A flexible zero-inflated model to address data dispersion

Sellers, Kimberly F.; Raim, Andrew M.

doi:10.1016/j.csda.2016.01.007

Cited by 51 publications

(47 citation statements)

References 13 publications

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“…Sellers and Shmueli (2010) presented a flexible regression model based on the COM-Poisson distribution that can deal with over and underdispersed data. The COM-Poisson model has also recently been extended to deal with zeroinflation (Sellers and Raim;2016). Zeviani et al (2014) discussed the analysis of underdispersed experimental data based on the Gamma-Count distribution.…”

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confidence: 99%

Extended Poisson–Tweedie: Properties and regression models for count data

Bonat

Jørgensen

Kokonendji

et al. 2017

Statistical Modelling

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We propose a new class of discrete generalized linear models based on the class of Poisson-Tweedie factorial dispersion models with variance of the form µ + φµ p , where µ is the mean, φ and p are the dispersion and Tweedie power parameters, respectively. The models are fitted by using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. This provides a flexible and efficient regression methodology for a comprehensive family of count models including Hermite, Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian. The estimating function approach allows us to extend the Poisson-Tweedie distributions to deal with underdispersed count data by allowing negative values for the dispersion parameter φ. Furthermore, the Poisson-Tweedie family can automatically adapt to highly skewed count data with excessive zeros, without the need to introduce zero-inflated or hurdle components, by the simple estimation of the power parameter. Thus, the proposed models offer a unified framework to deal with under, equi, overdispersed, zero-inflated and heavy-tailed count data. The computational implementation of the proposed models is fast, relying only on a simple Newton scoring algorithm. Simulation studies showed that the estimating function approach provides unbiased and consistent estimators for both regression and dispersion parameters. We highlight the ability * Generalized linear models (GLMs) (Nelder and Wedderburn;1972) have been the main statistical tool for regression modelling of normal and non-normal data over the past four decades. The success enjoyed by the GLM framework comes from its ability to deal with a wide range of normal and non-normal data. GLMs are fitted by a simple and efficient Newton score algorithm relying only on second-moment assumptions for estimation and inference. Furthermore, the theoretical background for GLMs is well established in the class of dispersion models (Jørgensen; 1987, 1997) as a generalization of the exponential family of distributions. In particular, the Tweedie family of distributions plays an important role in the context of GLMs, since it encompasses many special cases including the normal, Poisson, non-central gamma, gamma and inverse Gaussian.In spite of the flexibility of the Tweedie family, the Poisson distribution is the only choice for the analysis of count data in the context of GLMs. For this reason, in practice there is probably an over-emphasis on the use of the Poisson distribution for count data. A well known limitation of the Poisson distribution is its mean and variance relationship, which implies that the variance equals the mean, referred to as equidispersion. In practice, however, count data can present other features, namely underdispersion (mean > variance) and overdispersion (mean < variance) that is often related to zero-inflation or a heavy tail. These departures can make the Poisson distribution unsuitable, or at lea...

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confidence: 99%

Extended Poisson–Tweedie: Properties and regression models for count data

Bonat

Jørgensen

Kokonendji

et al. 2017

Statistical Modelling

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“…In fact, all other models produce a difference that associates with considerably less support to essentially no support. The binomial case can be viewed as the summation of three Bernoulli trials, thus we expect the corresponding sCMP estimates to beλ ≈ 2 andν ≥ 30; recall that the special CMP case that corresponds with a Bernoulli distribution occurs when ν → ∞ with probability λ 1+λ , where empirical evidence shows that dispersion parameter estimation is sufficiently achieved whenν ≈ 30 or more (see and Sellers and Raim (2016) for examples). In fact, for the simulated Binomial dataset, we obtainλ = 2.0000, ν = 33.6942; the obtained estimate for ν implies extreme under-dispersion, thus we have sufficient evidence implying that the estimates approximate a Bernoulli distribution with Sellers et al Journal of Statistical Distributions and Applications (2017) …”

Section: Simulation Studymentioning

confidence: 99%

“…The CMP distribution has quickly grown in popularity because of its ability to model count data in a flexible manner. Methodological developments are vast, including works in distribution theory (Sellers 2012;Sellers and Shmueli 2013;Borges et al 2014), regression analysis (Sellers and Shmueli 2009;2010;Sellers and Raim 2016), control chart Table 1 Well-known distributions associated with the Conway-Maxwell-Poisson (CMP) distribution for special cases of λ and ν…”

Section: Z(λe T ν)mentioning

confidence: 99%

A flexible distribution class for count data

2017

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The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution -a two-parameter generalization of the Poisson distribution that can accommodate data over-or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model's flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion.

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“…The CMP was reintroduced to the scientific community by Shmueli et al . () and since then has found broader biological application (Wu et al ., ; Lynch et al ., ; Choo‐Wosoba et al ., ; Sellers & Raim, ). The availability of software (e.g.…”

Section: Discussionmentioning

confidence: 99%

Probability distributions for marketable pods and white mould on snap bean

Shah

Dillard

Pethybridge

2017

Annals of Applied Biology

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White mould, caused by Sclerotinia sclerotiorum, is one of the most recalcitrant diseases of snap bean. Probability distributions suitable for describing the total number of marketable pods (hereafter simply referred to as pods) per plant, as well as for the number of pods and stems with white mould per plant, have not been identified. The total number of pods and the number of pods and stems with white mould were measured on a per plant basis in plots of processing snap bean (var. Hystyle) in New York. The total number of pods per plant ranged from 0 to 29, and was best described by the Pólya-Aeppli distribution. The number of pods and the number of stems with white mould per plant were well-described by the negative binomial (NB) distribution. A Sarmanov bivariate distribution with NB marginals was derived and fitted to the joint data on the number of pods and stems with white mould per plant, accounting for correlation between pods and stems with white mould on the same plant. The bivariate distribution was used to formulate an empirical equation for the incidence of plants with white mould as a function of the average number of pods and stems with white mould per plant. The results represented a more complete understanding of the distributional properties of white mould in snap bean.

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A flexible zero-inflated model to address data dispersion

Cited by 51 publications

References 13 publications

Extended Poisson–Tweedie: Properties and regression models for count data

Extended Poisson–Tweedie: Properties and regression models for count data

A flexible distribution class for count data

Probability distributions for marketable pods and white mould on snap bean

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