2.1 INTRODUCTION: In this chapter we are going to review some research work which has been carry out.
Crime is one of the continuous problems that bedevil the existence of mankind. Since forth early days, crime had been a disturbing threat to his personality, property and lawful authority (Louis et al., 1981). Today, in the modern complex world, the situation is most highly disturbing. Crime started in the primitive days as a simple and less organized issue, and ended today as very complex and organized. Therefore, the existence of crime and its problems have spanned the history of mankind. Nigeria has one of the alarming crime rates in the world (Uche, 2008 and Financial, 2011). Cases of armed robbery attacks, pickpockets, shoplifting and 419 have increased due to increased poverty among population (Lagos, undated). In the year 2011, armed robbers killed at least 12 people and possibly more in attacks on a bank and police station in North-Eastern Nigeria (Nossiter, 2011). However, Maritz (2010) has considered that image as merely exaggeration. He added that, as is the case with the rest of the world, Nigeria’s metropolitan areas have more problems with crime than the rural areas. Most crimes are however, purely as a result of poverty. Despite the fact that, crime is inevitable in a society Durkheim (1933), various controlling and preventive measures had been taken, and are still being taken to reduce the menace. However, crime control and prevention is still bedeviled by numerous complex problems. When an opportunity for crime is blocked, an offender has several alternative types of displacement (Gabor, 1978). However, the introduction of modern scientific and technical methods in crime prevention and control has proved to be effective. The application of multivariate statistics has made some contributions to many criminological explanations (Kpedekpo and Arya, 1981 and Printcom, 2003).
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Principal Component Analysis (PCA) is very useful in crime analysis because of its robustness in data reduction and in determining the overall criminality in a given geographical area. PCA is a data analysis tool that is usually used to reduce the dimensionality (number of variable) of a large number of interrelated variables while retaining as much of the information (variation) as possible. The computation of PCA reduced to an eigenvalue –eigenvector problem. It is performed either on a correlation or a covariance matrix. If some group of measures constitutes the scores of the numerous variables, the researchers may wish to combine the score of the numerous variables into smaller number of super variables to form the group of the measures (Jolliffe, 2002).This problem mostly happens in determining the relationship between socio-economic factors and crime incidences. PCA uses the correlation among the variables to develop a small set of components that empirically summarised the correlation among the variables. In a study to examine the statistical relationship between crime and socio-economic status in Ottawa and Saskatoon, the PCA was employed to replace a set of variables with a smaller number of components, which are made up of inter-correlated variables representing as much of the original data set as possible (Exp, 2008). Principal component analysis can also be used to determine the overall criminality. When the first eigenvector show approximately equal loadings on all variables then the first PC measures the overall crime rate. In Printcom (2003) for 1997 US crime data, the overall crime rate was determined from the first PC ,and the same result was achieved by Hardle and Zdenek (2007) for the 1985 US crime data. The second PC which is interpreted as “type of crime component” has successively classified the seven crimes into violence and property crime. U usman et al (2012) carried out a research on ‘An investigation on the Rate of crime in Sokoto Using Principal Component Analysis. From the results, three Principal Components was retained from seven, using the Scree plot and Loading plot indicating that correlation exist between crimes against persons and crime against properties. Yan Fang (2011) use multivariate methods analysis of crime data in Los Angeles Communities and from the findings Principal Component Analysis was successfully applied into the data by extracting five PCs out of the 15 original variable, which implies a great dimensionality reduction. In addition, this 85% variance of the original dataset, thus he does not loss much information. Shehu el al (2009) research on analysis of crime data using principal component analysis: A case study of Katsina State. The paper consists of the average eight major crimes reported to the Police for the period 2006-2008. The crime consist of robbery auto theft, house and store breakings, theft, and grievous hurt and wounding, murder, rape, and assault. Correlation matrix and Principal Component analysis were developed to explain the correlation between the crimes and to determine the distribution of the crimes over the Local Government areas of the State.
2.2 Classification of Crime
The classification of crime differs from one country to another. In the United States, the Federal Bureau of Investigation tabulates the annual crime data as Uniform Crime Reports (UCR). They classify violations of laws which derive from common law as part 1 (index) crimes in UCR data, further categorized as violent as property crimes. Part 1 violent crimes include murder and criminal homicide (voluntary manslaughter), forcible rape, aggravated assault, and robbery; while part 1 property crimes include burglary, arson, larceny/theft, and motor vehicle theft. All other crimes count as part II crimes (Wiki/Cr.2009).In Nigeria, the Police classification of crime also depends on what law prescribed. In Nigeria Police Abstract of Statistics (NPACS), offences are categorized into four main categories:
i. Offences against persons includes: manslaughter, murder and attempted murder, assault, rape, child stealing, grievous hurt and wounding, etc.
ii. Offences against property includes: armed robbery, house and store breakings, forgery, theft/stealing, etc.
iii. Offences against lawful authority include: forgery of current notes, gambling, breach of peace, bribery and corruption, etc.
iv. Offences against local act include: traffic offences, liquor offences, etc.
2.3 Causes of Crimes
Criminal behaviour cannot be explained by a single factor, because human behaviour is a complex interaction between genetic, environmental, social psychological and cultural factor. Different types of crimes are being committed by different types of people, at different times, in different places, and under different circumstances (Danbazau, 2007). Here we discuss some of the causes of crime:
Biogenetic factors: Criminologists are with the opinion that criminal activity is due to the effect of biologically caused or inherited factors (Pratt and Cullen, 2000). According to Lombrose (1911), a criminal is born, not made; that criminals were the products of a genetic constitution unlike that found in the non-criminal population.
Social and environmental factor (Sutherland, 1939): The environment is said to play significant role in determining criminal behaviour. Factors within the environment that mostly influence criminal behavior include poverty, employment, corruption, urbanization, family, moral decadence, poor education, technology, child abuse, drug trafficking and abuse, architectural or environmental design Oyebanji (1982) and Akpan (2002) have attribute the current crime problem in Nigeria to urbanisation, industrialisation and lack of education. Kutigi (2008) has said that the factors of crime in Nigeria and poverty and ignorance which are at the same time the opinion of many Nigerians (Azaburke, 2007). In another dimension, according to Ayoola (2008), lack of integrity, transparency and accountability in the management of public funds, especially at all levels of government have been identified as the factors responsible for the endemic corruption that has eaten deep into the fabric of the Nigerian society over the years.
2.4 The Nigerian Police
The most important aspect of criminal justice system is the police. Criminal justice system can be defined as a procedure of processing the person accused of committing crime from arrest to the final disposal of the case (Danbazau, 2007). However, for the past three decades there have been serious dissatisfaction and public criticisms over the conduct of the police (Danbazau, 2007). Then, what are the causes of the police failure in preventing and controlling the crimes? So many factors can be attributed to the problem. There are the issue of inadequate manpower, equipment and professionalism (Danbazau, 2007), corruption (Al-Ghazali, 2004) and poor public perception on the Nigeria Police (Okeroko, 1993), which has consequently made the Nigerian Public unwilling to corporate with the police in crime prevention and control.
2.5 Statistics of Crimes in Nigeria
Nigeria has one of the highest crime rates in the world. Murder often accompanies minor burglaries. Rich Nigerians live in high – security compounds. Police in some states are empowered to “shoot on sight” violent criminals (Financial Times, 2009).In the 1980s, serious crime grew to nearly epidemic proportions, particularly in Lagos and other urbanized areas characterised by rapid growth and change, by stark economic inequality and deprivation, by social disorganisation, and by inadequate government service and law enforcement capabilities (Nigeria,1991).Annual crime rates fluctuated at around 200 per100,000 populations until the early 1960s and then steadily increased to more than 300 per 100,000 by the mid-1970s. Available data from the 1980s indicated a continuing increase. Total reported crime rose from almost 211,000 in 1981 to between 330,000 and 355,000 during 1984 – 85. The British High Commission in Lagos cited more than 3000 cases of forgeries annually (Nigeria, 1991).In the early 1990s, there was growing number of robberies from 1,937 in 1990 to 2,419 in 1996, and later the figure declined to 2,291 in 1999. Throughout the 1990s, assault and theft constituted the larger category of the crime. Generally, the crime data grow from 244,354 in 1991 to 289,156 in 1993 (Cleen,1993) and continued to decline from 241,091 in 1994 to 167,492 in 1999 (Cleen, 2003). The number of crime slightly declined to 162,039 in 2006, a reduction of 8 percent from 2005 (Cleen, 2006).
2.6 Principal Component Analysis Theories
Having a large number of variables in a study makes it difficult to decipher patterns of association. Variables sometimes tend to repeat themselves. Repetition is a sign of multicolinearity of variables, meaning that the variables may be presenting some of the same information. Principal Components Analysis simplifies multivariate data in that it reduces the dimensionality of the data. It does so by using mainly the primary variables to explain the majority of the information provided by the data set. Analysis of a smaller number of variables always makes for a simpler process.
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Simply stated, in principal components analysis we take linear combinations of all of the original variables so that we may reduce the number of variables from p to m, where the number m of principal components is less than p. Further, the method allows us to take the principal components and use them to gain information about the entire data set via the correlation between the principal components and the original variables. Matrices of correlations or loadings matrices show which principal component each variable is most highly associated with. The first principal component is determined by the linear combination that has the highest variance. Variance measures the diffusion of the data.
After the first principal component is obtained, we must determine whether or not it provides a sufficient amount of or all of the information displayed by the data set. If it does not provide adequate information, then the linear combination that displays the highest variance accounted for after the first principal component’s variation is removed is designated as the second principal component. This process goes on until an ample amount of information/variance is accounted for. Each principal component accounts for a dimension and the process continues only on the remaining dimensions. Designating a dimension as a principal component often reveals information about correlations between remaining variables which at first was not readily available.
The main objective of Principal Components Analysis is to locate linear combinations , with the greatest variance. We want where Σ is the covariance matrix, to be the maximum among all the normalized coefficient vectors â„“i. This result is achieved by way of Lagrange Multipliers. Taking the partial derivative with respect to â„“i of the Var(yi) – λ(â„“iTâ„“i – 1), where λ is the Lagrange Multiplier results in the equation
where â„“i is not equal to the zero vector. From the above equations it can be easily verified that λ is a characteristic root of Σ and λi is equal to the variance of yi where λ1>λ2> … > λp are the characteristic roots. Note that they are positive. The characteristic vector corresponding to λ1, the root that accounts for the maximum variance, is â„“1. The percentage of variance that any particular principal component accounts for can be calculated by dividing the variance of that component by the sum of all the variances, i.e.
We use the high correlations between the principal components and the original variables to define which components we will utilize and which ones we will discard. One device that assists us in this decision process is a scree plot. Scree plots are graphs of the variance (eigenvalue) of each principal component in descending order. A point called an “elbow” is designated. Below this point is where the graph becomes somewhat horizontal. Any principal components whose variances lie above this point are kept and the others are discarded. The original variables that are highly correlated with each principal component that is kept determine what the label of that particular component will be.
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