Abstract

We propose a joint mean and correlation regression model for multivariate dis

crete and (semi-)continuous response data, that simultaneously regresses the mean of each

response against a set of covariates, and the correlations between responses against a set

of similarity/distance measures. A set of joint estimating equations are formulated to construct an estimator of both the mean regression coefficients and the correlation regression

parameters. Under a general setting where the number of responses can tend to infinity, the

joint estimator is demonstrated to be consistent and asymptotically normally distributed,

with differing rates of convergence due to the mean regression coefficients being heterogeneous across responses. An iterative estimation procedure is developed to obtain parame-

ter estimates in the required (constrained) parameter space. Simulations demonstrate the

strong finite sample performance of the proposed estimator in terms of point estimation

and inference. We apply the proposed model to a count dataset of 38 Carabidae ground

beetle species sampled throughout Scotland, along with information about the environmental conditions of each site and the traits of each species. Results show the relationship

between mean abundance and environmental covariates differs across the beetle species,

and that beetle total length is important in driving the correlations between species.

Information

Preprint No.SS-2024-0109
Manuscript IDSS-2024-0109
Complete AuthorsZhi Yang Tho, Francis K. C. Hui, Tao Zou
Corresponding AuthorsZhi Yang Tho
Emailszhiyang.tho@anu.edu.au

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Acknowledgments

Zhi Yang Tho was supported by an Australian Government Research Training

Program scholarship. Francis KC Hui was supported by an Australian Research

Council Discovery Project DP240100143. Tao Zou’s research was supported

by computational resources provided by the Australian Government through the

National Computational Infrastructure (NCI), under the ANU Startup Allocation

Scheme. The authors thank Alan Welsh for his helpful comments.

Supplementary Materials

The Supplementary Material includes all proofs and algorithms, as well as additional results for the simulation study and real data application.

Supplementary materials are available for download.