Artificial Neural Network and Multiple Linear Regression Models for

Building the predictive crime models which are presented in this thesis adopted both ANNs and statistical techniques. Both of these techniques have advantages and disadvantages. The objective of this study is to take advantage of both techniques for best performance of a predictive crime model. Multiple linear regression (MLR) analysis is the statistical technique used in this study to identify potentially significant predictive variables and the level of their contribution in the performance of the model and predicting of future crime. Every statistics computer software package contains a regression component. However, Neural Network analysis generates weights, which are difficult to interpret as they are affected by the program used to generate them. This drawback is one of the most criticized features in neural network models. The main advantage that neural networks offer is they do not require many assumptions before the model can be constructed, for example, nonlinearity. When applying regression, the user must have detailed knowledge about the appropriate non-linear relationship between the input and output variables. However, when applying neural networks, these relationships are determined implicitly by the model, since ANNs are non-linear systems. This property includes robust performance in dealing with noisy data. Another advantage of the ANN approach is that the model allows the inclusion of several input and output variables at the same time. This requires more care with a regression technique.

In this study statistical techniques start their construction model with 28 potential explanatory variables identified as input chosen among characteristics of burgled households. These include Resident Population, Occupation, Qualifications, Socio Economic, Household composition and Household spaces. The identification was shown in Table 6.1. The spatial distribution of actual residential burglary incident rate constituted the response (dependent) variable. The data standardized into rate per household within each polygon (census wards). A hierarchical neural network (HNN) starts their construction model with a number of explanatory variables with

statistical significance which were obtained and identified from regression model results.

6.4.1 Multiple Linear Regression Model

Statisticians and criminologists have been applying their skills and knowledge for a long time to predict when and where the next set of crimes will occur, with varying degrees of success. Multiple linear regression (outlined in section 1.1.4) was chosen in this thesis for a predictive crime model. The regression model is one of the popular methods of modelling and prediction. Regression analysis has major purposes: description, estimation and prediction. This methodology has wide applicability in prediction in a variety of areas (Bolzan 2008; Margaret 2002; carcoran 2003).

6.4.1.1 Regression Modelling Steps

This strategy involves:

Data collection and preparation;

Any regression analysis to perform the analysis requires data. The characteristics of the data vary with the nature of the study. In the procedures of data collection and preparation it is important that the user is conversant about the theory associated with the subject being analysed. Section 6.2 shows details of the data characteristics which are used in the regression model presented in this thesis.

Selection of Explanatory variables;

Selection of explanatory variables is an important aspect of regression analysis. The process of model building is to identify those variables which are significant partial contributors to the prediction of the response variable. Backward elimination and forward selection are one of the popular techniques for variable selection. Backwards elimination procedure begins with a regression on all potential explanatory variables. After the regression is run the explanatory variables are examined to determine which variable is non-significant and to be deleted. The statistical tests, t-test, and p-value are used for this purpose. However, forward

selection procedure starts with no explanatory variables. The first variable included in the equation is the one which has the highest simple correlation with a response variable. The significance of the regression coefficient of the first variable is then tested. The equation includes variables which are statistically significant. A search for a second variable is made in the same way. Variables are considered one by one until there is no significant improvement in the model brought about by adding another variable (Kutner 2004).

The regression analysis presented in this thesis used backward elimination. The procedure starts with 28 potential explanatory variables. The p-value used to identify significance of explanatory variable at chosen significance level was 0.05.

Estimate Unknown Model Parameters and Interpretation;

In multiple linear regression analysis the least-squares criterion is used to estimate the regression coefficients. The regression coefficients Bi measure the partial contribution of each predictor variable to the prediction of the response. If a predictor xi is changed by one unit, while all the other predictor variables are kept

fixed. Then the response variable y will change by Bi. Sings (plus or minus) of

regression coefficients refer to the direction of the relationship between the predictor variable and the response. If the coefficient Bi is positive, then the

relationship of the predictor xi to the response is positive, and if the coefficient Bi is

negative then the relationship is negative. Test for Multicollinearity.

In multiple linear regression analysis, estimation of regression parameters are unstable and have high standard errors, when a predictor variable is a linear combination of other predictors in the model (Feranadez 2003). Variance inflation factors (VIF) “measure how highly correlated each independent variable is with the other predictors in the model” (Kutner 2004:408). O’ Brein (2007) suggested that VIF ≥5 indicates a multicollinearity problem. VIF can be obtained on MINITAB by selecting the options in the regression dialog box.