On the Correlation Structure of Gaussian Copula Models for Geostatistical Count Data

Han, Zifei; Oliveira, Victor De

doi:10.1111/anzs.12140

Cited by 22 publications

(24 citation statements)

References 14 publications

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“…However, the computational time was excessive when we attempted to use it on one of our simulated sample with cluster size

N_{i} = 60

, making it unsuitable for our purpose. Han and De Oliveira (2016) developed an R package gcKrig to conduct simulation studies on dependent negative binomial or ZIP models. However, such tools are currently unavailable for correlated ZICMP data.…”

Section: Discussionmentioning

confidence: 99%

Analyzing longitudinal clustered count data with zero inflation: Marginal modeling using the Conway–Maxwell–Poisson distribution

2021

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Biological and medical researchers often collect count data in clusters at multiple time points. The data can exhibit excessive zeros and a wide range of dispersion levels. In particular, our research was motivated by a dental dataset with such complex data features: the Iowa Fluoride Study (IFS). The study was designed to investigate the effects of various dietary and nondietary factors on the caries development of a cohort of Iowa school children at the ages of 5, 9, and 13. To analyze the multiyear IFS data, we propose a novel longitudinal method of a generalized estimating equations based marginal regression model. We use a zero‐inflated model with a Conway–Maxwell–Poisson (CMP) distribution, which has the flexibility to account for all levels of dispersion. The parameters of interest are estimated through a modified expectation–solution algorithm to account for the clustered and temporal correlation structure. We fit the proposed zero‐inflated CMP model and perform a comprehensive secondary analysis of the IFS dataset. It resulted in a number of notable conclusions that also make clinical sense. Additionally, we demonstrated the superiority of this modeling approach over two other popular competing models: the zero‐inflated Poisson and negative binomial models. In the simulation studies, we further evaluate the performance of our point estimators, the variance estimators, and that of the large sample confidence intervals for the parameters of interest. It is also demonstrated that our longitudinal CMP model can correctly identify the time‐varying dispersion patterns.

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“…However, the computational time was excessive when we attempted to use it on one of our simulated sample with cluster size

N_{i} = 60

Section: Discussionmentioning

confidence: 99%

Analyzing longitudinal clustered count data with zero inflation: Marginal modeling using the Conway–Maxwell–Poisson distribution

2021

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“…Hence, COR{Y (s), Y (u)} can be quickly and accurately approximated by truncating the series in Equation 14 and approximating the coefficients in Equation 15 by numerical quadrature (e.g., using the R function integrate()). Han and De Oliveira (2016) used this expansion to investigate properties of this correlation function, founding it to be flexible in several regards; see Section 3.5 for computational details.…”

Section: Correlation Function Of the Gaussian Copula Random Fieldmentioning

confidence: 99%

“…in which case the mean-variance relation in Equation 2 holds; see Cameron and Trivedi (2013) and Han and De Oliveira (2016).…”

Section: Namementioning

confidence: 99%

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gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas

Han¹,

Oliveira²

2018

J. Stat. Soft.

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This work describes the R package gcKrig for the analysis of geostatistical count data using Gaussian copulas. The package performs likelihood-based inference and spatial prediction using Gaussian copula models with discrete marginals. Two different classes of methods are implemented to evaluate/approximate the likelihood and the predictive distribution. The package implements the computationally intensive tasks in C++ using an R/C++ interface, and has parallel computing capabilities to predict the response at multiple locations simultaneously. In addition, gcKrig also provides functions to simulate and visualize geostatistical count data, and to compute the correlation function of the counts. It is designed to allow a flexible specification of both the marginals and the spatial correlation function. The principal features of the package are illustrated by three data examples from ecology, agronomy and petrology, and a comparison between gcKrig and two other R packages.

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“…An alternative to SGLMMs for discrete data is Gaussian copula models which construct random fields given a pre-specified family of marginal distributions. Here, the joint cumulative distribution function (cdf) of the spatial responses is characterized by a Gaussian copula corresponding to an underlying Gaussian process; see, e.g., Madsen (2009), Kazianka and Pilz (2010), and Han and De Oliveira (2016). Gaussian copulas provide simplicity in specifying spatial dependence, and flexibility in selecting discrete marginal distributions.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Geostatistical Modeling for Discrete-Valued Processes

Zheng¹,

Kottas²,

Sansó³

2021

Preprint

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We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class characterizes spatial variability by a weighted combination of first-order conditional probability mass functions (pmfs) for each one of a given number of neighbors. The approach supports flexible modeling for multivariate dependence through specification of general bivariate discrete distributions that define the conditional pmfs. Moreover, the discrete NNMP allows for construction of models given a pre-specified family of marginal distributions that can vary in space, facilitating covariate inclusion. In particular, we develop a modeling and inferential framework for copula-based NNMPs that can attain flexible dependence structures, motivating the use of bivariate copula families for spatial processes. Compared to the traditional class of spatial generalized linear mixed models, where spatial dependence is introduced through a transformation of response means, our process-based modeling approach provides both computational and inferential advantages. We illustrate the benefits with synthetic data examples and an analysis of North American Breeding Bird Survey data.

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On the Correlation Structure of Gaussian Copula Models for Geostatistical Count Data

Cited by 22 publications

References 14 publications

Analyzing longitudinal clustered count data with zero inflation: Marginal modeling using the Conway–Maxwell–Poisson distribution

Analyzing longitudinal clustered count data with zero inflation: Marginal modeling using the Conway–Maxwell–Poisson distribution

gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas

Bayesian Geostatistical Modeling for Discrete-Valued Processes

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