Statistical Science

Marginalized multilevel models and likelihood inference (with comments and a rejoinder by the authors)

Patrick J. Heagerty and Scott L. Zeger

Full-text: Open access

Abstract

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.

Article information

Source
Statist. Sci., Volume 15, Number 1 (2000), 1-26.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.ss/1009212671

Digital Object Identifier
doi:10.1214/ss/1009212671

Mathematical Reviews number (MathSciNet)
MR1842235

Keywords
Generalized linear model latent variable logistic regression random effects model

Citation

Heagerty, Patrick J.; Zeger, Scott L. Marginalized multilevel models and likelihood inference (with comments and a rejoinder by the authors). Statist. Sci. 15 (2000), no. 1, 1--26. doi:10.1214/ss/1009212671. https://projecteuclid.org/euclid.ss/1009212671


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