The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions ...

It is well known that occurrence counts of words in documents are often modeled poorly by standard distributions like the binomial or Poisson. Observed counts vary more than simple models predict, prompting the use of overdispersed models like Gamma-Poisson or Beta-binomial mixtures as robust alternatives. Another deficiency of standard models is due to the fact that most words never occur in a...

This chapter gives an account of the recent literature on estimating models for panel count data. Specifically, the treatment of unobserved individual heterogeneity that is correlated with the explanatory variables and the presence of explanatory variables that are not strictly exogenous are central. Moment conditions are discussed for these type of problems that enable estimation of the parame...

Applications of zero-inflated count data models have proliferated in health economics. However, zero-inflated Poisson or zero-inflated negative binomial maximum likelihood estimators are not robust to misspecification. This article proposes Poisson quasi-likelihood estimators as an alternative. These estimators are consistent in the presence of excess zeros without having to specify the full di...

The contribution investigates the problem of estimating the size of a population, also known as the missing cases problem. Suppose a registration system is targeting to identify all cases having a certain characteristic such as a specific disease (cancer, heart disease, ...), disease related condition (HIV, heroin use, ...) or a specific behavior (driving a car without license). Every case in s...

As previously argued, the correlation between included and omitted regressors generally causes inconsistency of standard estimators for count data models. Non-linear instrumental variables estimation of an exponential model under conditional moment restrictions is one of the proposed remedies. This approach is extended here by fully exploiting the model assumptions and thereby improving efficie...

Poisson regression models provide a standard framework for the analysis of count data. In practice, however, count data are often overdispersed relative to the Poisson distribution. One frequent manifestation of overdispersion is that the incidence of zero counts is greater than expected for the Poisson distribution and this is of interest because zero counts frequently have special status. For...

Social networks are thought to be important for the investment and performance of mutual fund managers. We propose a measure of whether a manager is part of a network using only data on the distribution of the number of stocks headquartered in a given city that are held by managers. For some cities, the count distribution is roughly Poisson. However, for a significant fraction of cities, the co...

This paper proposes a flexible bivariate count data regression model that nests the bivariate negative binomial regression. An application to the demand for health services is given.  2000 Elsevier Science S.A. All rights reserved.

Experiment 2: We generate synthetic data from the above model. We run posterior inference over all parameters. For 25 random entries in the data matrix, we plot the histogram of posterior samples of the true underlying count (shown in red). Four equivalent generative processes Locally Private Bayesian Inference for Count Models Aaron Schein UMass Amherst Zhiwei Steven Wu Microsoft Research Ming...