Bayesian Conway–Maxwell–Poisson regression models for overdispersed and underdispersed counts

Huang, Alan; Kim, Andy Sang Il

doi:10.1080/03610926.2019.1682162

Cited by 12 publications

(8 citation statements)

References 16 publications

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“…The standard CMP model is not parameterised through its mean, however, restricting its wider applicability in regression settings since this renders effects hard to quantify, other than as a general increase or decrease. To counter this, two alternative parameterisations via the mean have been developed (Huang, 2017;Ribeiro Jr et al, 2018;Huang and Kim, 2019), each with associated R packages (Fung et al, 2019;Elias Ribeiro Junior, 2021). The mean of the standard CMP distribution can be found as…”

Section: Truncated Mean-parameterised Cmp Distributionmentioning

confidence: 99%

“…Hence, the CMP distribution can be mean-parameterised to allow a more conventional count regression interpretation, where λ ijk is a nonlinear function of µ ijk and ν under this reparameterisation. Huang (2017) suggested a hybrid bisection and Newton-Raphson approach to find λ ijk and applied this in small sample Bayesian settings (Huang and Kim, 2019), whereas Ribeiro Jr et al (2018) used an asymptotic approximation of G ∞ (λ ijk , ν)…”

Section: Truncated Mean-parameterised Cmp Distributionmentioning

confidence: 99%

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A truncated mean-parameterised Conway-Maxwell-Poisson model for the analysis of Test match bowlers

Philipson¹

2021

Preprint

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Assessing the relative merits of sportsmen and women whose careers took place far apart in time via a suitable statistical model is a complex task as any comparison is compromised by fundamental changes to the sport and society and often handicapped by the popularity of inappropriate traditional metrics. In this work we focus on cricket and the ranking of Test match bowlers using bowling data from the first Test in 1877 onwards. A truncated, mean-parameterised Conway-Maxwell-Poisson model is developed to handle the under-and overdispersed nature of the data, which are in the form of small counts, and to extract the innate ability of individual bowlers. Inferences are made using a Bayesian approach by deploying a Markov Chain Monte Carlo algorithm to obtain parameter estimates and confidence intervals. The model offers a good fit and indicates that the commonly used bowling average is a flawed measure.

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Section: Truncated Mean-parameterised Cmp Distributionmentioning

confidence: 99%

Section: Truncated Mean-parameterised Cmp Distributionmentioning

confidence: 99%

A truncated mean-parameterised Conway-Maxwell-Poisson model for the analysis of Test match bowlers

Philipson¹

2021

Preprint

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“…(Huang & Kim, 2019) instead develop a Bayesian MCMP1 regression model where they directly apply a multivariate normal prior for the coefficients associated with the mean, β ∼ N ( μ β , ∑ β ) and an exponential prior for the (constant) dispersion parameter, using the resulting joint posterior in their Metropolis–Hastings algorithm. Their algorithm uses the MLEs

\overset{β}{true}

and

\overset{ν}{true}

as the starting values with the estimated variance–covariance associated with

\overset{β}{true}

serving as an estimate for the variance–covariance matrix ∑ β , and alternates parameter updating in the Markov chain.…”

Section: Basic Constructmentioning

confidence: 99%

“…Their algorithm uses the MLEs

\overset{β}{true}

and

\overset{ν}{true}

as the starting values with the estimated variance–covariance associated with

\overset{β}{true}

serving as an estimate for the variance–covariance matrix ∑ β , and alternates parameter updating in the Markov chain. The authors meanwhile circumvent the issue of the intractable normalizing constants throughout the Metropolis‐Hastings algorithm by substituting the infinite summations with finite sums as approximations; see (Huang & Kim, 2019) for details. While the authors concede that this approach does not produce the most efficient algorithm, they note that it serves as a nice starting point for Bayesian regression modeling under the MCMP1 reparametrization.…”

Section: Basic Constructmentioning

confidence: 99%

Conway–Maxwell–Poissonregression models for dispersed count data

Sellers

Premeaux

2020

WIREs Computational Stats

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While Poisson regression serves as a standard tool for modeling the association between a count response variable and explanatory variables, it is well‐documented that this approach is limited by the Poisson model's assumption of data equi‐dispersion. The Conway–Maxwell–Poisson (COM‐Poisson) distribution has demonstrated itself as a viable alternative for real count data that express data over‐ or under‐dispersion, and thus the COM‐Poisson regression can flexibly model associations involving a discrete count response variable and covariates. This work overviews the ongoing developmental knowledge and advancement of COM‐Poisson regression, introducing the reader to the underlying model (and its considered reparametrizations) and related regression constructs, including zero‐inflated models, and longitudinal studies. This manuscript further introduces readers to associated computing tools available to perform COM‐Poisson and related regressions. This article is categorized under: Statistical Models > Linear Models Statistical Models > Generalized Linear Models

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“…The failure to provide regression coefficients with a simple interpretation as in Poisson regression is the major limitation to the routine use of many flexible regression approaches, as applied scientists will likely sacrifice any perceived gains in model flexibility for a simpler, more easily interpretable approach [8]. One of the currently most attractive flexible count regression approach is the Mean-parametrized Conway-Maxwell-Poisson (MCMP) regression model [5,17]. Although this regression model is based on the CMP distribution [18] which does not have a simple parametrization via the mean, it tries to circumvent this limitation by directly modelling the mean of the count response using a computationally demanding procedure.…”

Section: Introductionmentioning

confidence: 99%

A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference

Cf¹,

Rl²

2021

Preprint

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Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

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Bayesian Conway–Maxwell–Poisson regression models for overdispersed and underdispersed counts

Cited by 12 publications

References 16 publications

A truncated mean-parameterised Conway-Maxwell-Poisson model for the analysis of Test match bowlers

A truncated mean-parameterised Conway-Maxwell-Poisson model for the analysis of Test match bowlers

Conway–Maxwell–Poissonregression models for dispersed count data

A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference

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