Browsing by Author "Gurr, Benjamin William"

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    An application of geometric data analysis techniques to South African crime data
    (Stellenbosch : Stellenbosch University, 2016-12) Gurr, Benjamin William; Le Roux, Niel J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics & Actuarial Science.
    ENGLISH SUMMARY : Due to the high levels of violent crime in South Africa, improved methods of analysis are required in order to better scrutinize these statistics. This study diverges from traditional multivariate data analysis, and provides alternative methods for analyzing crime data in South Africa. This study explores the applications of several types of geometric data analysis (GDA) methods to the study of crime in South Africa, these include: correspondence analysis, the correspondence analysis biplot, and the log-ratio biplot. Chapter 1 discusses the importance of data visualization in modern day statistics, as well as the geometric data analysis and its role as a multivariate analytical tool. Chapter 2 provides the motivation for the choice of subject matter to be explored in this study. As South Africa is recognized as having the eighth highest homicide rate in the world, along with a generally high level of violent crime, the analysis is conducted on reported violent crime statistics in South Africa. Additionally, the possible data collection challenges are also discussed in Chapter 2. The study is conducted on the violent crime statistics in South Africa for the 2004-2013 reporting period, the structure and details of which are discussed in Chapter 3. In order for this study to be comparable, it is imperative that the definitions of all crimes included are well defined. Chapter 3 places a large emphasis on declaring the exact definition of the various crimes which are utilized in this study, as recorded by the South African Police Services. The more common approaches to graphically representing crime data in South Africa are explored in Chapter 4. Chapter 4 also marks the beginning of the analysis of the South African crime data for the 2004-2013 reporting period. Univariate graphical techniques are used to analyze the data (line graphs and bar plots) for the 2004-2013 time period. However, as it is to be expected, they are hampered by serious limitations. In an attempt to improve on the analysis, focus is shifted to geometric data analysis techniques. The general methodologies to correspondence analysis, biplots, and correspondence analysis biplots are discussed in Chapter 5. Both the algorithms and the construction of the associated figures are discussed for the aforementioned methods. The application of these methodologies are implemented in Chapter 6. The results of Chapter 6 suggest some improvement upon the results of Chapter 4. These techniques provided a geometric setting where both the crimes and provinces could be represented in a single diagram, and where the relationships between both sets of variables could be analyzed. The correspondence analysis biplot proved to have some advantages in comparison to the correspondence analysis maps, as it can display numerous metrics, provide multiple calibrated axes, and allows for greater manipulation of the figure itself. Chapter 7 introduced the concept of compositional data and the log-ratio biplot. The log-ratio biplot combined the functionality of the biplot, along with a comparability measure in terms of a ratio. The log-ratio biplot proved useful in the analysis of the South African crime data as it expressed differences on a ratio scale as multiplicative differences. Additionally, log-ratio analysis has the property of being sub-compositionally coherent. Chapter 8 provides the summary and conclusions of this study. It was found that Gauteng categorically has the largest number of reported violent crimes over the reported period (2004-2013). However, the Western Cape proved to have the highest violent crime rates per capita of all the South African provinces. It was noted that over the past decade South Africa has experienced a downward trend in the number of reported murders. However, there has been a spike in the number of reported cases of murder in more recent year. This is spike is mostly driven by the large increases in reported murder cases in the Western Cape, Gauteng and KwaZulu-Natal. The most notable trend seen in the South African crime data is the rapid increase in the number of reported cases of drug-related crimes over the reported period across all provinces, but more noticeably in the Western Cape and Gauteng. On a whole, a majority of the South African provinces share similar violent crime profiles, however, Gauteng and the Western Cape deviate away from other provinces. This is due to Gauteng’s high association to robbery with aggravating circumstances and the Western Cape’s high association to drug-related crime. This study presents some evidence that the use of geometric data analysis techniques provides an improvement upon traditional reporting methods for the South African crime data. Geometric data analysis and its related methods should thus form an integral part of any study conducted into the topic at hand.