A more general methodology for fitting global cross-ratio models for discrete longitudinal responses

Abstract

In this paper, we focus on repeated measurement problems, comprising an interesting research area in statistics. We study longitudinal data which arise when outcomes are observed repeatedly on each experimental subject at several points. We focus on a marginal approach for this type of data with lack of independence among the observations proposed by Dale [Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics. 1986;42(4):909–917] for bivariate, discrete, ordered responses. We propose an alternative estimation based on divergence measures to the full likelihood method proposed in that paper. Finally, a wide simulation study and a data example that illustrates the new methodology is provided.

Keywords:

• longitudinal data
• global cross-ratio
• ordinal data
• minimum divergence estimator

Acknowledgements

This work was partially supported by grant MTM2009-06997. The authors gratefully acknowledge the constructive comments and suggestions of the Associate Editor as well as of two anonymous referees, which led to great improvements in the manuscript.