Missing data is a commonly encountered problem in longitudinal research. Methodological articles provide advice on ways to handle missing data at the analysis stage, however, there is less guidance for researchers who wish to use supplemental samples (i.e., the addition of new participants to the original sample after missing data appear at the second or later measurement occasions) to handle attrition. The purpose of this study is to evaluate the effects of using supplemental samples when analyzing longitudinal data that are non-normally distributed. We distinguish between two supplemental approaches: a refreshment approach where researchers select additional participants using the same criteria as the initial participants (i.e., random selection from the population of interest) and a replacement approach where researchers identify auxiliary variables that explain missingness and select new participants based on those attributes. Overall, simulation results suggest that the addition of refreshment samples, but not replacement samples, is an effective way to respond to attrition in longitudinal research. Indeed, use of refreshment samples may reduce bias of parameter estimates and increase efficiency and statistical power, whereas use of replacement samples results in biased parameter estimates. Our findings may be utilized by researchers considering using supplemental samples and provide guidance for selecting an appropriate supplemental sample approach.
American gun-owners, uniquely, view firearms as a means of keeping themselves safe from dangers both physical and psychological. We root this belief in the experience of White Southerners during Reconstruction—a moment when a massive upsurge in the availability of firearms co-occurred with a worldview threat from the emancipation and the political empowerment of Black Southerners. We show that the belief-complex formed in this historical moment shapes contemporary gun culture: The prevalence of slavery in a Southern county (measured in 1860) predicts the frequency of firearms in the present day. This relationship holds above and beyond a number of potential covariates, including contemporary crime rates, police spending, degree of racial segregation and inequality, socioeconomic conditions, and voting patterns in the 2016 Presidential election; and is partially mediated by the frequency of people in the county reporting that they generally do not feel safe. This Southern origin of gun culture may help to explain why we find that worries about safety do not predict county-level gun ownership outside of historically slave-owning counties, and why we find that social connection to historically slaveholding counties predicts county-level gun ownership, even outside of the South.
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