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

From: Doran, Harold <>
Date: Sun 21 May 2006 - 22:55:25 EST

Prof Gelman:

I believe the answer is yes. It sounds as though persons are partially crossed within food items?

Assuming a logit link, the syntax might follow along the lines of

fm1 <- lmer(DV ~ foods + sex + age + (1|food_item), data, family = binomial(link='logit'), method = "Laplace", control = list(usePQL= FALSE) )

Maybe this gets you partly there.


-----Original Message-----

From: on behalf of Andrew Gelman
Sent:	Sat 5/20/2006 5:49 AM
Subject:	[R] Can lmer() fit a multilevel model embedded in a regression?

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.




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, 

Andrew Gelman
Professor, Department of Statistics
Professor, Department of Political Science

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