Flexible Tweedie regression models for continuous data

Bonat, Wagner Hugo; Kokonendji, Célestin C.

doi:10.1080/00949655.2017.1318876

Cited by 54 publications

(31 citation statements)

References 34 publications

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“…Discussion of the efficiency of the estimating function estimators is difficult due to the lack of a closed form for the Fisher information matrix. Bonat and Kokonendji (2016) showed in the context of Tweedie regression models that the quasi-score function provides asymptotically efficient estimators for the regression parameters, thus a similar result is expected for the Poisson-Tweedie regression model. Concerning the dispersion and power parameters, the fact that the sensitivity and variability matrices do not coincide indicates that the Pearson estimating functions are not optimum.…”

Section: Discussionsupporting

confidence: 59%

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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Section: Discussionsupporting

confidence: 59%

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

Bonat

Jørgensen

Kokonendji

et al. 2017

Statistical Modelling

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“…Of the fluency (WE, RE, SN), and network variables (, NC ), only M was best fit with a normal distribution. The tweedie variance function 109 was used to fit WE, RE, SN and , while the poisson-tweedie variance function 110 was used to fit the count variables, NC and Error.…”

Section: Resultsmentioning

confidence: 99%

Phonological network fluency identifies phonological restructuring through mental search

Neergaard

Luo

Huang

2019

Sci Rep

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We investigated network principles underlying mental search through a novel phonological verbal fluency task. Post exclusion, 95 native-language Mandarin speakers produced as many items that differed by a single lexical tone as possible within one minute. Their verbal productions were assessed according to several novel graded fluency measures, and network science measures that accounted for the structure, cohesion and interconnectedness of lexical items. A multivariate regression analysis of our participants’ language backgrounds included their mono- or multi-lingual status, English proficiency, and fluency in other Chinese languages/dialects. Higher English proficiency predicted lower error rates and greater interconnectedness, while higher fluency in other Chinese languages/dialects revealed lower successive similarity and lower network coherence. This inverse relationship between English and other Chinese languages/dialects provides evidence of the restructuring of the phonological mental lexicon.

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“…To evaluate if the diet shift was systematic, that is occurred each spring preceding a mast, we used a similar approach with the RQ i , investigating potential inter‐annual effects on the relative quantity of each food in the diet of the population (RQ i , model 3). The Tweedie distribution is adapted to treat data with a right‐skewed distribution and high proportions of exact 0s (Bonat & Kokonendji, ). We included beech mast (Yes/No, models 1 and 2) or years (model 3).…”

Section: Methodsmentioning

confidence: 99%

Consumption of red maple in anticipation of beech mast‐seeding drives reproduction in eastern chipmunks

Tissier

Réale

Garant

et al. 2020

Journal of Animal Ecology

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1. Understanding the determinants of reproduction is a central question in evolutionary ecology. In pulsed-resource environments, the reproduction and population dynamics of seed consumers are driven by pulsed production of seeds by trees or mast-seeding. In Southern Québec, eastern chipmunks Tamias striatus exclusively reproduce during the summer before and the spring after a mast-seeding event of American beech. They thus seem to anticipate beech mast by reproducing during early summer, so that juveniles can emerge at the time of maximum beechnut abundance during late summer.2. However, the cues allowing chipmunks to anticipate beech mast remain unknown, and the existence of the anticipation process itself has been questioned. To tackle those issues, we investigated the links between the nutritional ecology and reproduction of adult chipmunks and compared their spring diet in mast-versus postmast years.3. We monitored female reproductive status (N = 446), analysed cheek pouch contents at capture (n = 3,761 captures) and recorded seed production by deciduous trees on three different sites in Mont-Sutton from 2006 to 2018. 4. Results revealed a systematic shift in chipmunk diet towards red maple seeds in springs preceding a beech mast, with red maple seeds composing more than 77% of chipmunk diet. However, red maple consumption was unrelated to red maple production, but was related to beech seed production in the upcoming fall. We also found that red maple consumption best predicted the proportion of females in summer oestrus. Our results confirm that chipmunks anticipate beech mast-seeding and highlighta key role of red maple consumption in that anticipation. Results also suggest that red maple seeds may contain nutrients or secondary plant components essential to sustain or trigger the summer reproduction in chipmunks, which allow them to remain synchronized with pulsed productions of both red maple and beech and improve their fitness.Additional supporting information may be found online in the Supporting Information section. How to cite this article: Tissier ML, Réale D, Garant D, Bergeron P. Consumption of red maple in anticipation of beech mast-seeding drives reproduction in eastern chipmunks. J Anim

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Flexible Tweedie regression models for continuous data

Cited by 54 publications

References 34 publications

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

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

Phonological network fluency identifies phonological restructuring through mental search

Consumption of red maple in anticipation of beech mast‐seeding drives reproduction in eastern chipmunks

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