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In a Poisson model, do we need to check for multicollinearity between the offset variable and other covariates? For example, if I offset by population size, would it be problematic to include covariates that are correlated with population?

kjetil b halvorsen
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Sahit Menon
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    It is not problematic. In most software packages, the offset is specified *inside of* a function. In R, for example, `glm(y ~ x + offset(log(population))...)`, where population size is the offset/exposure variable. – Thomas Bilach May 25 '20 at 04:48
  • **NO**. For an extreme example, see https://stats.stackexchange.com/questions/306494/can-a-variable-be-used-both-as-an-offset-and-an-independent-variable – kjetil b halvorsen Nov 18 '20 at 15:16

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No. In a count model, the offset/exposure variable is not a covariate. Rather than being estimated as a coefficient, its value is constrained to equal 1. It allows you to model rates instead of counts. I would review this post for more information.

Incorporating additional predictors that may be correlated with population size should not concern you if you're using population as your offset.

Thomas Bilach
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