Inspired by this post on the difference between explaining and predicting. I want to ask

  • is mixed model primarily used to get better explanation (such as, but not limited to, getting better coefficients and standard errors, or being able to decompose the variation), or is it primarily used to get better prediction?

I imagine the answer would be the former (explaining), and if that's the case,

  • does it add any value to prediction?

(would appreciate any form of discussion, but would also be delighted to see published references on the issue)

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    $\begingroup$ If you have unbalanced clustered data, a mixed effects model will not only try to provide better standard errors but also better coefficients (and thus better predictions). $\endgroup$ – Michael M Jun 18 '14 at 13:32
  • $\begingroup$ @Michael. Better coefficients don't always translates to better prediction. The field of measurement error is a classic example. $\endgroup$ – qoheleth Jun 19 '14 at 2:08
  • $\begingroup$ Mixed model implies random effects, and random effects can be viewed as smoothed fixed effects. Smoothing increases bias while decreasing variance, like in ridge regression. Thus, if you're taking "explanation" to mean causal inference, you don't want mixed models, unless your group effects truly are IID. Note that there are newer ways of specifying mixed models better (a recent Battaglia paper) that get around this problem, but that basically come to the same answer as one would get using entirely fixed effects for groups. $\endgroup$ – generic_user Jun 19 '14 at 3:37

does it add any value to prediction?


  • When it doesn't. Imagine that you have thousands of subjects (say mice), each with thousands of measurements within subject (say cortisol over time), and you're estimating regression parameters that are known to vary considerably across each subject. Then mixed models methodology won't help you predict (in any practical sense). Just fit a separate regression for each subject, and that's about as good as you're going to do. For the explanatory part, you could still think of your coefficients as random after the fact, and look at the distribution of the coefficient estimates.
  • When it does. Now say you have thousands of subjects, but only 1 to 3 measurements per subject. Each subject's regression is going to be crap. This is where the mixed model methodology helps you. You're sharing information among the subjects by shrinking each coefficient to the mean of that distribution. You'll get better predictions, plus the random effects interpretation with considerably less to work with.

would also be delighted to see published references on the issue

In the case that pressing the "Publish" button in Blogger counts, here's something I wrote a while back. Hope it helps.

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Well mixed models are used to decompose and explain variance (e.g multilevel models). Variance may be substantively important (it is in my field, epidemiology). So my response is a toss up between "neither" and "to explain, but not in the sense that you mean."

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