Is it kosher to use random-intercept estimates as explanatory variables in another model?
The random effects are not independent "observations"; the amount of shrinkage depends on the model parameters which are estimated from all the data. So unless there is no shrinkage associated with the random effects this is not a good idea. It may be better to to think about including the other variables (plus suitable interaction terms) in the first model. Alternatively, a structural equation model may be a better path to pursue. Reinhold Kliegl
On Mon, Jun 6, 2011 at 7:55 PM, Jeremy Koster <helixed2 at yahoo.com> wrote:
I'm reviewing a paper for a colleague, and I haven't seen this done before. Imagine that she has a sample of 100 houses, all of which include children who raise chickens. ?She includes a random term for household and finds that there is substantial household-level variance in chicken husbandry by kids. She then takes the household-level estimates (i.e., plus/minus relative to the model intercept) and uses them as an explanatory variable in an OLS model with households as the sampling unit. ?For example, she would predict something like household-level income while using the random-intercept estimates from the chicken analysis (and other covariates). At first glance, this might seem relatively straightforward, but I haven't encountered similar analyses, and I'm wondering about potential pitfalls . . . particularly given the variable number of kids in each house. Any thoughts? Thanks!
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