Hi Paul. It's a good question. I thumbed through Snijders & Bosker (2012) and couldn't find an answer. So I did a small amount of Googling and the only clue I found (in the minute or so that I spent looking online) was the page here (LINK) which had the following to say:If you find a better answer be sure to update us in this thread!For a random intercept model, the intraclass correlation was identical to the variance partitioning coefficient, and it was quite simple to calculate. For a random slopes model, the intraclass correlation is not equal to the variance partitioning coefficient because the intraclass correlation will depend on the value of x1 for each of the two elements in question. The variance partitioning coefficient just depended on one value of x1 but if two different people each have a different value of x1, both those values are going to go into the formula for the intraclass correlation. The exact expression for the intraclass correlation is quite complicated; we're not going to give it here because the important thing is simply to note that the intraclass correlation will depend on the two values of x1 as well as σ2u1, σ2u0 and σu01.