title: An approximate marginal logistic distribution for the analysis of longitudinal ordinal data.
abstract: Subject-specific and marginal models have been developed for the analysis of longitudinal ordinal data. Subject-specific models often lack a population-average interpretation of the model parameters due to the conditional formulation of random intercepts and slopes. Marginal models frequently lack an underlying distribution for ordinal data, in particular when generalized estimating equations are applied. To overcome these issues, latent variable models underneath the ordinal outcomes with a multivariate logistic distribution can be applied. In this article, we extend the work of O'Brien and Dunson (2004), who studied the multivariate t-distribution with marginal logistic distributions. We use maximum likelihood, instead of a Bayesian approach, and incorporated covariates in the correlation structure, in addition to the mean model. We compared our method with GEE and demonstrated that it performs better than GEE with respect to the fixed effect parameter estimation when the latent variables have an approximately elliptical distribution, and at least as good as GEE for other types of latent variable distributions.
authors.affiliation: University of Groningen, University Medical Center Groningen, Groningen, The Netherlands.|Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands.
authors.forename: Nazanin
authors.initials: N
authors.lastname: Nooraee
authors.affiliation: Johann Bernoulli Institute of Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands.
authors.forename: Fentaw
authors.initials: F
authors.lastname: Abegaz
authors.affiliation: University of Groningen, University Medical Center Groningen, Interdisciplinary Center of Psychopathology and Emotion Regulation, Groningen, The Netherlands.
authors.forename: Johan
authors.initials: J
authors.lastname: Ormel
authors.affiliation: Johann Bernoulli Institute of Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands.
authors.forename: Ernst
authors.initials: E
authors.lastname: Wit
authors.affiliation: University of Groningen, University Medical Center Groningen, Groningen, The Netherlands.|Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands.
authors.forename: Edwin R
authors.initials: ER
authors.lastname: van den Heuvel
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D016013:Likelihood Functions; D016015:Logistic Models; D008137:Longitudinal Studies; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D064232:Visual Analog Scale
keywords: Flexible correlation matrix; Generalized estimating equations; Latent variable models; Maximum likelihood; Multivariate logistic distribution; Population-averaged (marginal) models; t-distribution