The Analysis of Longitudinal Polytomous Data: Generalized Estimating Equations and Connections with Weighted Least Squares

In recent years, methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual. Although situations in which the repeated response is binary or Poisson have been studied extensively, relatively little attention has been given to p...

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Bibliographic Details
Published in:Biometrics 1993-12, Vol.49 (4), p.1033-1044
Main Authors: Miller, Michael E., Davis, Charles S., Landis, J. Richard
Format: Article
Language:English
Subjects:
Analysis of Variance
Biological and medical sciences
Biometrics
Biometry - methods
Computer Simulation
Correlations
Covariance matrices
Data Interpretation, Statistical
Estimation methods
Humans
Jewelry
Least squares
Least-Squares Analysis
Logistic Models
Longitudinal Studies
Medical sciences
Models, Statistical
Odds Ratio
Parametric models
Psychology. Psychoanalysis. Psychiatry
Psychopathology. Psychiatry
Randomized Controlled Trials as Topic - statistics & numerical data
Statistical discrepancies
Statistical estimation
Statistical variance
Statistics
Techniques and methods
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Summary:In recent years, methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual. Although situations in which the repeated response is binary or Poisson have been studied extensively, relatively little attention has been given to polytomous categorical response variables. In this paper, we extend the estimating equations initially developed for clustered discrete data by Liang and Zeger (1986, Biometrika 73, 13-22), and subsequently extended by Prentice (1988, Biometrics 44, 1033-1048), to polytomous response variables. Under certain assumptions, we illustrate that these estimating equations simplify to the weighted least squares (WLS) equations formalized by Koch et al. (1977, Biometrics 33, 133-158). This connection provides a formal framework for obtaining iterated weighted least squares model parameter estimates. Cumulative logit models are developed and applied to a representative longitudinal data set. Simulation results comparing WLS, an iterative form of WLS, and independence estimating equations using a robust estimate of the variance are presented.
ISSN:0006-341X
1541-0420
DOI:10.2307/2532245