Are Repeatedly Extorted Businesses Different? A Multilevel Hurdle Model of Extortion Victimization

Objectives Research consistently shows that crime concentrates on a few repeatedly victimized places and targets. In this paper we examine whether the same is true for extortion against businesses. We then test whether the factors that explain the likelihood of becoming a victim of extortion also explain the number of incidents suffered by victimized businesses. The alternative is that extortion concentration is a function of event dependence. Methods Drawing on Mexico’s commercial victimization survey, we determine whether repeat victimization occurs by chance by comparing the observed distribution to that expected under a Poisson process. Next, we utilize a multilevel negative binomial-logit hurdle model to examine whether area- and business-level predictors of victimization are also associated with the number of repeat extortions suffered by businesses. Results Findings suggest that extortion is highly concentrated, and that the predictors of repeated extortion differ from those that predict the likelihood of becoming a victim of extortion. While area-level variables showed a modest association with the likelihood of extortion victimization, they were not significant predictors of repeat incidents. Similarly, most business-level variables significantly associated with victimization risk showed insignificant (and sometimes contrary) associations with victimization concentration. Overall, unexplained differences in extortion concentration at the business-level were unaffected by predictors of extortion prevalence. Conclusions The inconsistent associations of predictors across the hurdle components suggest that extortion prevalence and concentration are fueled by two distinct processes, an interpretation congruent with theoretical expectations regarding extortion that considers that repeats are likely fueled by a process of event dependence.

Event dependence in the analysis of cardiovascular readmissions postpercutaneous coronary intervention

Recurrent hospitalizations are common in longitudinal studies; however, many forms of cumulative event analyses assume recurrent events are independent. We explore the presence of event dependence when readmissions are spaced apart by at least 30 and 60 days. We set up a comparative framework with the assumption that patients with emergency percutaneous coronary intervention (PCI) will be at higher risk for recurrent cardiovascular readmissions than those with elective procedures. A retrospective study of patients who underwent PCI (January 2008–December 2012) with their follow-up information obtained from a regional database for hospitalization was conducted. Conditional gap time (CG), frailty gamma (FG) and conditional frailty models (CFM) were constructed to evaluate the dependence of events. Relative bias (%RB) in point estimates using CFM as the reference was calculated for comparison of the models. Among 4380 patients, emergent cases were at higher risk as compared with elective cases for recurrent events in different statistical models and time-spaced data sets, but the magnitude of HRs varied across the models (adjusted HR [95% CI]: all readmissions [unstructured data]—CG 1.16 [1.09 to 1.22], FG 1.45 [1.33 to 1.57], CFM 1.24 [1.16 to 1.32]; 30-day spaced—CG1.14 [1.08 to 1.21], FG 1.28 [1.17 to 1.39], CFM 1.17 [1.10 to 1.26]; and 60-day spaced—CG 1.14 [1.07 to 1.22], FG 1.23 [1.13 to 1.34] CFM 1.18 [1.09 to 1.26]). For all of the time-spaced readmissions, we found that the values of %RB were closer to the conditional models, suggesting that event dependence dominated the data despite attempts to create independence by increasing the space in time between admissions. Our analysis showed that independent of the intercurrent event duration, prior events have an influence on future events. Hence, event dependence should be accounted for when analyzing recurrent events and challenges contemporary methods for such analysis.

Understanding the Effect of Immunity on Over-Dispersed Criminal Victimizations: Zero-Inflated Analysis of Household Victimizations in the NCVS

This study aims to empirically test the immunity effect on the frequency distribution of household victimizations. To clarify the immunity effect, the statistical construction of zero-inflated models is reviewed and compared with that of non-zero-inflated models. The Benjamini and Hochberg correction is used to address the limitation of p values in multiple testing. Compared with the findings from the non-zero-inflated model, two sets of coefficients from the zero-inflated model reveal that there exist more complex and diverse statuses in the process of household victimization than predicted by risk heterogeneity and event dependence. With these findings, this study suggests that zero-inflated models should be introduced and compared with non-zero-inflated models for the clarification of victimization determinants.

Analyzing the Robustness of Semi-Parametric Duration Models for the Study of Repeated Events

Estimators within the Cox family are often used to estimate models for repeated events. Yet, there is much we still do not know about the performance of these estimators. In particular, we do not know how they perform given time dependence, different censoring rates, and a varying number of events and sample sizes. We use Monte Carlo simulations to demonstrate the performance of a variety of popular semi-parametric estimators as these data aspects change and under conditions of event dependence and heterogeneity, both, or neither. We conclude that the conditional frailty model outperforms other standard estimators under a wide array of data-generating processes, and data limitations rarely alter its performance.