Testing Approaches for Overdispersion in Poisson Regression versus the Generalized Poisson Model

2007 ◽  
Vol 49 (4) ◽  
pp. 565-584 ◽  
Author(s):  
Zhao Yang ◽  
James W. Hardin ◽  
Cheryl L. Addy ◽  
Quang H. Vuong
Keyword(s):  
Poisson Regression ◽  
Poisson Model ◽  
Generalized Poisson ◽  
Generalized Poisson Model

Migration Models Incorporating Interdependence of Movers

1995 ◽  
Vol 27 (9) ◽  
pp. 1493-1502 ◽  
Author(s):  
R Flowerdew ◽  
P J Boyle
Keyword(s):  
Goodness Of Fit ◽  
Spatial Interaction ◽  
Local Level ◽  
Poisson Model ◽  
Data Set ◽  
Generalized Poisson ◽  
Spatial Interaction Models ◽  
Generalized Poisson Model ◽  
Generalized Cost ◽  
Number Of Individuals

Models of migration between regions are often based on the assumption that individual moves can be modelled by a Poisson distribution whose parameter is a function of origin and destination characteristics, and generalized cost; this is true of Poisson regression models and spatial interaction models. The Poisson assumption is that each individual acts independently from others making the same move. In fact, migration is usually engaged in by household groups, not independent individuals, making the Poisson assumption invalid. It is possible instead to construct a model in which the probability of a household moving is given by a Poisson model and the number of individuals in a moving household is given by an observed household-size distribution. This generalized Poisson model is explained and fitted to a set of data on local-level migration within the English county of Hereford and Worcester. However, the sparse nature of the data set raises problems in assessing goodness of fit because the deviance value is unusually low. This is tackled here with a simulation methodology.

scholarly journals Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts

2017 ◽  
Vol 17 (6) ◽  
pp. 359-380 ◽  
Author(s):  
Alan Huang
Keyword(s):  
Poisson Regression ◽  
Regression Models ◽  
Negative Binomial ◽  
Asymptotic Properties ◽  
Poisson Model ◽  
Finite Sample ◽  
Generalized Poisson ◽  
The Mean ◽  
Generalized Poisson Regression ◽  
Log Linear

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. This note illustrates 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. Other link functions are also available, of course. In addition to establishing attractive theoretical and asymptotic properties of the proposed model, its good finite-sample performance is exhibited through various examples and a simulation study based on real datasets. Moreover, the MATLAB routine to fit the model to data is demonstrated to be up to an order of magnitude faster than the current software to fit standard CMP models, and over two orders of magnitude faster than the recently proposed hyper-Poisson model.

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