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I am looking for some help modelling overdispersed (zero-inflated negative binomial) count data as a rate. I want to model the survivability of villages in different municipalities given guerilla attack counts over a time period of 14 months in a cross-sectional data set.

  • My dependent variable is a count variable, civilian casualties, and it contains a large number of zeros.
  • I am interested in modelling civilian casualties as a rate, the rate of casualties per attack, given village characteristics.

I am unsure how to setup my model or do some feature engineering to model the rate given zeros (for villages with no casualties) which seem to complicate or make impossible the use of an offset.

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  • $\begingroup$ It is not clear why you think the use of an offset would be complicated or impossible. Please explain. $\endgroup$
    – Laura Lee
    Commented Mar 10, 2020 at 16:51
  • $\begingroup$ @LauraLee I think if I use offset to change the units of a rate, like casualties / # of attacks, then I get zeros as some attacks yield no casualties and thus I cannot take the log of 0. $\endgroup$
    – John Stud
    Commented Mar 10, 2020 at 17:14

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I don't see a problem. As you said, your response variable is the number of casualties. This allows the use of a Poisson or negative binomial--models for count data. The offset would be the number of attacks. Note that the use of the offset assumes that the number of casualties is proportional to the the number of attacks (is this reasonable for your data?). The offset option is needed for a Poisson or negative binomial when the response variable varies by something (the offset) that makes the response more like a rate or density. The presence of zeros is not an issue. I highly recommend Zuur et al. (2012) for an in-depth review of zero-inflated models.

Zuur, A.F., A.A. Saveliev, and E.N. Ieno. 2012. Zero inflated models and generalized linear mixed models with R. Highland Statistics Ltd, United Kingdom. 324 p.

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  • $\begingroup$ Thank you so much @LauraLee; The offset is assumption is reasonable. To double-check; I would then just log the variable for number of attacks and include that as my offset? It does not seem to run without it the log; but then lots of observations need to be tossed out due to the log of 0. $\endgroup$
    – John Stud
    Commented Mar 11, 2020 at 12:14
  • $\begingroup$ Yes, take the log of your offset only (number of attacks). There should be no issue with taking the log of zeros unless there is a case with zero attacks, which you wouldn't be modeling. It's ok if you had a positive number of attacks and no casualties. $\endgroup$
    – Laura Lee
    Commented Mar 11, 2020 at 14:15

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