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Discrete longitudinal data modeling with a mean-correlation regression approach
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Tang, Cheng Yong, Zhang, Weiping and Leng, Chenlei (2019) Discrete longitudinal data modeling with a mean-correlation regression approach. Statistica Sinica, 29 (2). SS-2016-0435. doi:10.5705/ss.202016.0435
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Official URL: https://doi.org/10.5705/ss.202016.0435
Abstract
Joint mean-covariance regression modeling with unconstrained parametrization for continuous longitudinal data has provided statisticians and practitionersJoint mean-covariance regression modeling with unconstrained parametrization for continuous longitudinal data has provided statisticians and practitioners with a powerful analytical device. How to develop a delineation of such a regression framework amongst discrete longitudinal responses remains an open and more challenging problem. This paper studies a novel mean-correlation regression for a family of generic discrete responses. Targeting the joint distributions of the discrete longitudinal responses, our regression approach is constructed by using a copula model whose correlation parameters are represented in hyperspherical coordinates with no constraint on their support. To overcome computational intractability in maximizing the full likelihood function of the model, we propose a computationally efficient pairwise likelihood approach. A pairwise likelihood ratio test is then constructed and validated for statistical inferences. We show that the resulting estimators of our approaches are consistent and asymptotically normal. We demonstrate the effectiveness, parsimoniousness and desirable performance of the proposed approach by analyzing three data sets and conducting extensive simulations with a powerful analytical device. How to develop a delineation of such a regression framework amongst discrete longitudinal responses remains an open and more challenging problem. This paper studies a novel mean-correlation regression for a family of generic discrete responses. Targeting the joint distributions of the discrete longitudinal responses, our regression approach is constructed by using a copula model whose correlation parameters are represented in hyperspherical coordinates with no constraint on their support. To overcome computational intractability in maximizing the full likelihood function of the model, we propose a computationally efficient pairwise likelihood approach. A pairwise likelihood ratio test is then constructed and validated for statistical inferences. We show that the resulting estimators of our approaches are consistent and asymptotically normal. We demonstrate the effectiveness, parsimoniousness and desirable performance of the proposed approach by analyzing three data sets and conducting extensive simulations
| Item Type: | Journal Article | |||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
| Divisions: | Faculty of Science > Statistics | |||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Regression analysis, Longitudinal method, Correlation (Statistics) | |||||||||||||||||||||
| Journal or Publication Title: | Statistica Sinica | |||||||||||||||||||||
| Publisher: | Academia Sinica * Institute of Statistical Science | |||||||||||||||||||||
| ISSN: | 1017-0405 | |||||||||||||||||||||
| Official Date: | April 2019 | |||||||||||||||||||||
| Dates: |
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| Volume: | 29 | |||||||||||||||||||||
| Number: | 2 | |||||||||||||||||||||
| Article Number: | SS-2016-0435 | |||||||||||||||||||||
| DOI: | 10.5705/ss.202016.0435 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Access rights to Published version: | Open Access | |||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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