# Correlation between offset and predictor in count data

I am fitting a Poisson model that requires an offset term to account for sampling effort. However the offset term is highly correlated with one of the linear predictors that is central to my hypothesis. What should I do in that case? I am suspecting that this collinearity is having undesired effects in the model.

Here I explain the mathematical rationale for my question.

In my model, the mean of the distribution ($μ$, in this case Poisson) is linked to the linear predictor ($η = {\rm cov}_1 + {\rm cov}_2 + \ldots. + {\rm cov}_p$) by $μ = E \exp(η)$ where $E$ is the offset term. Therefore: $\log(μ) = \log(E) + η$.

In my case, the Pearson correlation between $E$ and ${\rm cov}_1=-0.5$. Even more relevant, the correlation between $\log(E)$ and ${\rm cov}_1=-0.8$.

Any suggestion will be deeply appreciated.

• what answers did you arrive at for this problem (if any?)? – Joe Hoover Oct 22 '18 at 22:07