A generalized Waring regression model for count data

Avi, José Rodríguez; Sánchez, Antonio Conde; Sáez-Castillo, A. J.; Olmo-Jiménez, María José; Martínez-Rodríguez, Ana María

doi:10.1016/j.csda.2009.03.013

Cited by 41 publications

(34 citation statements)

References 9 publications

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“…For example, methods based on Waring distributions and regression (e.g. Irwin, 1968; Xekalaki, 1983, 1984; Rodríguez‐Avi et al, 2007, 2009) use parametric distributions based on Poisson, Gamma and Beta distributions to decompose variation into several components: randomness and between‐subject heterogeneity explainable by covariates (liability) or intrinsic to individuals (proneness). Our models could be viewed in terms of decompositions using random effects, into components between subjects described by u i and any subject‐level covariates (e.g.…”

Section: Discussionmentioning

confidence: 99%

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A statistical model for under- or overdispersed clustered and longitudinal count data

et al. 2011

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We propose a likelihood-based model for correlated count data that display under- or overdispersion within units (e.g. subjects). The model is capable of handling correlation due to clustering and/or serial correlation, in the presence of unbalanced, missing or unequally spaced data. A family of distributions based on birth-event processes is used to model within-subject underdispersion. A computational approach is given to overcome a parameterization difficulty with this family, and this allows use of common Markov Chain Monte Carlo software (e.g. WinBUGS) for estimation. Application of the model to daily counts of asthma inhaler use by children shows substantial within-subject underdispersion, between-subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. The model provides a major improvement over Poisson longitudinal models, and diagnostics show that the model fits well.

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Section: Discussionmentioning

confidence: 99%

“…This approach has been extended to further decompose components of variation in count data using generalized Waring distributions and Waring regression (e.g. Irwin, 1968; Xekalaki, 1983, 1984; Rodríguez‐Avi et al, 2007, 2009), and also to allow different forms of covariate effects in Negative Binomial models (e.g. Greene, 2007).…”

Section: Introductionmentioning

confidence: 99%

A statistical model for under- or overdispersed clustered and longitudinal count data

et al. 2011

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“…The mean is given by so ρ > 1 must be imposed in order to guarantee its existence. Again, considering the effect of the covariates on the mean as μ x = e x ′ β , the GWRM arises and For further details of this regression model see [6]. …”

Section: The Generalized Waring Regression Modelmentioning

confidence: 99%

“…In relation to the limiting cases of the GWRM , it may be proved [6] that if k , ρ → ∞ with the same order of convergence, the GWRM tends to a NegbinI model, while if ρ → ∞ and μ x / k is bounded, the GWRM tends to a NegbinII model.…”

Section: The Generalized Waring Regression Modelmentioning

confidence: 99%

“…And that is the ground of the Generalized Waring Regression Model ( GWRM ) [6]. If we have a sample consisting of n cases for which we know the result of the counting process, y i , and a series of common covariates, x i , for i = 1, …, n , a GWRM fitting this dataset would permit the inference that the counts are affected by a) pure chance (randomness); b) variability due to different exposures to risk related to the existent covariates (liability); and c) variability due exclusively to individual differences not related to the covariates (proneness).…”

Section: Introductionmentioning

confidence: 99%

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GWRM: An R Package for Identifying Sources of Variation in Overdispersed Count Data

2016

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Understanding why a random variable is actually random has been in the core of Statistics from its beginnings. The generalized Waring regression model for count data explains that inherent variability is given by three possible sources: randomness, liability and proneness. The model extends the negative binomial regression model and it is not included in the family of generalized linear models. In order to avoid that shortcoming, we developed the R package for fitting, describing and validating the model. The version we introduce in this communication provides a new design of the modelling function as well as new methods operating on the associated fitted model objects, so that the new software integrates easily into the computational toolbox for modelling count data in R. The release of a plug-in in order to use the package from the interface R Commander tries to contribute to the spreading of the model among non-advanced users. We illustrate the usage and the possibilities of the software with two examples from the fields of health and sport.

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A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets

Altun

2021

Comput Stat

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A generalized Waring regression model for count data

Cited by 41 publications

References 9 publications

A statistical model for under- or overdispersed clustered and longitudinal count data

A statistical model for under- or overdispersed clustered and longitudinal count data

GWRM: An R Package for Identifying Sources of Variation in Overdispersed Count Data

A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets

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