<scp>Conway–Maxwell–Poisson</scp>regression models for dispersed count data

Sellers, Kimberly F.; Premeaux, Bailey

doi:10.1002/wics.1533

Cited by 27 publications

(17 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…is not straightforward. Here, the R package COMPoissonReg was used for this purpose (Sellers et al 2018). Since stationarity cannot reasonably be assumed in our setting, we estimate the initial distribution = Pr(s m1 = 1), … , Pr(s m1 = N) , regarding the parameters of as N − 1 additional parameters to be estimated.…”

Section: A Baseline Modelmentioning

confidence: 99%

A copula-based multivariate hidden Markov model for modelling momentum in football

2021

View full text Add to dashboard Cite

We investigate the potential occurrence of change points—commonly referred to as “momentum shifts”—in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state dependence of the variables, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.

show abstract

Section: A Baseline Modelmentioning

confidence: 99%

A copula-based multivariate hidden Markov model for modelling momentum in football

2021

View full text Add to dashboard Cite

show abstract

“…logistic mixed model). Compute estimates and in the analytic approach, or compute and in the sampling approach. Compute estimates using (6) and (7). Compute for k = 1, …, n c using the R package COMPoissonReg (44). …”

Section: The Cmp Testmentioning

confidence: 99%

BinomiRare: A carriers-only test for association of rare genetic variants with a binary outcome for mixed models and any case-control proportion

Sofer

Lee

Kurniansyah

et al. 2021

Preprint

View full text Add to dashboard Cite

Whole genome and exome sequencing studies have become increasingly available and are being used to identify rare genetic variants associated with health and disease outcomes. Investigators routinely use mixed models to account for genetic relatedness or other clustering variables (e.g. family or household) when testing genetic associations. However, no existing tests of the association of a rare variant association with a binary outcome in the presence of correlated data controls the Type 1 error where there are (1) few carriers of the rare allele, (2) a small proportion of cases relative to controls, and (3) covariates to adjust for. Here, we address all three issues in developing the carriers-only test framework for testing rare variant association with a binary trait. In this framework, we estimate outcome probabilities under the null hypothesis, and then use them, within the carriers, to test variant associations. We extend the BinomiRare test, which was previously proposed for independent observations, and develop the Conway-Maxwell-Poisson (CMP) test, and study their properties in simulations. We show that the BinomiRare test always controls the type 1 error, while the CMP test sometimes does not. We then use the BinomiRare test to test the association of rare genetic variants in target genes with small vessel disease stroke, short sleep, and venous thromboembolism, in whole-genome sequence data from the Trans-Omics for Precision Medicine program.

show abstract

“…Indeed, real count data are often overdispersed (variance larger than mean) or underdispersed (variance smaller than mean). In either case, the inability of a model to account for underdispersion or overdispersion can cause standard errors to be biased downward or upward, thus under or over estimating the statistical significance of associated explanatory variables [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…A third limitation is the lack of a simple parametrization via the mean, leading to hardly interpretable regression fits [15]. The poisson polynomial regression [16], the Conway-Maxwell-Poisson (CMP) regression [1,8], the Gamma-count regression [4] and the discrete Weibull regression [6] are examples of models bearing this drawback.…”

Section: Introductionmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Cf¹,

Rl²

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Conway–Maxwell–Poissonregression models for dispersed count data

Cited by 27 publications

References 44 publications

A copula-based multivariate hidden Markov model for modelling momentum in football

A copula-based multivariate hidden Markov model for modelling momentum in football

BinomiRare: A carriers-only test for association of rare genetic variants with a binary outcome for mixed models and any case-control proportion

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

Contact Info

Product

Resources

About