Statistics and Its Interface

Volume 2 (2009)

Number 4

A mixed ordinal location scale model for analysis of ecological momentary assessment (EMA) data

Pages: 391 – 401



Hakan Demirtas (School of Public Health, University of Illinois at Chicago, Chicago, Il., U.S.A.)

Donald Hedeker (School of Public Health, University of Illinois at Chicago, Chicago, Il., U.S.A.)

Robin J. Mermelstein (Institute for Health Research and Policy, University of Illinois at Chicago, Chicago, Il., U.S.A.)


Mixed-effects logistic regression models are described for analysis of longitudinal ordinal outcomes, where observations are observed clustered within subjects. Random effects are included in the model to account for the correlation of the clustered observations. Typically, the error variance and the variance of the random effects are considered to be homogeneous. These variance terms characterize the within-subjects (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In this article, we describe how covariates can influence these variances, and also extend the standard logistic mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their responses. Additionally, we allow the random effects to be correlated. We illustrate application of these models for ordinal data using Ecological Momentary Assessment (EMA) data, or intensive longitudinal data, from an adolescent smoking study. These mixed-effects ordinal location scale models have useful applications in mental health research where outcomes are often ordinal and there is interest in subject heterogeneity, both between- and within-subjects.


complex variation, mood variation, heterogeneity, variance modeling

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