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Abstract:

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi-item / multi-period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it to an arbitrary continuous distribution with a specific correlation matrix. We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data.

Abstract:

While Poisson regression is a popular tool for modeling count data, it is limited by its associated model assumptions. One assumption is that the response variable follows a Poisson distribution. However, over- or under-dispersion are common in practice and are not accommodated by Poisson regression. In addition, the dispersion is assumed fixed across observations, whereas in practice dispersion may vary across groups or according to some other factor. Recently, Sellers and Shmueli (2008) introduced the Conway-Maxwell-Poisson (CMP) regression, based on the CMP distribution. CMP regression generalizes both Poisson and logistic regression models and allows for over- or under-dispersed count data. The model structure introduced, however, assumes a fixed dispersion level across all observations. In this paper, we extend the CMP regression model to account for observation-level dispersion. We discuss model estimation, inference, diagnostics, and interpretation, and present a variable selection technique. We then compare our model to several alternatives and illustrate its advantages and usefulness using datasets with varying types and levels of dispersion.

Abstract:

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive to Poisson regression. We propose a regression model based on the Conway-Maxwell-Poisson (CMP) distribution to address this problem. The CMP regression generalizes the well-known Poisson and logistic regression models, and is suitable for tting count data with a wide range of dispersion levels. With a GLM approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a CMP regression over a standard Poisson regression. We compare the CMP to several alternatives and illustrate its advantages and usefulness using three datasets with
varying dispersion.

Notes:

Attached are both the paper and the supplementary materials (two separate files). R code is available at http://www9.georgetown.edu/faculty/kfs7/research

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Abstract:

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive to Poisson regression. We propose a regression model based on the Conway-Maxwell-Poisson (CMP) distribution to address this problem. The CMP regression generalizes the well-known Poisson and logistic regression models, and is suitable for fitting count data with a wide range of dispersion levels. With a GLM approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a CMP regression over a standard Poisson regression. We compare the CMP to several alternatives and illustrate its advantages and usefulness using four datasets with
varying dispersion.

Notes:

R code is available at http://www9.georgetown.edu/faculty/kfs7/research/

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