Australian Gun Laws and Total Homicides – Marwan Hamed

As noted within the methods, descriptive values were retrieved through analyses of the means including variance and standard deviations. These values were successfully replicated as noted within the results, with the exception of a discrepancy of ± 0.01. It is assumed that this ± 0.01 discrepancy is due to calculation and/or estimation differences between statistical software used; such that the authors of the study used “Stata version 14” [2], whereas the analyses discussed within this document was ran through SAS version 9.4, so these software may operate differently.

For regression analyses, Models A, B, and C from the study were used to fit the data through NB model, then repeated via Poisson regression modeling and results were compared on goodness of fit via corrected Akaike information criterion (AICC). Based on the results, it would appear that NB model is better fit for the data from ‘AUdeaths_curated’ dataset than Poisson regression model.

It should be restated that although both, AIC and AICC, are developed as estimators for model fit of the data, AICC was used as opposed to AIC, since it contains a correction [3] for smaller sample sizes and the total sample size of the ‘AUdeaths_curated’ dataset was n = 35, which may be considered relatively small. Since the ratio of trends in annual total homicide death rates, model C – includes interaction term with residuals, was shown to be 389.028 and 354.785 through Poisson and NB model, respectively and 354.785 < 389.028, it would suggest that NB model is a better fit for the provided data than Poisson, because in terms of AICC, smaller is better than larger value.

It should be noted that Poisson regression is based on the Poisson distribution model, which entails that the data is distributed within a given period of time, for example: years (as was used within the referenced study). As such, Poisson regression can be used for modeling of count data as it involves trends and rates. It may be assumed that the authors of the study chose negative binomial distribution, since it is a form of Poisson regression modeling, but it is based in assumptions that may be considered less strict in comparison to Poisson regression, on the basis that negative binomial regression does not assume that variance and mean are equal. In addition, the reason the NB model was a better fit than the Poisson model may be due to the fact that the assumptions of the NB model are less strict in comparison to the Poisson model. As such, the residual deviance for the Model C estimate with the interaction term was lesser via NB model than Poisson model, 36.445 vs. 117.406, respectively. In terms of comparison of residual plots in appendix, it should be noted that residual plots I and II are based on NB and Poisson models, respectively. Although both appear similar, differences exist; for example: highlighted within the plots, difference in observations, such that where NB model shows 1 observation (‘A’), Poisson model shows 2 observations (‘B’).

Based on the nature of this study and the fact that it utilized data from the entire population of Australia throughout the years, it may be assumed that there are minimal limitations in terms of sampling. However, it should be noted that there remain several probable limitations to the referenced study [2] and to this study and its interpretations. For example: random error or statistical error may be responsible for the aforementioned discrepancy at the ± 0.01 for mean trend rates. In addition, as stated by the authors, “case numbers in the 3 years before 2006 is largely due to a change in data collection method, which resulted in some cases being coded to other categories, mostly accidental injury due to firearms”. This may have affected the data, as well as calculations, estimations, and/or interpretations made through it. Beyond this, there is probable doubt, although this may be limited, on the basis of misclassification of causes of death, for example: it may be true that a number of cases of death due to ‘suicide’ may have been considered as ‘homicide’ upon initial documentation. However, this probable discrepancy is beyond the scope or knowledge of the study authors as their analyses and data methods were dependent upon population-level data and not individual, case-by-case, data input or interpretation. In addition, it should be noted that any number of plausible limitations may exist beyond the scope of current knowledge, within or beyond this document.