Patterns of Crime in Canadian Cities :  A Multivariate Statistical Analysis

Section 3. Components of Crime


3. Components of Crime

The first part of the analysis involved submitting the 25 offence rates for all 600 cities to a factor analysis.[2] Based on an analysis of the results, the optimal number of components was determined to be four.[3] In other words, the 4 crime components could then be used to represent the 25 crime rates.

Table 3 shows the factor loadings of the 4 crime components. All factor loadings range from ‑1 to +1. The higher the factor loadings (in terms of absolute values), the greater that particular variable is represented by that component. In the table, significant factor loadings with an absolute value of greater than 0.4 are underlined.[4]

Table 3. Factor Loadings of the 4 Crime Components [5]
Offence Category Comp. 1 Comp. 2 Comp. 3 Comp. 4
Homicide 0.03 -0.13 0.26 0.06
Sexual assault I 0.29 0.69 0.05 0.24
Major sexual assault -0.08 0.49 0.03 -0.11
Other sexual offences 0.00 0.10 -0.07 0.54
Non-sexual assault I 0.33 0.75 0.09 0.33
Major non-sexual assault 0.09 0.71 0.06 0.46
Other non-sexual assault 0.31 0.70 -0.15 0.13
Robbery 0.02 -0.15 0.69 0.28
Abduction kidnapping -0.06 0.23 0.10 0.42
Break enter 0.09 0.52 0.68 0.07
Theft motor vehicle 0.16 0.21 0.73 0.17
Theft over $5000 0.15 0.44 0.39 -0.28
Theft $5000 under 0.61 0.12 0.54 0.16
Possession of stolen goods 0.68 0.04 0.28 0.13
Fraud counterfeiting 0.87 0.03 -0.09 -0.10
Arson -0.10 0.24 0.56 -0.14
Vandalism 0.33 0.56 0.30 0.06
Moral offences 0.13 0.02 0.27 0.64
Offensive weapons 0.30 0.50 0.05 0.35
Miscellaneous Criminal Code 0.66 0.50 0.18 0.17
Narcotics possession 0.85 0.15 0.12 0.00
Narcotics trafficking 0.09 0.11 0.58 -0.05
Controlled restricted drugs 0.63 0.07 -0.19 0.06
Misc. Federal Statutes -0.01 0.37 0.07 0.04
Criminal Code traffic 0.81 0.23 0.24 -0.08

NOTE: Factor loadings of greater than 0.4 are underlined.

Component 1 contains high factor loadings for 7 offence categories. In other words, this component can be used to represent the offence rates of those 7 offence categories. They include 3 minor property crimes (fraud and counterfeiting, possession of stolen goods, theft $5000 and under) and 4 other minor crimes (narcotics possession, controlled and restricted drugs, Criminal Code traffic offences, miscellaneous Criminal Code offences). Three of these offences have factor loadings of over 0.8 meaning that this component alone explains over 65% of the total variation of each of these offences.[6] This component is designated as “Minor Crimes”. Significant loadings include the following offences:

COMPONENT 1: Minor Crimes
Fraud counterfeiting 0.87
Narcotics possession 0.85
Criminal Code traffic 0.81
Possession of stolen goods 0.68
Miscellaneous Criminal Code 0.66
Controlled restricted drugs 0.63
Theft $5000 under 0.61

Component 2 contains high factor loadings for 10 offence categories. Five of these are violent crimes (non-sexual assault I, major non-sexual assault, other non-sexual assault, sexual assault I, major sexual assault). Two others are major property crimes (break and enter, theft over $5000). Two others are also related crimes: offensive weapons offences are related to violent crimes; vandalism is related to property crimes. This component is designated as “Violent Crimes”. Of course, this component represents not only the 5 violent crimes but also the other 5 non-violent offences. Three of the offences have factor loadings of 0.7 or higher meaning that this component alone explains over 50% of the variation of each of these offences. Significant loadings include the following offences:

COMPONENT 2: Violent Crimes
Non-sexual assault 0.75
Major non-sexual assault 0.71
Other non-sexual assault 0.70
Sexual assault 0.69
Vandalism 0.56
Break enter 0.52
Offensive weapons 0.50
Miscellaneous Criminal Code 0.50
Major sexual assault 0.49
Theft over $5000 0.44

Component 3 contains high factor loadings for 6 offence categories. Four of them are major property crimes. In addition, robbery (sometimes regarded as a major property crime) and narcotics trafficking are also included. A seventh offence, theft over $5000 (a major property crime), is only slightly below the 0.4 cut-off line. This component is designated as “Major Property Crimes”. Significant loadings include the following offences:

COMPONENT 3: Major Property Crimes
Theft motor vehicle 0.73
Robbery 0.69
Break enter 0.68
Narcotics trafficking 0.58
Arson 0.56
Theft $5000 under 0.54
Theft over $5000 0.39

Component 4 contains high factor loadings for 4 offence categories. They include other sexual offences, abduction and kidnapping, moral offences, and major non-sexual assault (this last offence is represented to a greater extent by Component 2). The category “other sexual offences” normally does not involve violence and is similar to moral offences. This component is designated as “Moral Offences”. Significant loadings include the following offences:

COMPONENT 4: Moral Offences
Moral offences 0.64
Other sexual offences 0.54
Major non-sexual assault 0.46
Abduction kidnapping 0.42

In the above scheme, 2 of the 25 offence categories are not included in any of the 4 components. These are homicide, and miscellaneous federal statutes. The implication is that these two offences are not associated with any other offences. There are also 4 other variables that have significant factor loadings on two of the 4 components. The implication is that those offences are associated with two different offence groupings.

It is interesting to see how different offences associate with each other. Component 1 shows that wherever there are minor property crimes in a city, it is likely that minor drug offences and traffic offences are also found, or vice versa. Component 2 shows that wherever there are various kinds of violent crimes in a city, it is likely that offensive weapons offences, break and enter, vandalism, major theft (over $5000) are also found. Component 3 shows that wherever there are major property crimes in a city, it is likely that robbery, arson, and narcotics trafficking are also found. Component 4 shows that moral offences (including prostitution, gaming and betting, indecent acts, public morals), non-violent sexual offences, abduction and kidnapping commonly occur together in the same cities.

As a whole, the scheme successfully grouped most offences into 4 components which could then be used to describe the crime patterns of individual cities. The 4 components are summarized here:

Summary of 4 Crime Components
Component 1 Minor crimes
Component 2 Violent crimes
Component 3 Major property crimes
Component 4 Moral offences



Date modified: