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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).

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If you need to explain fixed/random as terms, I'd go with this. If you were simply giving an example, I'd suggest using the terms "group effect" and "individual effect", which I believe are also correct but less mysterious to the layman. – Wayne Oct 19 '11 at 11:26
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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).

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Thanks, both answers helped a lot. – rob Oct 20 '11 at 17:56

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