In the analysis of clustered data, when a generalized linear model with a random intercept term is fitted using maximum marginal likelihood and maximum conditional likelihood, respectively, a discrepancy between estimated regression coefficients from the two methods has been observed. This discrepancy happens when some cluster-level confounders are omitted from the model. Here we offer a straightforward explanation for the discrepancy in terms of different modeling assumptions underlying the use of the two likelihood functions. Specifically, the marginal likelihood approach requires a full distributional assumption on random effects, and this assumption is violated when some cluster-level confounders are omitted from the model. We also propose to use residual plots to uncover the problem.
Bibliographical noteFunding Information:
WePaniis Assistant Profe, Divisiossnoof Biorstatisti,cSchosol of Public Hlth,eA460aMayo Building,MMC 303,University of Minnesota, Minneaolis,p MN 55455 (E-mail: firstname.lastname@example.org). The author thanks John Neuhaus for kindly providing the birth weight data. The author is grateful to an associate editor and the editor for many construvecandthelpiful commts. Theis rneseh arc ws supaported by NIH grant R01-HL65462.
- Generalized linear models
- Modeling assumptions
- Residual plots