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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, thank you all of your comments

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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

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