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Using Functional Distance Measures When Calibrating Journey-To-Crime Distance Decay Algorithms

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Using Functional Distance Measures When Calibrating Journey-To-Crime Distance Decay Algorithms USING FUNCTIONAL DISTANCE MEASURES WHEN CALIBRATING JOURNEY-TO-CRIME DISTANCE DECAY ALGORITHMS A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Natural Sciences in The Interdepartmental Program of Natural Sciences by Joshua David Kent B.S., Louisiana State University, 1994 December 2003 ACKNOWLEDGMENTS The work reported in this research was partially supported by the efforts of Dr. James Mitchell of the Louisiana Department of Transportation and Development - Information Technology section for donating portions of the Geographic Data Technology (GDT) Dynamap®-Transportation data set. Additional thanks are paid for the thirty-five residence of East Baton Rouge Parish who graciously supplied the travel data necessary for the successful completion of this study. The author also wishes to acknowledge the support expressed by Dr. Michael Leitner, Dr. Andrew Curtis, Mr. DeWitt Braud, and Dr. Frank Cartledge - their efforts helped to make this thesis possible. Finally, the author thanks his wonderful wife and supportive family for their encouragement and tolerance. ii TABLE OF CONTENTS ACKNOWLEDGMENTS .............................................................................................................. ii LIST OF TABLES.......................................................................................................................... v LIST OF FIGURES ....................................................................................................................... vi ABSTRACT.................................................................................................................................. vii CHAPTER 1. INTRODUCTION ................................................................................................... 1 CHAPTER 2. REVIEW OF LITERATURE................................................................................ 11 2.1 Perception of Distance and Space within Behavioral Geography ...................................... 12 2.2 Concepts in Environmental Criminology ........................................................................... 17 2.3 Journey-to-Crime Modeling ............................................................................................... 23 2.4 Distance Decay Functions .................................................................................................. 30 2.5 Geographic Profiling........................................................................................................... 34 2.6 Characteristics of a Serial Offender.................................................................................... 48 CHAPTER 3. MATERIALS AND METHODS .......................................................................... 52 3.1 Modeling Environment....................................................................................................... 55 3.2 Test Subjects....................................................................................................................... 58 3.3 Data Sets ............................................................................................................................. 60 3.4 The Geographic Profile Procedure ..................................................................................... 62 3.4.1 Calibration Routine...................................................................................................... 62 3.4.2 Journey-to-Crime Routine ........................................................................................... 65 3.5 Determining the Best-Fit Distance Decay Model............................................................... 67 CHAPTER 4. RESULTS AND DISCUSSION............................................................................ 69 4.1 Frequency Distributions by Metric..................................................................................... 69 4.2 Journey-To-Crime Calibration Models............................................................................... 73 4.2.1 Euclidean Distance Decay Model................................................................................ 73 4.2.2 Travel-Path Distance Decay Model............................................................................. 77 4.2.3 Temporal-Path Distance Decay Model........................................................................ 77 4.3 Assumptions........................................................................................................................ 78 4.4 Best Performing Geoprofiles .............................................................................................. 78 4.5 Geographic Profiles by Euclidean Metric........................................................................... 85 4.5.1 Straight-Line Path Distances........................................................................................ 86 4.5.2 Manhattan Distance ..................................................................................................... 86 4.6 Functional Distance Measures............................................................................................ 87 4.6.1 Travel-Path Distances .................................................................................................. 87 4.6.2 Temporal-Path Distances............................................................................................. 88 4.7 Further Discussion .............................................................................................................. 89 iii CHAPTER 5. SUMMARY AND CONCLUSIONS.................................................................... 96 5.1 Conclusions......................................................................................................................... 98 5.2 Recommendations............................................................................................................. 101 5.3 Further Topics of Study .................................................................................................... 103 REFERENCES ........................................................................................................................... 107 APPENDIX A TRAVEL DIARY QUESTIONNAIRE ............................................................. 111 APPENDIX B COMMUTER SURVEY.................................................................................... 112 VITA........................................................................................................................................... 114 iv LIST OF TABLES Table 4.1 Geographic Profiling Results: Best Performing Geoprofiles ....................................... 79 Table 4.2 Geographic Profile Results: Direct Path Euclidean Metric .......................................... 85 Table 4.3 Geographic Profile Results: Manhattan Euclidean Metric ........................................... 86 Table 4.4 Geographic Profile Results: Travel-Path Functional Distance Metric ......................... 87 Table 4.5 Geographic Profile Results: Temporal-Path Functional Distance Metric .................... 88 Table 4.6 Geographic Profiling Results: Cumulative Results by Metric ..................................... 89 Table 4.7 Commuter Survey Results ............................................................................................ 92 v LIST OF FIGURES Figure 1.1 Travel Structure Characteristics .................................................................................. 7 Figure 1.2 Travel Cost Paradox .................................................................................................... 9 Figure 2.1 Routine Activity Theory .............................................................................................19 Figure 2.2 Journey-to-Crime Distance Decay Curves ................................................................. 32 Figure 2.3 Negative Exponential Functions ................................................................................. 41 Figure 3.1 Mathematical Calibration Algorithms .........................................................................65 Figure 3.2 Geographic Profiling Metric Calibration Matrix ........................................................ 67 Figure 4.1 Frequency Distributions By Metric .............................................................................70 Figure 4.2 Calibrated Distance Decay Algorithms for Euclidean Distance Metrics ....................74 Figure 4.3 Calibrated Distance Decay Algorithms for Travel-Path Functional Distance Metrics ......................................................................................................... 75 Figure 4.4 Calibrated Distance Decay Algorithms for Temporal-Path Functional Distance Metrics ......................................................................................................... 76 Figure 4.5 Geographic Profiling Results: Best Performing Geoprofiles – Test-Sample 1 ...........81 Figure 4.6 Geographic Profiling Results: Best Performing Geoprofiles – Test-Sample 2 ...........82 Figure 4.7 Geographic Profiling Results: Best Performing Geoprofiles – Test-Sample 3 ...........83 Figure 4.8 Geographic Profiling Results: Best Performing Geoprofiles – Test-Sample 4 ...........84 Figure 4.9 Potential Edge Effects When Using Artificial Boundaries ......................................... 93 vi ABSTRACT Spatial analysis has long been a valuable
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