Flexible bivariate correlated count data regression

We develop a model‐based boosting approach for multivariate distributional regression within the framework of generalized additive models for location, scale, and shape. Our approach enables the simultaneous modeling of all distribution parameters of an arbitrary parametric distribution of a multivariate response conditional on explanatory variables, while being applicable to potentially high‐dimensional data. Moreover, the boosting algorithm incorporates data‐driven variable selection, taking various different types of effects into account. As a special merit of our approach, it allows for modeling the association between multiple continuous or discrete outcomes through the relevant covariates. After a detailed simulation study investigating estimation and prediction performance, we demonstrate the full flexibility of our approach in three diverse biomedical applications. The first is based on high‐dimensional genomic cohort data from the UK Biobank, considering a bivariate binary response (chronic ischemic heart disease and high cholesterol). Here, we are able to identify genetic variants that are informative for the association between cholesterol and heart disease. The second application considers the demand for health care in Australia with the number of consultations and the number of prescribed medications as a bivariate count response. The third application analyses two dimensions of childhood undernutrition in Nigeria as a bivariate response and we find that the correlation between the two undernutrition scores is considerably different depending on the child's age and the region the child lives in.

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“…A further alternative allowing for overdispersion in the marginal distributions is the bivariate negative binomial distribution. 25,30,40…”

Section: Bivariate Bernoulli Distributionmentioning

confidence: 99%

Section: Boosting Multivariate Distributional Regressionmentioning

confidence: 99%

Boosting multivariate structured additive distributional regression models

Strömer

Klein

Staerk

et al. 2023

Statistics in Medicine

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“…This definition also allows for negative correlations, but results in more difficult interpretations. A further alternative allowing for overdispersion in the marginal distributions is the bivariate negative binomial distribution (Kocherlakota and Kocherlakota, 1992;Ma et al, 2020). We refrain from describing this distribution in more detail given our application in Section 4.2, where previous works have considered the bivariate Poisson distribution to be a reasonable modeling choice (Karlis and Ntzoufras, 2005).…”

Section: Bivariate Poisson Distributionmentioning

confidence: 99%

Boosting Multivariate Structured Additive Distributional Regression Models

Strömer¹,

Klein²,

Staerk³

et al. 2022

Preprint

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We develop a model-based boosting approach for multivariate distributional regression within the framework of generalized additive models for location, scale, and shape. Our approach enables the simultaneous modeling of all distribution parameters of an arbitrary parametric distribution of a multivariate response conditional on explanatory variables, while being applicable to potentially high-dimensional data. Moreover, the boosting algorithm incorporates data-driven variable selection, taking various different types of effects into account. As a special merit of our approach, it allows for modelling the association between multiple continuous or discrete outcomes through the relevant covariates. After a detailed simulation study investigating estimation and prediction performance, we demonstrate the full flexibility of our approach in three diverse biomedical applications. The first is based on high-dimensional genomic cohort data from the UK Biobank, considering a bivariate binary response (chronic ischemic heart disease and high cholesterol). Here, we are able to identify genetic variants that are informative for the association between cholesterol and heart disease. The second application considers the demand for health care in Australia with the number of consultations and the number of prescribed medications as a bivariate count response. The third application analyses two dimensions of childhood undernutrition in Nigeria as a bivariate response and we find that the correlation between the two undernutrition scores is considerably different depending on the child's age and the region the child lives in.

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“…They presented an application of the Frank and Gaussian copula to model dependence, and marginal time series were modeled using Poisson and negative binomial INAR(1) distributions. Ma et al (2020) proposed a copula approach utilizing a Gaussian copula with random effects to model correlated bivariate count data regression.…”

Section: Review Of Copula For Discrete Datamentioning

confidence: 99%

Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data

Fernando¹,

Alqawba²,

Samad³

et al. 2022

IJSP

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The class of bivariate integer-valued time series models, described via copula theory, is gaining popularity in the literature because of applications in health sciences, engineering, financial management and more. Each time series follows a Markov chain with the serial dependence captured using copula-based distribution functions from the Poisson and the zero-inflated Poisson margins. The copula theory is again used to capture the dependence between the two series. However, the efficiency and adaptability of the copula are being challenged because of the discrete nature of data and also in the case of zero-inflation of count time series. Likelihood-based inference is used to estimate the model parameters for simulated and real data with the bivariate integral of copula functions. While such copula functions offer great flexibility in capturing dependence, there remain challenges related to identifying the best copula type for a given application.  This paper presents a survey of the literature on bivariate copula for discrete data with an emphasis on the zero-inflated nature of the modelling. We demonstrate additional experiments on to confirm that the copula has potential as greater research area.

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Flexible bivariate correlated count data regression

Cited by 11 publications

References 30 publications

Boosting multivariate structured additive distributional regression models

Boosting multivariate structured additive distributional regression models

Boosting Multivariate Structured Additive Distributional Regression Models

Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data

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