# Correcting data using poisson-regression

I'm new to stats and I was wondering if anyone had any good resources that could explain to me:

How one can correct their data (false-positives) using Poisson-regression. I've been looking for some resources to explain it simply and give a step by step (in R) but I've had trouble.

The reason I ask is because I was trying to reproduce the following:

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: Bowman et al. 2012

• Do you mean how do you get the $\alpha_0$ and $\alpha_1$? It's a simple Poisson GLM. You merely create a data structure which has one row for each pair of nodes assessed at a particular time. The # of DTT streams is the Y and the X is the Euclidean distance between them, or some other suitable metric. – AdamO Dec 13 '18 at 19:44
• It's the first time we see $\pi_{ij}$ but I'm assuming it's a latent intensity for the DTT streams. Subtract from the observed streams the predicted streams given by the Poisson model. – AdamO Dec 13 '18 at 20:32