A Random-Effects Ordinal Regression Model for Multilevel Analysis

Abstract

A random-effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data. This model is developed for both the probit and logistic response functions. The threshold concept is used, in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects. A maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of random effects. An analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random-effects analysis of clustered ordinal data, while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random-effects approach for longitudinal ordinal data.

Comparison of sulfasalazine and placebo in the treatment of psoriatic arthritis. A department of veterans affairs cooperative study

“…Mixed-model analyses (12) were done to characterize the response patterns over time using SAS PROC MIXED (13) for continuous data and a freeware program named MIXOR (14) for categorical and ordinal data. All other analyses were conducted using SAS version 6.08 (15).…”

Seroepidemiology of Helicobacter pylori infection in a Jamaican community

“…Associations between seroprevalence of H. pylori and the major principal components were then sought using logistic regression -Mixed Effects Ordinal Regression (MIXOR) -for the analysis of clustered responses. This computer program was developed by Drs D Hedeker and RD Gibbons of the University of Illinois at Chicago (Hedeker & Gibbons 1994;Goldstein 1995), and controls any influence of inherent clustering of participants within households and yards in the study.…”

Methods for testing theory and evaluating impact in randomized field trials: Intent-to-treat analyses for integrating the perspectives of person, place, and time

“…Such methods have evolved from simple comparisons of proportions, as with the CD analyses above, to adjusted means in analysis of covariance, to methods that incorporate nonlinear modeling (Brown, 1993b;Hastie and Tibshirani, 1990), growth modeling (Muthén, 1997(Muthén, , 2003(Muthén, , 2004Muthén and Curran, 1997;Muthén and Shedden, 1999;Muthén et al, 2002) and multilevel modeling (Gibbons et al, 1988;Goldstein, 2003;Hedeker and Gibbons, 1994;Raudenbush, 1997;Raudenbush and Bryk, 2002;Raudenbush and Liu, 2000). Since a recent listing of such methods and their use in the BPP First generation trial is available elsewhere , we highlight only a few novel applications for RFTs in this paper.…”

“…For computations, we have used R with the contributed package MGCV (R Project, 2007). In RFTs, clustering at different levels can be incorporated in the model by adding random covariate effects (Gibbons and Hedeker, 1997;Gibbons et al, 1988;Hedeker and Gibbons, 1994). To test if inclusion of random effects helps with the model fitting, we can perform a likelihood ratio test.…”

“…In epidemiology, which seeks to identify the causes of a disorder in a population, we first start descriptively by identifying the person, place, and time factors that link those with the disorder to those without such a disorder (Lilienfeld and Lilienfeld, 1980). From the perspective of prevention methodology, these same person, place, and time considerations play a fundamental roles in trial design (Brown and Liao, 1999;Brown et al, 2006Brown et al, , 2007a and analysis Bryk and Raudenbush, 1987;Goldstein, 2003;Hedeker and Gibbons, 1994;Muthén, 1997;Muthén and Shedden, 1999;Muthén et al, 2002;Raudenbush, 1997;Wang et al, 2005;Xu and Hedeker, 2001). Randomized trial designs have extended beyond those with individual level randomization to those that randomize at the level of the group or place (Brown and Liao, 1999;Brown et al, 2006;Donner and Klar, 2000;Murray, 1998;Raudenbush, 1997;Raudenbush and Liu, 2000;Seltzer, 2004).…”