# What is the $X_{ij}\, Z_{.j}\,\gamma_{k0}\,\gamma_{0k}$ term in this equation of a multilevel regression from a paper?

reading a sociology paper (https://link.springer.com/article/10.1007/s11577-015-0343-4, german) for a course today, I stumbled upon the following equation: It's supposed to describe a 2-level "random intercept" (intercept-as-outcome) regression model where j denotes a level 2 group and i denotes level 1 case within a group. I take the sums to sum over the number of variables on each level respectively. Obviously terms 1, 3 und 5 stem from the level 2 equation. What I for the life of me can't figure out is the fourth term. Is that supposed to be an interaction? Are there two sum signs missing before it or where do the ks come from? Why is there a product of coefficients? What am I missing here?

• It's best not to ask questions to which the answer is simply "yes" or "no" -- (as in your title). Better to rephrase it to be about what you seek (an explanation of something, rather than simply to know if someone else understands it). I have attempted a rewording of your title – Glen_b Jun 7 '17 at 0:42

## 1 Answer

I've had a look at the paper and (with the help of Google translate) concluded that this part is just terribly written. It's just really bad notation and spending time trying to figure out what the authors might or might not have meant is futile, IMO.

It's always good to at least do a cursory check of how reputable a journal is. The impact factor is flawed as a measure, but this journal has an IF of 0.393, which is in the bottom 14% of journals worldwide. Don't waste your time.

• The state of German sociology journals is indeed pitiful. Thanks for having a look. The authors have some interactions in their final model, but those have their own coefficients. So my prima facie guess is that $\gamma_{k0}\,\gamma_{0k}$ denotes not a product, but the separate coefficients for the interactions (maybe it's even a typo). But this interpretation is quite a stretch and it might mean something completely different although there is no indication of this anywhere in the text. Truth be told, I've never seen this kind of product of coefficients in a multilevel regression equation... – Jonas Jun 7 '17 at 16:38
• I guess what I should be asking is: Does a product of coefficients in a regression ever make sense? – Jonas Jun 7 '17 at 16:52
• That's interesting and probably worth posting as a new question :) – Will Jun 7 '17 at 16:55
• I have some ideas on this but I don't have space in the comments. – Will Jun 7 '17 at 18:40