Mass Killings in the United States from 2006 to 2013: Social Contagion or Random Clusters?

A Sequence Analysis of the Behaviors and Experiences of the Deadliest Public Mass Shooters

Researchers of public mass shooters are increasingly focusing on the pre-attack behaviors and experiences of these offenders. Varying in scope from consideration of individual factors to more generalized life course and threat assessment analyses, their scholarship has identified behavioral and experiential factors associated with public mass shooters. However, what is generally missing from this body of research is consideration of the order in which the offender encounters these factors, and prior related research has shown that analyzing sequences allows for insights not available from a catalogue of common characteristics. To address this shortcoming, we use a sample of offenders from 1999 to 2020 for whom the most detailed data is available and conduct a sequence analysis of their stressors, antisocial behaviors, mental health issues, and planning and preparation activities. We calculate proximity coefficients for each variable in relation to all others, capturing both local and distant connections between and among them. Our findings reveal relatively coherent phases in the lives of attackers, highlight the centrality of family problems and interest in past mass killings in the overall sequence, and provide new context to understanding the effect of mental health issues and firearms acquisition in the lives of offenders. A discussion of findings illustrates potential intervention points that may have been overlooked, as well suggestions for future research.

Key Guidelines in Developing a Pre-Emptive COVID-19 Vaccination Uptake Promotion Strategy

This paper makes the case for immediate planning for a COVID-19 vaccination uptake strategy in advance of vaccine availability for two reasons: first, the need to build a consensus about the order in which groups of the population will get access to the vaccine; second, to reduce any fear and concerns that exist in relation to vaccination and to create demand for vaccines. A key part of this strategy is to counter the anti-vaccination movement that is already promoting hesitancy and resistance. Since the beginning of the COVID-19 pandemic there has been a tsunami of misinformation and conspiracy theories that have the potential to reduce vaccine uptake. To make matters worse, sections of populations in many countries display low trust in governments and official information about the pandemic and how the officials are tackling it. This paper aims to set out in short form critical guidelines that governments and regional bodies should take to enhance the impact of a COVID-19 vaccination strategy. We base our recommendations on a review of existing best practice guidance. This paper aims to assist those responsible for promoting COVID-19 vaccine uptake to digest the mass of guidance that exists and formulate an effective locally relevant strategy. A summary of key guidelines is presented based on best practice guidance.

Detecting the contagion effect in mass killings; a constructive example of the statistical advantages of unbinned likelihood methods

Background

When attempting to statistically distinguish between a null and an alternative hypothesis, many researchers in the life and social sciences turn to binned statistical analysis methods, or methods that are simply based on the moments of a distribution (such as the mean, and variance). These methods have the advantage of simplicity of implementation, and simplicity of explanation.

However, when null and alternative hypotheses manifest themselves in subtle differences in patterns in the data, binned analysis methods may be insensitive to these differences, and researchers may erroneously fail to reject the null hypothesis when in fact more sensitive statistical analysis methods might produce a different result when the null hypothesis is actually false.

Here, with a focus on two recent conflicting studies of contagion in mass killings as instructive examples, we discuss how the use of unbinned likelihood methods makes optimal use of the information in the data; a fact that has been long known in statistical theory, but perhaps is not as widely appreciated amongst general researchers in the life and social sciences.

Methods

In 2015, Towers et al published a paper that quantified the long-suspected contagion effect in mass killings. However, in 2017, Lankford & Tomek subsequently published a paper, based upon the same data, that claimed to contradict the results of the earlier study. The former used unbinned likelihood methods, and the latter used binned methods, and comparison of distribution moments.

Using these analyses, we also discuss how visualization of the data can aid in determination of the most appropriate statistical analysis methods to distinguish between a null and alternate hypothesis. We also discuss the importance of assessment of the robustness of analysis results to methodological assumptions made (for example, arbitrary choices of number of bins and bin widths when using binned methods); an issue that is widely overlooked in the literature, but is critical to analysis reproducibility and robustness.

Conclusions

When an analysis cannot distinguish between a null and alternate hypothesis, care must be taken to ensure that the analysis methodology itself maximizes the use of information in the data that can distinguish between the two hypotheses.

The use of binned methods by Lankford & Tomek (2017), that examined how many mass killings fell within a 14 day window from a previous mass killing, substantially reduced the sensitivity of their analysis to contagion effects. The unbinned likelihood methods used by Towers et al (2015) did not suffer from this problem.

While a binned analysis might be favorable for simplicity and clarity of presentation, unbinned likelihood methods are preferable when effects might be somewhat subtle.