Zero-inflated Count Research Articles

Hierarchical Bayesian Analysis of Correlated Zero‐inflated Count Data

AbstractThis article presents two‐component hierarchical Bayesian models which incorporate both overdispersion and excess zeros. The components may be resultants of some intervention (treatment) that changes the rare event generating process. The models are also expanded to take into account any heterogeneity that may exist in the data. Details of the model fitting, checking and selecting alternative models from a Bayesian perspective are also presented. The proposed methods are applied to count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The History of Sinks - An Analysis of Negotiating Positions in the Climate Regime

The issue of terrestrial carbon sinks, officially labelled as Land use, Land-use change and Forestry (LULUCF) has been one of the most contentious and difficult issues in the international climate change negotiations. This study analyses the negotiation process on sinks from the third Conference of the Parties (COP 3) to COP 7 by using a multinomial logit model to identify factors influencing the negotiating positions on LULUCF of 166 Parties to the United Nations Framework Convention on Climate Change (UNFCCC). The results show that the importance of the forestry sector of a country does not seem to have affected the negotiation positions on LULUCF. However, the results suggest that the LULUCF issue was used by those Parties with a rather negative attitude towards international climate policy to reduce their Kyoto commitments. Pro-sinks Annex I Parties seem to have been motivated by the amount they were able to reduce their reduction target due to sinks, but not necessarily by the stringency of their target. By applying a zero-inflated count model, the study examines which factors influenced the participation in the submission process on LULUCF. Those Parties having taken a pro-sink position on Article 3.4 have been participating most in the submission process. The exact opposite is the case for the CDM, where the opponents of forestry projects have been the most active Parties in providing submissions. Delegation size has some, but rather modest influence on the participation in the submission process.

Modeling zero-inflated count series with application to occupational health

A zero-inflated Poisson mixed autoregression model is presented for analyzing time series of count events with excess zeros. The model is motivated by the evaluation of a participatory ergonomics intervention intended to reduce manual handling workplace injuries over a specified time period. Random effects are introduced into the linear predictor of the model to account for serial correlation between successive observations. Parameter estimation is achieved by maximizing an appropriate log-likelihood function to obtain approximate residual maximum likelihood estimates. The method enables the evaluation of occupational intervention using population level aggregated count data series containing extra zeros.

Modeling crashes involving pedestrians and motorized traffic

This paper presents an empirical inquiry into the predictive modeling of crashes involving pedestrians and motorized traffic on roadways. Empirical models based on the negative binomial distribution and mixing distributions, such as the zero-inflated Poisson distribution, are presented and discussed in terms of their applicability to pedestrian crash phenomena. Key modeling issues relating to the presence of excess zeros as well as unobserved heterogeneity in pedestrian crash distributions are addressed. The empirical results show that zero-inflated count distributions, such as the zero-inflated Poisson, are promising methodologies for providing explanatory insights into the causality behind pedestrian-traffic crashes.

Paying the Piper? Implications of Social Insurance Payments for Conflict Propensity

State leaders must often address domestic and foreign-policy concerns simultane-ously, though doing so can be complicated and risky. One way in which leaders can seek to satisfy domestic demands and pursue foreign policy goals simultaneously is by implementing policies that complement one another; i.e., the implementation of one policy influences the ease with which the other policy can be implemented. For instance, one manner in which leaders can placate domestic audiences is via distributive policies such as social insurance payments that provide economic security to individuals. By providing economic security guarantees, leaders may gain greater discretion over other policy areas, including foreign policy. However, while the social insurance effort may satisfy an audience and enable a leader to take foreign- policy action, especially high payment levels may indicate that a leader must devote an inordinate portion of his budget to domestic concerns, making foreign policy more difficult to implement. Thus, guarantees of economic security might provide leaders with greater foreign policy latitude until domestic expenditures reach sufficient levels that foreign-affairs budgets are reduced. We employ zero-inflated event count models to estimate the relationship between social-insurance levels and the number of Militarized Interstate Disputes in which states engage. Our analyses include 69 states between 1975 and 1990. Our models support the hypothesis that lower levels of social insurance lead to greater numbers of disputes, but that, after a certain level of insurance effort is passed, dispute involvement declines. Our findings suggest a differential effect of social insurance on a leader's ability to act in the foreign policy arena and support the notion that leaders may employ the welfare state to enhance their foreign-policy capabilities, though they appear to meet with conditional and limited success.

Zero-inflated models with application to spatial count data

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.

Impact of roadside features on the frequency and severity of run-off-roadway accidents: an empirical analysis

In the US, single-vehicle run-off-roadway accidents result in a million highway crashes with roadside features every year and account for approximately one-third of all highway fatalities. Despite the number and severity of run-off-roadway accidents, quantification of the effect of possible countermeasures has been surprisingly limited due to the absence of data (particularly data on roadside features) needed to rigorously analyze factors affecting the frequency and severity of run-off-roadway accidents. This study provides some initial insight into this important problem by combining a number of databases, including a detailed database on roadside features, to analyze run-off-roadway accidents on a 96.6-km section of highway in Washington State. Using zero-inflated count models and nested logit models, statistical models of accident frequency and severity are estimated and the findings isolate a wide range of factors that significantly influence the frequency and severity of run-off-roadway accidents. The marginal effects of these factors are computed to provide an indication on the effectiveness of potential countermeasures. The findings show significant promise in applying new methodological approaches to run-off-roadway accident analysis.

Models for zero-inflated count data using the Neyman type A distribution

We explore the possibility of modelling zero-inflated count data using the Neyman type A distribution. We extend three parameterizations of the Neyman type A distribution to allow their parameters to depend on covariates. We develop models which relate counts of Leadbeater’s possum to various habitat variables to illustrate the methodology. Half-normal plots are constructed for each model to explore the quality of the fit. We then formally compare the Neyman type A models using the method of Cox to test non-nested hypotheses. Finally, we compare each of the Neyman type A models with a model from a competing family, the conditional Poisson model.

Grouped zero-inflated count data models of coital frequency

Various count data models are applied to data collected from a sample of Norfolk young persons, who were asked how many times they had had sexual intercourse during the previous two-week period. The models take account of the fact that the data are “grouped”, meaning that for some observations, the count is not known exactly but is known to fall in a particular range. Using a formal testing procedure, we find overwhelming evidence of the presence of excess zeros, and this we attribute to the fact that, at any time, a certain proportion of the population are sexually inactive. Our final model contains two equations, the first being the participation equation which determines whether an individual is sexually active, and the second being the frequency equation which determines the count, conditional on being active. Age, gender, salary, occupational status, marital status and type of living environment all have interesting effects on either participation or frequency. Since a significant proportion of the original sample declined to reveal coital frequency, we address the potential problem of selection bias by including a Heckman-type correction term during the model selection process.

Semiparametric estimation of count regression models

This paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity. We use the generalized Laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a Poisson mixture model. We establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated, censored, and zero-inflated count regression models. Monte Carlo evidence shows that the finite sample behavior of the estimator is quite good. The paper applies the method to a model of individual shopping behavior.