I already checked out the answer to this: enter link description here It is not a duplicate and that did not answer my question.

I wanted to try to ask a different question regarding a similar problem I've been having (so far I haven't quite found the answer I was looking for).

To give some background info to the problem I'm having:

I'm studying the structural connectivity between brain regions i and j.

The structural connectivity as a function of distance between regions i and j seem to follow a poisson distribution (higher connectivity values for shorter distance between i and j and vice versa).

However, it was noted that for distance values less than 17.4 there is a bias in the model. The shorter the distance, the higher the connectivity values (so just because two brain regions are close together... they will automatically have a higher structural connectivity). This may not be a true connection.

So it was suggested that in order to correct this BIAS one would have to adjust the Poisson regression model.

Now, my question is: how do I statistically adjust poisson regression bias?

I came across this reference: statistical adjustment

And this reference discussed how one could statistically adjust a dependent variable by the following model.

where:

Yj= dependent variable mean before adjustment

bw = common regression coefficient

Xj=mean of covariate variable for group j

X=grand mean of covariate variable

So should I use this approach to adjust the model? Should I subtract the bias distance from the actual distance in order to correct the structural connectivity strength?

For anymore clarification, there is this paper that I'm referring to:

We perform our analysis at a region level, where all region pairs are separated by more than 17.4 mm, which based on simulations (not shown), leads to negligible bias due to distance-related false positive connections. We also employ a Poisson regression-based statistical adjustment that yields measures of $$SC$$ adjusted for the physical distances between region locations. Specifically, we apply a model that assumes that the number of $$DTT$$ streams $$S_{ij}$$ connecting regions $$i$$ and $$j$$ follows a Poisson distribution with the mean $$\mu(S_{ij}|g_{ij})$$ dependent on the physical distance $$g_{ij}$$ between these regions, i.e. $$S_{ij}|g_{ij}\sim \mathcal{Pois}(\mu(S_{ij}|g_{ij}))$$. Therefore, we estimate and subsequently adjust for the association between the physical distances and the $$DTT$$ counts using the effect $$\alpha_1$$ in the log-linear model $$\log(\mu(S_{ij}|g_{ij}))=\alpha_0+\alpha_1 g_{ij}$$ Henceforth, assume that each $$\pi_{ij}$$ is adjusted for physical (geometric) distance to reduce the potential impact of false structural connections on our awFC method.

source: awFC paper