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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.

Y(adj)= Yj -bw(Xj-X)

where:

Y(adj) is the adjusted count variable

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

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