Open Access
1 February 2000 Marginalized multilevel models and likelihood inference (with comments and a rejoinder by the authors)
Patrick J. Heagerty, Scott L. Zeger
Statist. Sci. 15(1): 1-26 (1 February 2000). DOI: 10.1214/ss/1009212671


Hierarchical or ‘‘multilevel’’ regression models typically parameterize the mean response conditional on unobserved latent variables or ‘‘random’’ effects and then make simple assumptions regarding their distribution. The interpretation of a regression parameter in such a model is the change in possibly transformed mean response per unit change in a particular predictor having controlled for all conditioning variables including the random effects. An often overlooked limitation of the conditional formulation for nonlinear models is that the interpretation of regression coefficients and their estimates can be highly sensitive to difficult-to-verify assumptions about the distribution of random effects, particularly the dependence of the latent variable distribution on covariates. In this article, we present an alternative parameterization for the multilevel model in which the marginal mean, rather than the conditional mean given random effects, is regressed on covariates. The impact of random effects model violations on the marginal and more traditional conditional parameters is compared through calculation of asymptotic relative biases. A simple two-level example from a study of teratogenicity is presented where the binomial overdispersion depends on the binary treatment assignment and greatly influences likelihood-based estimates of the treatment effect in the conditional model. A second example considers a three-level structure where attitudes toward abortion over time are correlated with person and district level covariates. We observe that regression parameters in conditionally specified models are more sensitive to random effects assumptions than their counterparts in the marginal formulation.


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Patrick J. Heagerty. Scott L. Zeger. "Marginalized multilevel models and likelihood inference (with comments and a rejoinder by the authors)." Statist. Sci. 15 (1) 1 - 26, 1 February 2000.


Published: 1 February 2000
First available in Project Euclid: 24 December 2001

MathSciNet: MR1842235
Digital Object Identifier: 10.1214/ss/1009212671

Keywords: generalized linear model , latent variable , logistic regression , random effects model

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.15 • No. 1 • February 2000
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