A random-effects ordinal regression model for multilevel analysis. (English) Zbl 0826.62049

Hedeker, Donald; Gibbons, Robert D.

Biometrics 50, No. 4, 933-944 (1994).

Summary: 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 function 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.

MSC:

62J05	Linear regression; mixed models
62P10	Applications of statistics to biology and medical sciences; meta analysis
65C99	Probabilistic methods, stochastic differential equations

Keywords:

logistic regression; probit regression; repeated observations; random- effects ordinal regression model; ordinal response data; threshold; maximum marginal likelihood; Gauss-Hermite quadrature; clustered ordinal data; longitudinal ordinal data