Practical Marginalized Multilevel Models

Abstract

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate the MMM and approximate MMM approaches on a cerebrovascular deficiency crossover trial using SAS and an epidemiological study on race and visual impairment using R. Datasets, SAS and R code are included as supplemental materials.

Keywords: generalized linear mixed model; latent variable; likelihood inference; marginal model; nonlinear mixed model; random effects.

Figure 1

Crossover Trial Profile Likelihoods: All methods provide similar evidence about the marginal treatment effect. Tabled values are the k = 8; 16 Support Intervals (SI) and the Likelihood Ratio comparing the MLE for the treatment effect ${\widehat{\alpha }}_1$ to no treatment effect, α₁ = 0 (LR₀).