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Title: mpcmp: Mean-parametrized Conway-Maxwell-Poisson regression Authors:  Thomas Fung - Macquarie University (Australia) [presenting]
Justin Wishart - Macquarie University (Australia)
Alan Huang - University of Queensland (Australia)
Aya Alwan - Macquarie University (Australia)
Abstract: Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the mean of counts, making them not compatible with nor comparable to competing count regression models, such as the log-linear Poisson, negative-binomial or generalized Poisson regression models. We review how CMP distributions can be parametrized via the mean, so that simpler and more easily interpretable mean-models can be used, such as a log-linear model. Moreover, we introduce the R package: mpcmp which provides a collection of functions for estimation, testing and diagnostic checking for the proposed model. The performance of the R routine against the earlier proposed MATLAB routine will also be discussed.