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A growing body of applied research on political violence employs split-population models to address problems of zero inflation in conflict event counts and related binary dependent variables. Nevertheless, conflict researchers typically use standard ordered probit models to study discrete ordered dependent variables characterized by excessive zeros (e.g., levels of conflict). This study familiarizes conflict scholars with a recently proposed split-population model—the zero-inflated ordered probit (ZiOP) model—that explicitly addresses the econometric challenges that researchers face when using a "zero-inflated" ordered dependent variable. We show that the ZiOP model provides more than an econometric fix: it provides substantively rich information about the heterogeneous pool of "peace" observations that exist in zero-inflated ordinal variables that measure violent conflict. We demonstrate the usefulness of the model through Monte Carlo experiments and replications of published work and also show that the substantive effects of covariates derived from the ZiOP model can reveal nonmonotonic relationships between these covariates and one's conflict probabilities of interest.

Closed access. ; Based on the Eurobarometer data from 2009 (N = 26,788), this paper investigates the correlates of sports participation. In addition to examining standard socio-demographic, economic and lifestyle factors, the paper also focuses on the impact of motivational factors, the availability of sports infrastructure and government support, for the first time collectively at the European level. A further contribution of the paper is that it simultaneously investigates both the decision to participate in sport and the frequency of sports participation in this context. This is made possible through the application of a Zero-Inflated Ordered Probit estimator. This estimator also takes into account two types of non-participants: those who have never participated in sport and those who did not participate at the time of the survey. The results show that the decision to participate in sports and the frequency of sports participation of males and females are affected by different factors, therefore distinct government policies should be applied to attract new, and retain the existing, participants. For example, women are affected more by a need to improve self-esteem, while the men to produce social integration. The provision of sports facilities is of more importance for males, which may indicate a male-oriented nature of the sports facilities, for example, the gym. However, the number of adults and the number of children in the household reduce the probability of sports participation by females. Therefore, higher provision of childcare may be important if female participation is to be increased.

Abstract
Ordered dependent variables are widely employed in international relations (IR). These ordered dependent variables often suffer from inflated observations in their highest outcome category due to distinct processes. The application of standard ordered probit and ordered logit models to such ordinal measures will fail to capture these distinct processes, often producing biased inferences as a result. Yet IR researchers have thus far ignored the potential for top-category inflation in ordered outcome variables. We sensitize researchers to top-category inflation in ordered IR outcomes. We then intuitively extend the widely used zero-inflated ordered probit model to the top-category inflated setting, providing resources to facilitate the proper modeling of top-category inflation in ordered outcomes. Finally, we provide two applications to published IR research related to trade politics and political repression. Together, these applications illustrate the substantive and methodological potentials of our proposed tools for diagnosing and modeling top-category inflation in IR outcomes.

Purpose: The purpose of this paper is to analyze the differential impact each of the dominant theoretical explanations has on innovation persistence. The authors hereby differentiate the degree of novelty, distinguishing between innovation based on invention (new products for the international market) and those based on imitation or adoption processes (new products for the company or new products in the national market). Design/methodology/approach: Placing this study in the context of a developing country, the authors apply an ordered probit model inflated in zeros (ZIOP). This methodology enables one to not only provide results not biased by the excess of zeros but also take into account the unobserved heterogeneity with respect to the sources of zeros (that is those firms which do not innovate). The empirical analysis is based on three Colombian innovation surveys carried out between 2003 and 2008 by the Colombian National Statistics Department. Findings: The results provide empirical evidence that two elements are essential for both types of innovation persistence: accessing external financial resources and learning through interaction. Furthermore, the sunk R&D cost approach and technological learning explain persistence in innovation of new products for the international market. Research limitations/implications: The limitations of this study are directly related to the methodological choice. The authors were unable to take into consideration two sources of heterogeneity: the one related to initial conditions and the one related to the source of the many non-innovators. They opted to focus on the latter due the research question and setting of this study. Additionally, macroeconomic instability did not allow to consider a long panel; instead the authors had to rely on a short panel. Practical implications: The results provide important insights to managers. Continuous investments in innovation activities are important bot to become an innovative firm as well as to improve the odds of persistently innovating. Particularly, R&D investments are a pre-requisite for new-to-the-world innovations. Finally, it is not one specific set of capabilities which is a prerequisite for the generation of innovation; rather it is a strategic combination of various skills that increase the probability to (persistently) innovate. Social implications: With innovation persistence being especially relevant for long-run dynamics behind economic growth, the results of this study provide insights into potential public policies. Governments are in a position to at least lower barriers, which might enable more firms to persistently innovate. Continuous access – less than the actual amount – to financial resources aimed at innovation activities and learning through interaction with external agents is fundamental for both kinds of innovation persistence. Both are market characteristics where governments can – at least indirectly – intervene. Originality/value: Despite the existence of various theoretical approaches, the bulk of empirical research focuses on the verification of true state innovation persistence. Thus, while innovation persistency has been widely confirmed to exist to a certain degree, knowledge regarding which theoretical approach is likely to drive a firm to persistently innovation is still scarce. Additionally, this study is placed in the context of a developing country, which by most empirical research has been overlooked but is characterized by one element which is decisive for the empirical methodology: many firms do not innovate, let alone persistently innovate.

The score test statistics for testing zero inflation and covariance parameter are proposed in the bivariate zero‐inflated Poisson (BZIP) regression model. The Monte Carlo studies show that the score test and likelihood ratio test for testing zero inflation underestimate the nominal significance level, while the score test for covariance parameter keeps the significance level close to the nominal one. To overcome this nominal level underestimation, we propose a bootstrap method of the score test for the testing problem of zero inflation. An empirical example with covariates is provided to illustrate the results. In addition, score test for zero inflation is also proposed in the BZIP model, which allows a flexible dependence structure using copula.

Count data are most commonly modeled using the Poisson model, or by one of its many extensions. Such extensions are needed for a variety of reasons: (1) a hierarchical structure in the data, e.g., due to clustering, the collection of repeated measurements of the outcome, etc.; (2) the occurrence of overdispersion (or underdispersion), meaning that the variability encountered in the data is not equal to the mean, as prescribed by the Poisson distribution; and (3) the occurrence of extra zeros beyond what a Poisson model allows. The first issue is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. Overdispersion is often dealt with through a model developed for this purpose, such as, for example, the negative-binomial model for count data. This can be conceived through a random Poisson parameter. Excess zeros are regularly accounted for using so-called zero-inflated models, which combine either a Poisson or negative-binomial model with an atom at zero. The novelty of this paper is that it combines all these features. The work builds upon the modeling framework defined by Molenberghs et al.(2010) in which clustering and overdispersion are accommodated for through two separate sets of random effects in a generalized linear model. ; The authors are grateful to M. Assefa and F. Tessema for the permission to use the data. Financial support from the Institutional University Cooperation of the Council of Flemish Universities (VLIR-IUC) is gratefully acknowledged. The authors gratefully acknowledge support from IAP research Network P7/06 of the Belgian Government (Belgian Science Policy).

Empirical count data are often zero‐inflated and overdispersed. Currently, there is no software package that allows adequate imputation of these data. We present multiple‐imputation routines for these kinds of count data based on a Bayesian regression approach or alternatively based on a bootstrap approach that work as add‐ons for the popular multiple imputation by chained equations (mice) software in R (van Buuren and Groothuis‐Oudshoorn, Journal of Statistical Software, vol. 45, 2011, p. 1). We demonstrate in a Monte Carlo simulation that our procedures are superior to currently available count data procedures. It is emphasized that thorough modeling is essential to obtain plausible imputations and that model mis‐specifications can bias parameter estimates and standard errors quite noticeably. Finally, the strengths and limitations of our procedures are discussed, and fruitful avenues for future theory and software development are outlined.