A quick note on Hierarchical Linear Models
Owen, Harris, & Jones have a pretty cool new paper out discussing strengths & weaknesses of hierarchical/multilevel linear modelling. In a wonderfully readable review paper, they pretty simply state in the review that hierarchical models don’t directly answer the classic question at the heart of tons of geographic research:
Given that you live where you do, talk to who you do, and interact with the social milleau that you do, how is your behavior different?
But, of course one model (or set of models) can’t answer this alone. Better models typically provide better estimates according to some statistical objective. But, these estimates are useless if they’re not supported by reasonable operationalizations of the concepts at hand. And, even then, better models don’t necessarily improve model helpfulness.
And, I know that the authors are hardly not anti-HLM or don’t understand it; I’ve been working with others at the GeoDa Center & some in the Geographic Data Science Lab at the University of Liverpool on replicating & extending some of the work done by a student of Harris.
Rather, I think the legitimate critiques presented in the Owen et al paper is playing with a larger tension I’ve joked about before:
All the limitations mentioned in the Owen et al paper are about the concepts & contexts onto which MLMs are applied. That is, they’re about the context of the statistical modelling, not the math of the model itself. In fact, most of the critiques focus on mismatch between “How is this used?” and “What can this do?”, like other famous critiques in this field.
And, these are legitimate critiques. It’s important to demonstrate where practitioners interpret a statistically sound model to say something it cannot (and does not) mean. So, in this sense, this article is a perfect example of statistics qua “complaining about anything that isn’t statistics,” although with much more meaningful complaints than that joke might presume.
Scholars that I’ve encountered occasionally confound these, judging a model unsound when it’s only misapplied. But, at their core, they are different issues. Unsound models can be applied in accordance with their warrants, and sound models can be applied in contexts where they have no hope of being correct.
The Owens et al. article is decidedly about contemporary MLM methods in the public health literature. And, again, I’m sure the authors are aware of that, but it’s otherwise too good of an article to avoid recognizing this distinction. But, when we ask
What do our models mean?
this involves both soundness and application. Owens presents discussion wholly about the latter.
imported from: yetanothergeographer