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Marginally Interpretable Generalized Linear Mixed Models

Gory, Jeffrey J.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Statistics.
A popular approach for relating correlated measurements of a non-Gaussian response variable to a set of predictors is to introduce latent random variables and fit a generalized linear mixed model. The conventional strategy for specifying such a model leads to parameter estimates that must be interpreted conditional on the latent variables. In many cases, interest lies not in these conditional parameters, but rather in marginal parameters that summarize the average effect of the predictors across the entire population. Due to the structure of the generalized linear mixed model, the average effect across all individuals in a population is generally not the same as the effect for an average individual. Further complicating matters, obtaining marginal summaries from a generalized linear mixed model often requires evaluation of an analytically intractable integral or use of an approximation. Another popular approach in this setting is to fit a marginal model using generalized estimating equations. This strategy is effective for estimating marginal parameters, but leaves one without a formal model for the data with which to assess quality of fit or make predictions for future observations. Thus, there exists a need for a better approach. We define a class of marginally interpretable generalized linear mixed models that lead to parameter estimates with a marginal interpretation while maintaining the desirable statistical properties of a conditionally specified model. The distinguishing feature of these models is an additive adjustment that accounts for the curvature of the link function and thereby preserves a specific form for the marginal mean after integrating out the latent random variables. We discuss the form and interpretation of marginally interpretable generalized linear mixed models under various common link functions and compare inferences obtained from these models to those obtained from conventional generalized linear mixed models, highlighting the advantages of the marginally interpretable formulation over the conventional one. We also address computational issues associated with marginally interpretable generalized linear mixed models in both a classical framework and a Bayesian framework. Namely, we introduce an accurate and efficient method for evaluating the logistic-normal integral that arises in logistic mixed effects models and, for the Bayesian setting, we propose a modification of a standard Markov chain Monte Carlo algorithm that allows for more efficient posterior simulation in models with many latent random variables.
Peter Craigmile, Ph.D. (Advisor)
Steven MacEachern, Ph.D. (Advisor)
Eloise Kaizar, Ph.D. (Committee Member)
Jennifer Sinnott, Ph.D. (Committee Member)
177 p.
Statistics
marginal model; conditional model; logistic-normal integral; population-averaged; subject-specific predictions

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Citations

  • Gory, J. J. (2017). Marginally Interpretable Generalized Linear Mixed Models [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606

    APA Style (7th edition)

  • Gory, Jeffrey. Marginally Interpretable Generalized Linear Mixed Models. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606.

    MLA Style (8th edition)

  • Gory, Jeffrey. "Marginally Interpretable Generalized Linear Mixed Models." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606

    Chicago Manual of Style (17th edition)

osu1497966698387606
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This open access ETD is published by The Ohio State University and OhioLINK.
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