Let me first try to explain what is intraclass correlation coefficients (ICCs).

I see Intraclass Correlation Coefficient (ICC) as a statistical estimation used to measure how similar the observations within a group or cluster or class (intra-class means what then! within class, right?) in comparison to the total variation across all the observations of the dataset. Now another question! What makes total variation. In this case, total variation is between group variation and within group variation.

Other way speaking, ICC is basically the ratio of between-group variation and total variation. Why we are accounting "between-group variation" here, why not "within group variation"! To understand this, we have to know the purpose of ICC. ICC is formulated to get the measure how much of the total variation can be attributed to group differences. If it is not clear yet, it will be within no time!

The range of ICC is from 0 to 1. ICC = 0 indicates no similarity among the members of a group and ICC = 1 indicates perfect similarity within the groups.

Let's consider a simple example to understand the concept. Suppose, you are the secretary general of UNO, and you have three blocks of countries. Each block gates the same intervention to improve physically activity level of adolescents, and you are interested to know how similar the intervention effect within each block compared to the other blocks.

If the ICC value is near to 1, it means that countries within each block have shown very similar physical activity improvement, and most of the total variation is attributable to between block variation. Other way speaking, within block variation does not have much contribution to total variation. For example: Europe block might have shown very high improvement in physically activity level of adolescents, Africa block might have shown "so so" improvement in physical activity level of adolescents, and Arab block might have shown poor improvement in physical activity level of adolescents.

If the ICC value is near to 0, it means that countries within each block have shown very diverse physical activity improvement, and most of the total variation is attributable to within block variation. Other way speaking, between block variation does not have much contribution to total variation. It is because all the blocks similarly contain countries which have shown high, "so so", and poor improvement in physical activity level of adolescents.

If the ICC value is around 0.5, you may attribute half (or near about) of the variation to between group and other half (or near about) to the within group variation.

You may use two packages to extract ICC for multiple poisson regression in R - lme4 and performance.

install.packages("lme4")

install.packages("performance")

library(lme4)

library(performance)

Fit the multilevel poisson regression

pa_model