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Suppose I am running a standard OLS multiple regression on the incomes of college graduates 10 years after graduation. I include a mess of individual-specific predictors (e.g., gender, ethnicity, height, major, GPA at graduation, high school GPA, etc.). But suppose I also want to include variables that are specific to the institution they graduated from, e.g., the U.S. News and World Report national ranking of the university/program they graduated from, a public/private university flag, some kind of university selectivity variable (e.g., admission rate, or yield rate from admissions), etc. So I have an individual response, predicted by variables that are both specific to those individuals and variables that are common to all individuals from a specific group (university), so that every person from the same university has the same values on that set of variables.

What are the foreseeable consequences of such a situation from a regression standpoint, in terms of validity/efficiency of parameter estimates, intelligibility of their interpretation, etc.?

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  • $\begingroup$ you might consider grouping students according to one particularly important characteristic (e.g., private vs public school or their GPA in intervals, ...) - you could then build a hierarchical/clustered data model not very different from what is often done in panels $\endgroup$ – Jeremias K Feb 16 '16 at 15:34
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My recollection is that in most cases this will reduce the power of the statistical test, but its complicated by the specifics of the design - for example how much of the variability is present at the level of the university vs variability at the person level.

But it begs the question - why not use a multi-level model? The MLM would allow you to see explicitly how much of the variability in the response is present at the level of the university (level 2) vs at the person level (level 1). When that variance at level 2 is significant, the model would allow for the estimates of the person level parameters to be calculated correctly.. There is just a better way to do it.

What software are you using?

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  • $\begingroup$ Thanks for your input, Marina_ANOVA. That is my instinct as well: introducing group-level variables into the model is going to be a problem. At the moment, I'm switching back and forth between SAS and R. $\endgroup$ – sw85 Feb 16 '16 at 15:02
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    $\begingroup$ +1 for mentioning multi-level model. I would encourage you to write more about why multi-level model is an obvious choice in here (because it is!) as this is the answer to the question. $\endgroup$ – Tim Feb 16 '16 at 15:12

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