Multiple inflated negative binomial regression for correlated multivariate count data

Mathews Joseph (), Bhattacharya Sumangal (), Sen Sumen () and Das Ishapathik ()
Additional contact information
Mathews Joseph: Department of Statistical Science, Trinity College of Arts & Sciences, Duke University, Durham, North Carolina, United States
Bhattacharya Sumangal: Department of Mathematics, Indian Institute of Technology Tirupati, Tirupati, India
Sen Sumen: Department of Mathematics and Statistics, Austin Peay State University, Clarksville, Tennessee, United States
Das Ishapathik: Department of Mathematics, Indian Institute of Technology Tirupati, Tirupati, India

Dependence Modeling, 2022, vol. 10, issue 1, 290-307

Abstract: This article aims to provide a method of regression for multivariate multiple inflated count responses assuming the responses follow a negative binomial distribution. Negative binomial regression models are common in the literature for modeling univariate and multivariate count data. However, two problems commonly arise in modeling such data: choice of the multivariate form of the underlying distribution and modeling the zero-inflated structure of the data. Copula functions have become a popular solution to the former problem because they can model the response variables’ dependence structure. The latter problem is often solved by modeling an assumed latent variable Z Z generating excess zero-valued counts in addition to the underlying distribution. However, despite their flexibility, zero-inflation models do not account for the case of m m additional inflated values at k 1 , k 2 , … , k m {{\bf{k}}}_{1},{{\bf{k}}}_{2},\ldots ,{{\bf{k}}}_{m} . We propose a multivariate multiple-inflated negative binomial regression model for modeling such cases. Furthermore, we present an iterative procedure for estimating model parameters using maximum likelihood estimation. The multivariate distribution functions considering the dependence structure of the response vectors are found using copula methods. The proposed method is illustrated using simulated data and applied to real data.

Keywords: Copulas; inflated distribution; multivariate count data; negative binomial distributions; regression models (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/demo-2022-0149 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:10:y:2022:i:1:p:290-307:n:1

DOI: 10.1515/demo-2022-0149

Access Statistics for this article

Dependence Modeling is currently edited by Giovanni Puccetti

More articles in Dependence Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().