgroup$kjetil b halvorsen– kjetil b halvorsen ♦2024-02-19 14:03:34 +00:00Commented Feb 19, 2024 at 14:03
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2 Answers
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1 One possible model that could be used here is the Conway-Maxwell-Poisson distribution. See, for example, this R package: https://cran.r-project.org/web/packages/compoisson/compoisson.pdf
- 2$\begingroup$ Or, for regression, this may be more useful: cran.r-project.org/web/packages/COMPoissonReg/COMPoissonReg.pdf $\endgroup$Brent Kerby– Brent Kerby2015-12-03 01:51:47 +00:00Commented Dec 3, 2015 at 1:51
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You can use a glm model with a quassipoisson family which relaxes the relationship between variance and mean. For the Poisson regression this is $VAR[X] = E[X]$, the variance is equal to the mean. For a quassipoisson family the relationship is also linear but with an additional constant $VAR[X] = \phi E[X]$. This constant is estimated seperately from fitting the glm model. The estimates of the model describing the mean will not change, and it is just the estimate of the dispersion that changes.
A description for how to do this in spss is here: https://www.ibm.com/docs/en/spss-statistics/saas?topic=models-fitting-overdispersed-poisson-regression
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