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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

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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
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:
DateEvent
April 2019Published
27 September 2017Accepted
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:
Project/Grant IDRIOXX Funder NameFunder ID
2016YFC0800100National Basic Research Program of China (973 Program)UNSPECIFIED
11671374[NSFC] National Natural Science Foundation of Chinahttp://dx.doi.org/10.13039/501100001809
71631006[NSFC] National Natural Science Foundation of Chinahttp://dx.doi.org/10.13039/501100001809
SES-1533956National Science Foundationhttp://dx.doi.org/10.13039/100000001
IS-1546087National Science Foundationhttp://dx.doi.org/10.13039/100000001
EP/N510129/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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