Joint Regression Analysis for Discrete Longitudinal Data

• Published in: Biometrics Vol. 67; no. 3; pp. 1171 - 1175
• Main Authors: Madsen, L, Fang, Y
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.09.2011; Wiley-Blackwell; Blackwell Publishing Ltd
• Subjects: Approximation; Biometrics; biometry; Biometry - methods; Continuous extension; Correlated data; Correlations; Dependent data; Discrete data; equations; Estimators; Gaussian copula; Humans; Infection; Likelihood Functions; Longitudinal data; Longitudinal Studies; Maximum likelihood estimation; Models, Statistical; Nail Diseases - microbiology; Parameter estimation; READER REACTION; Regression Analysis; Standard error; Statistical variance; Toes; Vibration
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2010.01494.x

We introduce an approximation to the Gaussian copula likelihood of Song, Li, and Yuan (2009, Biometrics 65, 60–68) used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes. Our approximation allows estimation of parameters from response vectors of length much larger than three, and is asymptotically equivalent to the Gaussian copula likelihood. We estimate regression parameters from the toenail infection data of De Backer et al. (1996, British Journal of Dermatology 134, 16–17), which consist of binary response vectors of length seven or less from 294 subjects. Although maximizing the Gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation (GEE) estimators, our simulation study illustrates that for finite samples, GEE estimators can actually be as much as 20% more efficient.