[R] Can lmer() fit a multilevel model embedded in a regression?

[Andrew Gelman]

I would like to fit a hierarchical regression model from Witte et al. 
(1994; see reference below).  It's a logistic regression of a health 
outcome on quntities of food intake; the linear predictor has the form,
X*beta + W*gamma,
where X is a matrix of consumption of 82 foods (i.e., the rows of X 
represent people in the study, the columns represent different foods, 
and X_ij is the amount of food j eaten by person i); and W is a matrix 
of some other predictors (sex, age, ...).

The second stage of the model is a regression of X on some food-level 
predictors.

Is it possible to fit this model in (the current version of) lmer()?  
The challenge is that the persons are _not_ nested within food items, so 
it is not a simple multilevel structure.

We're planning to write a Gibbs sampler and fit the model directly, but 
it would be convenient to be able to flt in lmer() as well to check.

Andrew

---

Reference:

Witte, J. S., Greenland, S., Hale, R. W., and Bird, C. L. (1994).  
Hierarchical regression analysis applied to a
study of multiple dietary exposures and breast cancer.  Epidemiology 5, 
612-621.

-- 
Andrew Gelman
Professor, Department of Statistics
Professor, Department of Political Science
gelman at stat.columbia.edu
www.stat.columbia.edu/~gelman

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