A Mixed-Effects Regression Model for Longitudinal Multivariate Ordinal Data

• Published in: Biometrics Vol. 62; no. 1; pp. 261 - 268
• Main Authors: Liu, Li C., Hedeker, Donald
• Format: Journal Article
• Language: English
• Published: 350 Main Street , Malden , MA 02148 , U.S.A , and P.O. Box 1354, 9600 Garsington Road , Oxford OX4 2DQ , U.K Blackwell Publishing 01.03.2006; International Biometric Society; Blackwell Publishing Ltd
• Subjects: Alcoholic beverages; Biometrics; Cigarettes; Consultant's Forum; Data Interpretation, Statistical; Gaussian quadratures; Humans; Item response theory models; Likelihood Functions; Logistics; Longitudinal Studies; Marijuana use; Maximum marginal likelihood; Modeling; Multilevel data; Multilevel models; Multiple outcomes; Multivariate Analysis; Nonproportional odds assumption; Ordinal data; Parametric models; Random-effects models; Regression Analysis; Substance-Related Disorders; Two-parameter model
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.1541-0420.2005.00408.x

A mixed-effects item response theory model that allows for three-level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies. This model allows for the estimation of different item factor loadings (item discrimination parameters) for the multiple outcomes. The covariates in the model do not have to follow the proportional odds assumption and can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is proposed utilizing multidimensional Gauss-Hermite quadrature for integration of the random effects. An iterative Fisher scoring solution, which provides standard errors for all model parameters, is used. An analysis of a longitudinal substance use data set, where four items of substance use behavior (cigarette use, alcohol use, marijuana use, and getting drunk or high) are repeatedly measured over time, is used to illustrate application of the proposed model.