On generating multivariate Poisson data in management science applications

Yahav, Inbal; Shmueli, Galit

doi:10.1002/asmb.901

Cited by 75 publications

(40 citation statements)

References 34 publications

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“…Examples include the overlapping sums (Madsen and Dalthorp 2007;Mardia 1970;Kocherlakota 1992, 2001); lognormalPoisson hierarchy; a method named "normal-to-anything" (NORTA; Cario and Nelson 1997;Cario and Nelson 1998;Nelsen 2006;Mardia 1970;Li and Hammond 1975), and extensions thereof (Yahav and Shmueli 2012;Ghosh and Pasupathy 2012;Shin and Pasupathy 2010;Avramidis, Channouf, and L'Ecuyer 2009;Park and Shin 1998;Downer and Moser 2001). Next, we briefly describe these methods in turn.…”

Section: Introductionmentioning

confidence: 99%

Generating Correlated and/or Overdispersed Count Data: ASASImplementation

Kalema

Molenberghs²

2016

J. Stat. Soft.

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Analysis of longitudinal count data has, for long, been done using a generalized linear mixed model (GLMM), in its Poisson-normal version, to account for correlation by specifying normal random effects. Univariate counts are often handled with the negativebinomial (NEGBIN) model taking into account overdispersion by use of gamma random effects. Inherently though, longitudinal count data commonly exhibit both features of correlation and overdispersion simultaneously, necessitating analysis methodology that can account for both. The introduction of the combined model (CM) by Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs, Verbeke, Demétrio, and Vieira (2010) serves this purpose, not only for count data but for the general exponential family of distributions. Here, a Poisson model is specified as the parent distribution of the data with a normally distributed random effect at the subject or cluster level and/or a gamma distribution at observation level. The GLMM and NEGBIN model are special cases. Data can be simulated from (1) the general CM, with random effects, or, (2) its marginal version directly. This paper discusses an implementation of (1) in SAS software (SAS Inc. 2011). One needs to reflect on the mean of both the combined (hierarchical) and marginal models in order to generate correlated and/or overdispersed counts. A pre-specification of the desired marginal mean (in terms of covariates and marginal parameters), a marginal variance-covariance structure and the hierarchical mean (in terms of covariates and regression parameters) is required. The implied hierarchical parameters, the variance-covariance matrix of the random effects, and the variance-covariance matrix of the overdispersion part are then derived from which correlated Poisson data are generated. Sample calls of the SAS macro are presented as well as output.

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Section: Introductionmentioning

confidence: 99%

Generating Correlated and/or Overdispersed Count Data: ASASImplementation

Kalema

Molenberghs²

2016

J. Stat. Soft.

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“…Krummenauer [4], Cai and Kendall [5], Minhajuddin et al [6], Shin and Pasupathy [7], Yahav and Shmueli [8], and Barbiero and Ferrari [9] have developed various methods for generating simulated data from multivariate Poisson distribution. The Barbiero and Ferrari [9] approach was shown to be comparatively more efficient, user-friendly, and often more accurate than the prior methods.…”

Section: Introductionmentioning

confidence: 99%

Concurrent generation of multivariate mixed data with variables of dissimilar types

Amatya

Demirtaş

2016

Journal of Statistical Computation and Simulation

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Data sets originating from wide range of research studies are composed of multiple variables that are correlated and of dissimilar types, primarily of count, binary/ordinal and continuous attributes. The present paper builds on the previous works on multivariate data generation and develops a framework for generating multivariate mixed data with a pre-specified correlation matrix. The generated data consist of components that are marginally count, binary, ordinal and continuous, where the count and continuous variables follow the generalized Poisson and normal distributions, respectively. The use of the generalized Poisson distribution provides a flexible mechanism which allows under- and over-dispersed count variables generally encountered in practice. A step-by-step algorithm is provided and its performance is evaluated using simulated and real-data scenarios.

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“…Yahav and Shmueli proposed a modification of the NORmal To Anything method: the idea is to first generate an m ‐vector from the multivariate Normal distribution with correlation matrix R C and then to transform it into any desired distribution, using the inverse cumulative distribution function. However, the correlation matrix R of the desired multivariate distribution does not match R C , and this discrepancy is more evident as the target distributions get far from the multivariate Normal (i.e., continuous asymmetrical or discrete distributions).…”

Section: Introductionmentioning

confidence: 99%

“…Other multivariate models and corresponding simulation methods have been proposed, but they all present drawbacks in terms of computational complexity or applicability; for a complete survey, see . From these considerations, the need for a general and efficient simulation technique for correlated Poisson data emerges.…”

Section: Introductionmentioning

confidence: 99%

Simulation of correlated Poisson variables

Barbiero

Ferrari

2014

Appl Stoch Models Bus & Ind

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Generating correlated Poisson random variables is fundamental in many applications in the management and engineering fields, and in many others where multivariate count data arise. Multivariate Poisson data are often approximately simulated by either independent univariate Poisson or multivariate Normal data, whose implementation is provided by the most common statistical software packages such as R. However, such simulated data are often not satisfactory. Alternatively, methods for simulating multivariate Poisson data can be used, but they are adversely affected by limitations ranging from computational complexity to restrictions on the correlation matrix, which dramatically reduce their practical applicability. In this work, we propose a new method that is highly accurate and computationally efficient and can be usefully employed even by non‐expert users in generating correlated Poisson data (and, more generally, any discrete variable), with assigned marginal distributions and correlation matrix. Copyright © 2014 John Wiley & Sons, Ltd.

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On generating multivariate Poisson data in management science applications

Cited by 75 publications

References 34 publications

Generating Correlated and/or Overdispersed Count Data: ASASImplementation

Generating Correlated and/or Overdispersed Count Data: ASASImplementation

Concurrent generation of multivariate mixed data with variables of dissimilar types

Simulation of correlated Poisson variables

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