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I did the over-dispersion test for my Poisson regression model in R, to check whether negative binominal is a better option.

I used stats package for conducting Poisson regression and AER package for testing overdispersion.

dispersiontest(m2.int,trafo=1)

Below is the output of the test

Overdispersion test

data:  m1.int
z = 8.0174, p-value = 0.0000000000000005401
alternative hypothesis: true alpha is greater than 0
sample estimates:
   alpha 
0.5118541

I don't know how to interpret the result. Does the significant p-value mean that the model is over-dispersed?

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  • $\begingroup$ Yes ............ $\endgroup$
    – Ben Bolker
    Commented Jul 29, 2022 at 0:42
  • $\begingroup$ @noone Please see ?AER::dispersiontest to understand how the null and alternative hypotheses are defined. By default, you are testing for overdispersion (alternative = "greater") with α > 0. With that in mind, the output is pretty self-explanatory. $\endgroup$
    – Maurits Evers
    Commented Jul 29, 2022 at 1:50
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    $\begingroup$ @MauritsEvers Why not add that (along with an explicit 'yes') as an answer? Even short answers are worth posting as answers and not as comments $\endgroup$
    – mkt
    Commented Jul 29, 2022 at 8:16

1 Answer 1

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Does the significant p-value mean that the model is over-dispersed?

Yes.

If you inspect ?AER::dispersiontest you will see that the function assesses

the hypothesis that this assumption holds (equidispersion) against the alternative that the variance is of the form: $$ \mathrm{Var}[y] = \mu + \alpha \cdot\mathrm{trafo}(\mu)\,. $$

By default (alternative = "greater"), AER::dispersiontest checks for overdispersion ($\alpha > 0$).

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  • $\begingroup$ Thanks a lot! It is really helpful. $\endgroup$
    – noone
    Commented Jul 30, 2022 at 19:45
  • $\begingroup$ @noone If this answered your question, you can accept it by clicking the green tick mark to the left of the answer. $\endgroup$
    – mkt
    Commented Jul 31, 2022 at 21:19

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