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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?

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    $\begingroup$ 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. $\endgroup$
    – Thomas Bilach
    Commented May 25, 2020 at 4:48
  • $\begingroup$ NO. For an extreme example, see stats.stackexchange.com/questions/306494/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Nov 18, 2020 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.

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  • $\begingroup$ Thanks, Thomas! I appreciate your clear response. $\endgroup$
    – Sahit Menon
    Commented May 25, 2020 at 23:31

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