I need to explain the concept of linear mixed models in an article targeted at a mainstream audience. Is there a way of communicating the gist of the concept in a sentence or two?
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Test grades (dependent variable) could be related to how much the students study (fixed effect), but might also be dependent on the school they go to (random effect), as well as simple variation between students (residual error).
A sentence or two? Yikes!
It's all about random vs fixed effects, I suppose, and so I would focus on shrinking individual estimates toward the population mean (aka BLUP).