UFDC Home  myUFDC Home  Help 



Full Text  
PAGE 1 1 A METHODOLOGY FOR EXPLORING THE RELATIONSHIP BETWEEN INTERSECTION FORM FACTORS AND TRAFFIC CRASHES USING GEOGRAPHICALLY WEIGHTED REGRESSION By REGINALD PIERRE JEAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREM ENTS FOR THE DEGREE OR MASTER OF ARTS IN URBAN AND REGIONAL PLANNING UNIVERSITY OF FLORIDA 2011 PAGE 2 2 2011 Reginald Pierre Jean PAGE 3 3 ACKNOWLEDGEMENTS I would like to thank my committee members Dr. Ilir Bejleri, Dr. Paul Zwick and Dr. Andres Blanco who have guided me through this thesis process. I would also like my mother, wife and family for the encouragement they provided me to get where I am today. And finally I would like to thank the Geoplan crew, Kate, Crystal, Lex, Lance, Sam and Danny for knowledge and assistance provided throughout my graduate education. PAGE 4 4 TABLE OF CONTENTS p age ACKNOWLEDGEMENTS ................................ ................................ ............................... 3 LIST OF TABLES ................................ ................................ ................................ ............ 6 LIST OF FIGURES ................................ ................................ ................................ .......... 7 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 11 Background of the Problem ................................ ................................ .................... 11 Problem Statement ................................ ................................ ................................ 11 Purpose of the Study ................................ ................................ .............................. 12 Importance of the Study ................................ ................................ .......................... 12 2 REVIEW OF THE LITERATURE ................................ ................................ ............ 14 Intersection definition ................................ ................................ .............................. 14 Inte rsection Safety ................................ ................................ ................................ .. 18 Crash Reduction Factors ................................ ................................ ........................ 25 Intersection Form Elements ................................ ................................ .................... 28 Intersection Design Principles ................................ ................................ ................. 28 3 METHODOLOGY ................................ ................................ ................................ ... 30 Research Design ................................ ................................ ................................ .... 30 Geographic Setting ................................ ................................ ................................ 31 Data Prepa ration ................................ ................................ ................................ ..... 33 Intersection Database Creation ................................ ................................ ........ 33 Crash rate ................................ ................................ ................................ ......... 34 Intersection Form Explanatory Variables ................................ .......................... 36 Assigning attributes to intersections ................................ ................................ 45 Data Review ................................ ................................ ................................ ........... 46 Assumptions of the Study ................................ ................................ ....................... 50 Research method ................................ ................................ ................................ ... 50 Ordinary lea st squares ................................ ................................ ..................... 50 Geographically Weighed Regression ................................ ............................... 50 4 RESEARCH FINDINGS ................................ ................................ .......................... 52 Ordinary least squares ................................ ................................ ............................ 52 Explanatory Variable Assessment ................................ ................................ .... 55 PAGE 5 5 Stationarity Assessment ................................ ................................ ................... 57 Model Bias ................................ ................................ ................................ ........ 58 Geographically Wei ghted Regression ................................ ................................ ..... 60 Local R 2 ................................ ................................ ................................ ............ 62 GWR Variable Analysis ................................ ................................ .................... 63 5 DISC USSION ................................ ................................ ................................ ......... 77 Ordinary Least Squares ................................ ................................ .......................... 78 Geographically Weighted Regression ................................ ................................ ..... 78 Weaknesses in the GWR model ................................ ................................ ............. 79 Limitations of the Study ................................ ................................ ........................... 80 Conclusion ................................ ................................ ................................ .............. 81 Suggestions for Future Research ................................ ................................ ........... 82 REFERENCES ................................ ................................ ................................ .............. 83 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 86 PAGE 6 6 LIST OF TABLES Table page 2 1 S teps used by drivers to negot iate unsignalized intersections ........................... 16 2 2 S ummary of motor vehicle crashes relat ed to junction severity in the U nite d S tates during 2002 ................................ ................................ ............................. 17 2 3 2007 N ational intersection crashes ................................ ................................ ..... 18 2 4 C rash reduction factor adapted from desktop referen ce for crash reduction factors ................................ ................................ ................................ ................ 27 4 1 O LS results ................................ ................................ ................................ ......... 54 4 2 O LS diagnostics ................................ ................................ ................................ 54 4 3 G WR results output table ................................ ................................ ................... 60 PAGE 7 7 LIST OF FIGURES Figure page 2 1 Physical intersection. ................................ ................................ ........................ 14 2 2 F unctional intersect ion. ................................ ................................ ..................... 15 2 3 E lements of the functional area of an intersection. ................................ ........... 15 2 4 A ngle crashes. ................................ ................................ ................................ .. 19 2 5 Rear end crashes. ................................ ................................ ............................ 20 2 6 Left turn crashes ................................ ................................ ............................... 21 2 7 Sideswipe crashes ................................ ................................ ............................ 23 2 8 Pedestrian/bicycle crashes ................................ ................................ ............... 24 2 9 Crash reduction factor formula. ................................ ................................ ........ 26 3 1 P ortland oregon ................................ ................................ ................................ 31 3 2 I ntersection database ................................ ................................ ....................... 33 3 3. C rash rate portland ................................ ................................ ........................... 35 3 4 T raffic volume ................................ ................................ ................................ ... 36 3 5 I ntersection legs ................................ ................................ ............................... 37 3 6 P otential conflicts at intersections ................................ ................................ ..... 38 3 7 T ypical traff ic signal intersection pattern ................................ .......................... 39 3 8 S i dewalk crossing at intersection ................................ ................................ ...... 40 3 9 T ypes of curbs ................................ ................................ ................................ .. 40 3 10 Curb ramp ................................ ................................ ................................ ......... 41 3 11 R aised intersection ................................ ................................ ........................... 42 3 12 B us s tuck on baxter street drop off ................................ ................................ .. 43 3 13 B ridges association with intersection ................................ ................................ 43 PAGE 8 8 3 14 R ed arrows denote number o f lanes ................................ ................................ 44 3 15 R ed area denotes lane width. ................................ ................................ ........... 44 3 16 G is intersection overview ................................ ................................ .................. 45 3 17 C rash rate descriptive statistics ................................ ................................ ........ 47 3 18 N ormalized crash rate descriptive statistics ................................ ...................... 48 3 19 T raffic volume descriptive statistics ................................ ................................ .. 48 3 20 N ormalized traffic volume descriptive statistics ................................ ................ 48 3 21 S patial clustering of crash rates ................................ ................................ ........ 49 4 1 O rdinary least square regression results ................................ .......................... 53 4 2 O LS residual histogram ................................ ................................ .................... 58 4 3 S patial autocorrelation of OLS residuals ................................ .......................... 59 4 4 G eographically weighted regression results standard deviations of residuals .. 62 4 5 S patial autocorrelation of GWR residuals ................................ ......................... 62 4 6 G WR local r 2 ................................ ................................ ................................ ..... 63 4 7 S idewalk coefficients gwr ................................ ................................ ................. 64 4 8 C oefficient variation surface ................................ ................................ ............. 65 4 9 S idewalk coefficient histogram ................................ ................................ ......... 66 4 10 T raffic signal coefficients GWR ................................ ................................ ......... 66 4 11 T raffic signal coefficient variation surface ................................ ......................... 67 4 12 T raffic signal coefficient histogram ................................ ................................ ... 68 4 13 L ane width coefficient GWR ................................ ................................ ............. 68 4 14 L ane width coeffici ent variation surface ................................ ............................ 69 4 15 L ane width coefficient histogram ................................ ................................ ...... 70 4 16 T raffic calming coefficient GWR ................................ ................................ ....... 70 4 17 T raffic calming coefficient variation surface ................................ ...................... 71 PAGE 9 9 4 18 T raffic calming coefficient histogram ................................ ................................ 72 4 19 I ntersection leg coefficient variation surface ................................ ..................... 72 4 20 I ntersection leg coefficient variation surface ................................ ..................... 73 4 21 I ntersection legs coefficient histogram ................................ .............................. 74 4 22 T raffic volume coefficient surface ................................ ................................ ..... 74 4 23 T raffic volume coefficient surface ................................ ................................ ..... 75 4 24 T raffic volume coefficient histogram ................................ ................................ 76 5 1 M odel performance vs. OLS ................................ ................................ ............. 77 PAGE 10 10 Abstract o f Thesis Presented to t he Graduate School Of the University Of Florida in Partial Fulfillment of the Requirements f or the Degree Master Of Arts In Urban And Regional Planning A METHODOLOGY FOR EXPLORING THE RELATIONSHIP BETWEEN INTERSECTION FORM FACTORS AND TRAFFIC CRASHES USING GEOGRAPHICALLY WEIGHTED REGRESSION By Reginald Pierre Jean December 2011 Chair: Ilir Bejleri Cochair: Paul Zwick Major: Urban and Regional Planning Crashes at i ntersections are a prominent and problematic traffic safety issue. Crashes at i ntersections have been studied using global linear regression and before and after analytical methods. The Intersection form factors measured are; intersection Leg s traffic signals, traffic calming devices, corners preset, curbs present, sidewalks, percent slope, bridge intersection, park intersection, l ane width, number of lanes, and traffic volume. Geographically W eighted R egression (GWR) is novel methodological approach in intersection analysis that models the relationships of these form factors to crash rates with in a spatial context. GWR proves to be a more accurate modeling method overall than global linear regression. In addition to higher model performance that GWR exhibits GWR shows the strength and variation in relationships along the data distribution for each observation GWR also produces a v isual representation of the relationships this allows for greater interpretation of the explanatory variables. In future GWR models with higher specification will produce crash rate prediction layers that will help aid in crash intersection analysis PAGE 11 11 CHAP TER 1 INTRODUCTION Background of the Problem Traffic accidents (referred in this work as crashes) often occur at intersections due to multiple conflicts created by users travelling through When studying intersection crashes, crash analys is on why they occur and how to reduce them is always a main priority Traffic safety analysts use various analytical methods to assess the relationship of contributing causes on crashes. Contributing causes are the factors that may cause a crash Understanding how cont ributing causes may lead to safer intersection design and policy decisions. Contributing causes can be organized in three groups. The first groups of factors are T hese are situations resulting from external factors not related to driver error or intersection form. An e xample of external contributing causes is weather. The second group of contributing causes is driver behavior factors. For example driver used alcohol or improper driving maneuver. The third c ontributing c ause and the focus for this thesis is the physical intersection form design Intersection characteristics or i ntersection form is defined as the structural composition of traffic intersection components. Problem Statement Before and after studies or with and without studies are perhaps the most widespread methods used to evaluate system performance. (Levinson and Chen 2006) The (Levinson and Chen 2006) state : But this method ( before and after analysis) will meet difficulties when the object of study is a long existing traffic management system. Firstly, it is usually impossible to PAGE 12 12 isolate the effects of traffic management from the eff ects of external variations Before and afte r study is persuasive for evaluation of short run impact under the condition that there is no significant variation in external circumstances, however, the evolution of traffic management from initialization to full operation usually covers decades. (p.4) This statement addresses the main issue of system performance analysis which can be applicable to intersection performance analysis Before and after type analysis has certain disadvantages when analysis of the data needs to cover long and continuous peri ods of time. O ther methods of analyzing relationships found in intersection performance analysis need to be explored. Purpose of the s tudy This Study intends to explore the relationship of intersection form factors to intersection crashes using a geograp hically weighted regression model What Intersection traffic form factors are the most important in reducing c rashes at intersections? What factors increase the crash rate (number of crashes normalized by traffic volume) the most? How do spatial regression models compare to global regression models ? Does spatial regression reveal relationships in a concise and useful manner? I t is important to look at different ways of measuring the effectives of intersection design. Spatial regression may be an efficient m ethod of analysis look at traffic intersections. This study explains the processes and techniques used to analyze this relationship using Portland Oregon data as a case study area Importance of the Study Levinson & Chen s tate (2006) Regression analysis is different from before and after study in that it tries to search out all the potential elements (including traffic management) that effect system performance, record their variation and use these PAGE 13 13 elements as the regression predictor variables to test th e association between traffic This study analyz es form effect on intersection crashes using spatial regression Evaluating the relationships of these variables on large and continuous timescales has been a deficiency in the before and after analysis. The findings may contribute to measuring the causational effect of physical intersection characteristics on crashes at intersections. PAGE 14 14 CHAPTER 2 REVIEW OF THE LITERATURE In order to determine the characteristi cs of intersection form and how they relate to crashes this study will first look at supporting literature related to intersection crash factors i ntersection form and intersection analysis methods Intersection definition An intersection is defined as cross, including the roadway and roadside facilities for traffic movements within the (Highway Safety Manual 2010) An p hysical areas. (Highway Safety Manual 2010) The phy sical area is shown in Figure 2 1 it consists of the area where the road segments occupy the same area. l area denoted by the Figure 2 2 contains the basic eleme nts: Decision distance maneuver distance and queue storage distance. Figure 2 1. Physical Intersection Highway Safety Manual. (2011) PAGE 15 15 Figure 2 2 Functional Intersection Highway Safety Manual (2011) Figure 2 3. Elements of the Functional Area of an Intersection Highway Safety Manual ( 2011) An i ntersection crash is somewhat harder to define as there is no absolute consensus about its definition. Many agencies define it as any crash that has occurred within the physical intersection area. Other agencies consider all crashes a certain distance from the physical intersection like 250 f ee t. Not every crash occurring within a 250 foot distance of an intersection is considered to be at an intersection crash PAGE 16 16 (Highway Safe ty Manual 2010) In almost every case any crash that occur s within 100 ft. of the physical intersection is considered to be an at intersection crash. This is the default measurement used when relating crashes to intersection. Intersection studies are often done in context of fatalities. Fatalities are usually the priority when researching automobile crashes. As we review traffic issues relating to intersections we will see this a s a driving concern for improvement of intersection design and safety. The re are two main categories of intersections u nsignalized intersection s and signalized intersections. Unsignalized are defined as intersections with stop signs, or intersections where the driver must judge whether stopping is appropriate ( such as roundabou ts or yield signs). Unsignalized intersections are unique because traffic flow is directed by driver action. These actions vary and are unpredictable because of the lack of structured signaling. According to 2009 data from National Highway Traffic Safety A dministration General Estimates System (NHTSA GES) Fatality Analysis Reporting System (FARS) unsignalized intersections account for half of the fatalities observed in urban intersection crashes. Table 2 1 Steps used by Drivers to Negotiate Unsignalized Intersections National Highway Traffic Safety Administration (1994) 1. Detect the presence of the intersection during an approach 2. Correctly identify signage 3. Anticipate Sudden deceleration from lead vehicle(s) 4. Detect presence of cross traffic 5. Recognize crash hazards posed by cross traffic, perhaps by estimating the speed, acceleration, and distance of the approaching vehicles 6. Watch for and anticipate other traffic or pedestrians that may cause a cross traffic vehicle to suddenly stop in the SV travel lane. 7. such problems 8. Stop the vehicle 9. Estimate when it is safe to proceed through the intersection PAGE 17 17 Traffic signals are by far the most common feature observed at signalized intersections. Traffic signals are automatic indication devices used facilitate the flow of vehicles, pedestrians and bicyclist automatically using signal timing techniques Traffic signals play a significant role in achievi ng safer performance at intersections. Previous research has shown that in certain situations traffic lights will reduce the number and severity of crashes. (Rodegerdts, Nevers and Robinson 2004) Table 2 2 Summary of motor Vehicle Crashes related to Junction severity In the United States during 2002 Total Crashes Fatalities/Injuries Number Percent Number Percent Non Intersection Crashes 3,599,000 57 1,022,549 52 Signalized Intersection Crashes 1,299,00 21 462,766 24 Non Signalized Intersection Crashes 1,418,000 22 481,994 25 Total 6,316,000 100 1,967,309 100 Source: Adapted from table 28 of Traffic Safety Facts 2002 (p.50) National Highway Traffic Safety Administration (2004) http://www nrd.nhtsa.dot.gov/Pubs/TSF2002.pdf According to the Fatality Analysis Reporting system ( FARS) and the National Automotive Sampling System General Estimates System about 40% of the crashes were intersection related crashes. (Choi 2010) Intersections constitute a small part of transportation networks yet a large amount of crashes are concentrated at them. It is fairly obvious that there are conflict s of travel direction and many other factors that explain this concentration of crashes Around 50% of total fatal crashes happen at intersections. The majority of these fatalities happen on unsignalized two lane roadways traveling at moderate speeds ~55MPH Most crashes happen betwe e n 3pm and midnight Automobile fatalities are the leading cause of death for people aged fifteen to forty four. (National Highway Traffic Safety Administration 2009) Intersections represent PAGE 18 18 a dispr oportionate share of the traffic safety issues and should be looked at as a priority for analysis. (Federal Highway Administration 2009) Table 2 3 2007 National Intersection Crashes Federal Highway Administration Office of Sa fety (2009) Number Percentage Total Fatal Crashes 37,435 Total intersection and intersection related crashes 8,061 21.5% Total Injury crashes 1,711,000 Total Intersection and intersection related injury crashes 767,000 44.8% Total property Damage Only (PDO) Crashes 4,275,000 Total intersection and intersection related PDO crashes 1,617,000 37.8% All Crashes 6,024,000 Total intersection and intersection related crashes 2,392,061 39.7% Intersection Safety highway intersections and interchanges are ample evidence that strategies to improve the safety of these crash prone areas are urgently needed. On average, there are five crashes at intersections every minute and one per son dies every hour of every day a (AASHTO 2004) Federal Highway Administration (FHWA) as identified 4 areas of primary focus in improving safety and reducing crashes. These area s of focus are Intersections Roa dway Departure, Pedestrians, and speeding. Intersections account for 21% of crash fatalities and around 53% of all crashes from 2002 2006 are associated with intersections. (Federal Highway Administration n.d.) PAGE 19 19 An intersection safety design has to fulfill dual objectives: mobility and safety. These objectives conflict more often than not and some feature need to be compromised for the sake of mobility. Balancing the efficient operation and safety of an intersection is top priori ty. The most common types of crashes at intersections help engineers prioritize safety elements to reduce crashes. Below are the most common crash types at intersections for signalized and unsignalized intersections and their respective suggested counterme asures according to a recent FHWA study 2004 Figure 2 4 Angle Crashe s Federal Highway Administration Angle c rashes Account for 42% of fatal cras hes at signalized intersections p otential countermeasures are as follows : optimize change intervals improve sight distance restrict access provide targeted enforcement PAGE 20 20 restrict parking Account for 53% of fatal crashes at unsignalized intersections p otential countermeasures are as follows : clear sight triangles improve awareness of intersection apply access management improve turn lane design construct roundabouts construct acceleration lanes close/relocate intersections reduce/eliminate skew post appropriate speed limits Figure 2 5 Rear end Crashes. Federal Highway Administration Rear end c rashes Account for 8% of fatal crashes at signalized intersections p otential countermeasures are as follows : PAGE 21 21 increase visibility of intersection and/or traffic signals increase awareness improve signal coordination install turn lanes control approach speeds optimize change intervals Account for 6% of fatal crashes at unsignalized intersections p otential countermeasures are as follows : install turn lanes supplemental overhead signing provide shoulder bypass lanes provide pavement markings provide right turn acceleration lanes provide left turn acceleration lanes provide lighting post appropriate speed limits Figure 2 6 Left Turn Crashes Federal Highway Administration PAGE 22 22 Left Turn Crashes Account for 21% of fatal crashes at signalized intersections p otential countermeasures are as follows : employ protected left turn phasing implement turn restrictions improve turning lane design reconstruct approaches improve sight distance improve signal coordination Account for 8% of fatal crashes at unsignalized intersections p otential countermeasures are as follows : improve turn lane design implement turn restrictions use indirect left turn treatments provide lighting clear sight triangles provide left turn acceleration lanes construct roundabouts close/relocate high risk intersections PAGE 23 23 Figure 2 7 Sideswipe Crashes. Federal Highway Administration Sideswipe Crashes Account for 13% of fatal crashes at signalized intersections p otential countermeasures are as follows : install pavement markings provide protected left turn phasing Account for 2% of fatal crashes at unsignalized intersections p otential countermeasures are as follows : install pavement markings provide lane assignment signing or marking provide right turn acceleration lanes PAGE 24 24 Figure 2 8 Pedestria n/Bicycle Crashes. Federal Highway Administration Pedestrian Crashes Account for 25% of fatal crashes at signalized intersections p otential countermeasures are as follows : improve signal hardware improve pedestrian/bicycle facilities provide information and education Account for 14% of fatal crashes at unsignalized intersection crashes p otential countermeasures are as follows : improve pedestrian/bicycle facilities provide traffic calming information and education PAGE 25 25 Crash Reduction F actors Cr ash reduction factors (CRF) are the percentage reduction that might be expected after implementing a given crash countermeasure. In some cases the CRF can be negative meaning that the counter measure lead s to an increase in crashes. A CRF can be regarded as a general es timate of affect. As long steps are taken to ensure that the countermeasures apply to the condition being measure. (Hovey and Chowdhury 2005, 14) Before and after and cross sectional study methods are two of the methods used to develop I n a before and after study, the safety effect of a countermeasure is determined by the difference in the number of crashes occurring before the after study; the cross sectional approach usually uses regression methods to estimate crash frequencies from a large sample of roadway segments whose design attributes vary systematically. Such regression models estimate the marginal effects of changes in highway desig n attributes on crash frequencies. 1 (Shen and Gan 2007) Before and After M ethod This more widely used approach to C RF development uses data before and after countermeasures are implemented C rash count data for a 2 3 year pe riod is used D ata during the construction of the countermeasure is removed from that time perio d A few factors must be considered between the periods also. Vehicles miles is needed to calculate exposure, traffic volumes should be equal, traffic compositi on should be similar and variation in crash data should not vary any more that 20 percent. 1 The key difference between before and after and cross sectional studies is not in the different methods used to analyze the data (as a matter of fact, they can be similar) but rather in the different concept of how to investigate the safety effect. In the before and after study, the idea is to investigate these locations where a given improvement has been applied within the period of analysis, while for the cross sectional analysis; the investigated locations do not experience any major changes within the period of analysis. Thus, the before and after study focuses on the changes in safety over time, while the cross sectional analysis focuses on the differences in safety between locations. (Tarko, Eranky and Sinha 1998) PAGE 26 26 The concept of the simple before and after study is straightforward. It is based on the assumption that if nothing has changed, the crash experience before improve ment is a good estimate of what would have happened during the after period without improvement. The formula for deriving a CRF based on this method is : Figure 2 9 Crash Reduction Factor Formula Transportation Research Record 1840 (2007) Nb and Na are the numbers of crashes at a treated site before and after the improvement took place, respectively According to Shen & Gan (2007) study; Before and after method is subject to some pitfalls. These factors are the Regression to the mean issue, crash migration issue maturation and external casual factors. Regression to the mean is a statistical phenomenon that occurs whenever a nonrandom sample is selected from a population. In this case the crash intersection. Since intersections with large crash co unts are usually selected these areas tend to have higher reductions than seen on average, even without any treatments, the crash frequencies would likely be reduced simply because the number of crashes at the sites tends to regress or return to the long term mean number of crashes. T he Empirical Bayes (EB) method has been developed to adjust for the regression to the mean bias. The method is based on the following three assumptions: The number of crashes at any site follows a Poisson distribution. The me ans for a population of systems can be approximated by a gamma distribution. Changes from year to year from different factors are similar for all reference sites. PAGE 27 27 Also noted by Shen & Gan; c rash migration is the movement of the observed crashe s to a new location or situation T his can be witnessed geographically and non geographically Crashes can geographically move to a new location. Or c rashes can move to a new situation i.e. light pole installed reduced night time crashes but inc reased fixe d object crashes. Maturation is the change in crash counts due to changing trends in the economy weather or traffic flow. Maturation is an issue that can have an effect on analysis if not accounted for. External Causal Factors are factors that affect the c rash counts that are hard or cannot be measured for precipitation and economic conditions cannot be measured for their affect easily. There are some external factors that can be accounted for such as new development causing higher vehicle conflict exposure etc., but these situations are hard to measure nonetheless. Despite the potential problems the before and after method is the widely accepted form o f CRF development. (Shen and Gan 2007) The US D error that is based on the standard deviation of the error in the estimate. An example is shown in Tab le 2 9 ; Table 2 4 Crash Reduction factor Adapted from Desktop Reference for Crash Reduction Factors ( 2007) Federal Highway Administration Countermeasure Crash type Intersection type CRF CRF (std error) Install right turn lane Right turn 4 Leg 50 5 Remove left turn lance all 4 leg 45 10 PAGE 28 28 In the T able 2 9 the first row shows us that for the countermeasure of installing a right turn at 4 legged intersections has a 50% reduction in right turn crashes with a standard error of 5 percent. Alternatively the second row tells us that if we remo ve a left turning lane from a 4 legged intersection of any crash type we will witness a 45% increase in all crash types with a standard error of 10 percent. Intersection F orm Elements Intersections are designed with safety and ease of movement in mind. Designs of intersection vary from location to location based on the functional classification of intersection; the traffic volume observed by the intersection and land use characteristics it the vicinity. Intersection design should facilitate mobility all users of the intersection in a clear and safe manner. These are the principle s of intersection design. s died and roughly 1.5 million Americans were injured in intersection related crashes. In (Institute of Transportation Engineers 2004) Inter section Design Principles At grade intersections are junctions where two or more axes cross at the same level. Like other highway feature safety cannot be achieved through design alone it requires collaboration between traffic controls, planning officials and traffic enforcement. The five general topics that are consi dered during traffic design according to the Too lbox on Intersection Safety and design (2004) are; Human factors: Drivers and Pedestrian actions like reaction time and interpretation Road way uses : This includes traffic volume and characteristics of users at intersections PAGE 29 29 Physical e lements : Topography a nd intersection angle or environmental factors Economic factors: This includes factors like cost of intersection or effect of intersection on land use Functional Intersection areas: Includes intersection legs and width and size of intersection. Indicates complexity These elements compose the components of both physical intersection and the larger functional intersection. And lead to a decision on what design elements will be incorporated into the intersection. Some significant elements of intersection de sign are approach angle, traffic signals corn ers / curbs, gradients/percent slope s, lane widths, number of lanes, t raffic calming devices, angle/skew of intersection and corner radius. PAGE 30 30 CHAPTER 3 METHODOLOGY Research Design In this section the methodology will be explained along with the reason ing behind the methods chosen. The objective of this study is to analyze the relationship between intersection form factors and intersection crashes. Portland Oregon is chosen as the study area d ue to data availability and quality data. The strength and direction of the relationships are illustrated us ing spatial regression modeling. Eleven variables represent the intersection form factors; Traffic Volume, Intersection Legs, Traffic Signals, Sidewalks Cur bs, Corners/Curb ramps, Traffic calming, percent slope, Bridges, Number of lanes and Lane width. T he relationship of these explanatory variables is revealed in the form of coefficients created by the regression model. Two regression models were used to model the characteristics of crash counts The first model used is the Ordinary Least Squares ( OLS) regression model that predicts global model dependent to independent variables The second model, a geographically weighted regression (GWR) predicts the relationships of each observation using a local regression calculation. The modeling process uses the intersection node feature layer t hat has been processed to contain the explanatory variables that relate to each of the intersection characte ristics. The OLS results are compared to the GWR results and independent dependent relationships are interpreted from the results. PAGE 31 31 Figure 3 1 Portland Oregon Geographic S etting Portland, Oregon is a populous and dense city in the Pacific Northwest. It is a part of the greater Portland metropolitan area which also includes Vancouver, Gresham and Hillsboro. As of 2010 it is the most populated area in Oregon with an estimated population was 583,776. (U. S Census Bureau 2010) Portland is known for its strong land use planning and dense urban environment. (Orski 2003) The Willamette River runs north through the city center Major interstates I 85 and I 5 also join in Portla nd. PAGE 32 32 Transit Oriented development 1 network. Mixed use and high density development is promoted throughout the city. (Oregon Metro Council 2011) Portland is known for having many one way roads down town narrow roads this is known as having an alternating grid pattern. This pattern is not universal through out the city but mainly it is the case In Report Port land was found to have the 13 th worse travel time Index in the county, while co ngestions makes commutes to 123% longer than expected (Schrank, Lomax and Eisele 2011) Portl and maintai ns a very detailed GIS street network database. This includes data like roads, bridges, automobile, crash points and many other features that allow for a complex representation of the street network. This was the most important factor in choosing this loca tion for the study. Also it is important to note street layout which allows for a robust study of many different types of intersectio ns. online GIS data warehouses. The key data layers that were s ourced were the Portland streets GIS layer and Portland automobile accidents for 2007 to 2008. These layers are the basis of the study and much of network dataset is calculated from spatial relationships between these two layers. Next any data relating to intersection infrastructure was added to the database for the data preparation phase. 1 Transit oriented development (TOD) is a mixed use residential or commercial area designed to maximize access to public transport, and often incorporates features to encourage transit ridership.(Federal Transit Administration) PAGE 33 33 Figure 3 2 Intersection Database Data Preparation The goal of data preparation is to organize the data into a form suitable for analysis This involves preparation of the intersection database and association of the relevant attribute with each intersection. Each variable used in the regression model is defined in this section Intersection Database Creation In order to run the statistic al model the data has to be aggregated into one single feature layer This was done by first creating a network dataset out of the Portland streets segments. Nodes are then calculated for each segment and a node segment PAGE 34 34 association table is created Intersections are defined where 3 or more segments share a node The intersection s layer is included into the GIS database along with all the related Portland transportation data. Crash rate It is known that crash counts increase with increasing traffic volume; however this relationship has only proven to be con sistent for up to about 20,000 v ehicles per day (Vpd).Volumes above 60,000 Vpd have a complex and erratic effect on crash count. The crash counts are high in some areas and much lower in others com pare to crash (Joksch and Kostyniuk 1998) This contradicts our perception that crash counts should vary simply with traffic volume. We also cannot fully assume that the deviations betwee n crash points are due only to the intersection characteristics since traffic volume has a hard to measure relationship with intersection traffic crashes. A potential explanation for this phenomenon is that there might be intersection feature that are more common at high volumes. Another is that different crash types may have a high er potential of occurring at different t raffic volumes. How do you represent the relationship between crash counts and traffic volumes for the more mild traffic volumes? One way we can do this is to smooth the crash counts based on the traffic volume estimated at the intersection This would require fitting a Gaussian kernel and a moving window bandwidth to smooth the various data points. (Joksch and Kosty niuk 1998) Another way to normalize the relationship between crash count and traffic volume is to calculate a crash rate. This method is the one used in most traffic safety studies. Crash rate is a measure of crashes in a given period of time against traffic volume PAGE 35 35 given priority for traffic safety improvement. According to MassHighway DOT,(2011) the formula for calculatin g the crash rate for an intersection is presented below, which is standard to the Traffic Engineering profession: Figure 3 3 Crash Rate Portland (3 1) R is crash rate calculated in MEV C is the number of crashes at the intersection is the daily traffic volume at intersection PAGE 36 36 365 is the amount of days the crash data covers 2 is the amount of years the data covers Intersection F orm Explanatory Variables Buffer zones were created around all intersection nodes using a radius 100 feet. These buffer zones were used to select the intersection form features associated with the physical and functional intersection. The ArcMap 9.3 Geoprocessing tools S patial J oi n S elect by B uffer D istance and near tool were used to append the explanatory variables to the intersection nodes. Figure 3 4 Traffic Volume PAGE 37 37 Traffic Volume at Intersection Traffic volume is defined as the average daily combined bulk of directional travel coming into the intersection. This is the most common type of traffic count In areas with a lot of multi axle trucks the number recorded by the traffic counter can be larger than the actual number of vehicles. Volume counts are typically 24 hour s in length The t raffic volumes given in the Portland dataset are given with the total volume already calculated. In order to calculate crash rate at each intersection a traffic volume surface was produced. into a surface by inverse distance weighted calculation. This multivariate interpolation process uses the known traffic volume points to calculate traffic volume for intersections that are not known. Considerations for transportation network relationships were taken into account to create the best possible surface calculation for traffic volume. Parameters like search radius and power were manipulated to get the best surface possible. Figure 3 5 Intersection Legs Photograph Credit and Copyright: www.p ortlandmaps.com, ( 2004 ) PAGE 38 38 Intersection Legs Intersection legs are all the road segments that intersect the center of an intersection. While the geometry of various types of intersections may vary, the complexity of an intersection increases with an increasi ng number of approach legs to the intersections. The number of potential conflicts for all users increases substantially at intersections with more than four legs. (Rodegerdts, Nevers and Robinson 2004) Refer to Figure 3 6 for an example of the type on conflicts possible at 3 and 4 leg intersections. T hese examples show how the conflict points increase as intersection leg count increases. (Rodegerdts, Nevers, & Robinson, 2004) Figure 3 6. Potential Conflicts at Intersec tions Ro degerdts, Nevers, & Robinson, 2004) In intersection design five or more intersection leg implementations are to be avoided where ever possible. (Fitzpatrick, Wooldridge and Blaschke 2005) Intersection s PAGE 39 39 get more complex as the number of intersection approach legs increase. With an increase in the potential number of conflicts for all users this causes, an increase in crash count is expected. Figure 3 7 Typical Traffic Signal Intersection Pattern (R od egerdts, Nevers, & Robinson, 2004 ) Traffic S ignals Traffic signals are used to assign vehicular and pedestrian right of way. They are used to promote the orderly movement of vehicular and pedestrian traffic and to prevent excessive delay to traffic. (Federal Highway Administration 2009) A ll signalized and unsignalized i ntersections in Portland are included in the GIS database for this study. In addition to promoting orderly movement of traffic, traffic signals also increase capacity of intersections, reduce the frequency of some types of crashes, and provide periodic continuous movement along a route. Also traffic signals interrupt heavy tra ffic to allow othe r to permit other traffic types. Traffic signals are expected to have reduced crashes at intersections compared to unsignalized intersections. PAGE 40 40 Figure 3 8 Sidewalk Crossing at Intersection Institute of Transpo rtation Engineers, 2010 Sidewalks Sidewalks and paths are the primary travel way for pedestrians as they approach intersections in developed suburban and urban districts. Properly designed sidewalks provide mobility, accessibility and safety to all users. (Institute of Transportation Engineers 2004) Th e sidewalks polygon feature layer is part of the Bureau of Although sidewalks are designed to provide accessibility, mobility, and safety they also increase the complexity at intersections. Therefore an increase in crashes is likely. Figure 3 9 Types of Curbs (Rodegerdts, Never s, & Robinson, 2004) PAGE 41 41 Curbs This linear feature layer system. Curbs facilitate pedestrian movement throughout an intersection. Curbs also control where the conflict points are in left and right turning crashes Curbs create deli mitation between the roadway and sidewalk. Curbs are also part of the pedestrian and bicycle network which facilitates the traversal of the intersection. Curb s create an increase in complexity at intersections higher crash counts are plausible in the pedestrian and bicyclist crash types. Figure 3 1 0 Curb Ramp Designing Sidewalks and Trails for Access (2001) Corners/Curb Ramps Curbs are generally designed with a gutter to form a combination curb ramp and gutter section. They are used to provide drainage control and to improve delineation of the roadway. Curbs are used extensively on all types of urban highways with design speeds less than 50 mph. (Institute of Transportation Engineers 2004) This point feature layer Curb ramps PAGE 42 42 (crosswalks) are the point of traversal for most pedestrians and bicyclist, because of this i t is probable that an increase in crashes will be witnessed. This increase may be offset in the fact that gutters are also associated with this feature. Gutters increase the safety in wet road conditions by drainage and may offset the increased crash count s witnessed from curb ramps Figure 3 1 1 Raised intersection Drawing by B. Kim Erslev ( 2003 ) (Beneficial Designs Inc. 2001) Traffic Calming Traffic calming is actions or devices to reduce vehicular traffic's intrusion into and its effects on urban life. Speed humps or textured road surfaces. This point feature layer includes a variety of devices whose purpose is to address the negative impac ts of traffic in areas by reducing speeding, reducing traffic volumes and making the streets friendlier to pedestrians and bicyclists (New York City Department of Transportation 2003) Traffic calming devices are specially impl emented devices to safeguard an intersection by reducing vehicle speed in and increasing driver awareness at intersection. Traffic calming devices are expected to lower crash counts at intersections. PAGE 43 43 Figure 3 1 2 Bus stuck on Baxter Street drop off (Photo credit: Ingrid Peterson) Percent Slope The recorded ground slope of intersection. (5% intervals) At grade intersections have a slope of 0%. The gradient of the intersection may reduce visibility at intersections, which in turn may increase conflicts of the users. Figure 3 1 3 Bridges Association with Intersection (Photo credit: Google Maps Imagery) Bridges Bridges associated with intersections. This point feature layer includes bridge structures which are part of an intersection leg. Bridge intersections are complex PAGE 44 44 feature s usually associated various signage and high traffic volume. These factors may increase crashes at intersections because of the confusion and complexity that may arise in the driver decision making process. F igure 3 1 4 Red arrows Denote Number of Lanes Adapted from Urban Intersection Design Guide Volume 1 Number of Lanes Number of lanes of intersection legs section observed at intersection. Large number of lanes may be indicative of high vehicle traffic a long with more vehicle lane switches; this may lead to an increase in crash count. Figure 3 1 5 Red area denotes Lane Width Adapted from Urban Intersection Design Guide Volume 1 Lane width Width of intersection legs section observed at intersection. The width of the lanes can be expected to increase crash count just as number of lanes may. Lane width may also be an indicator of high traffic volume which is known to increase crashes up to a certain point. PAGE 45 45 Park Intersection A park intersection is an i ntersection that has a park associated with one or more of its corners. Park intersections may present distractions, high pedestrian or bicycle conflicts which may inadvertently increase the amount of crashes witnessed. Assigning attributes to intersectio ns Crash rates were selected and assigned an intersection node using buffers. Crash locations within a 100 f oot buffer were aggregated to the intersection node table. Each intersection form layer was spatially joined to its nearest intersection and the at tributes added to the in tersection node database table. An example of an intersection form T his variable was created using a pavement type feature layer Many different approaches were utilized in aggregating the variable dat a to the intersections nodes feature layer Spatial joins and field calculations allow the data to be transferred over to intersections of analysis Figure 3 16 GIS Intersection Overview PAGE 46 46 The result of this process was a c rash i ntersection node layer that re presents the form of each intersection (explanatory variables) and contains intersection crashes. This feature layer is a subset of the intersection nodes layer except it contains only the intersection nodes that have crashes associated Strict cri teria are used to maintain data consistency for the analysis. These criteria are used to trim and standardize the intersection database before any analysis is performed. The criteria are as follows. 1. Overpasses or o ther cases when the streets do no t physically intersect are eliminated from the database using supporting data to locate and deduce whether the intersection is physical or not. 2. Intersec tions must not be located on an Interstate 3. Highway r amps must not be associated with the intersections. 4. Intersection types that are not consistent with the scope of the study are removed. For example road intersections in parks. Data Review The purpose of preliminary data review is to ensure the data usability and feasibility for a linear regression analysis. The data must be checked for outliers, linearity and spatial clustering. These attributes are important to the successful operation of a linear regression model. For example OLS regression optimal attributes include remov al of outliers, stationarity normal distributions and linear relationships, while GWR models work specificall y well on data is spatially clustered. Traffic stre et data has its own specific characteristics ; nearness is measured in right angle distance also known as Manhattan distance 2 instead of Euclidean 3 distance. 2 The Manhattan distance func tion computes the distance that would be traveled to get from one data point to the other if a grid like path is followed. The Manhattan distance between two items is the sum of the differences of their corresponding components. (De za and Deza 2009) PAGE 47 47 Access corridors also play a role in how the data is patterned. Traffic volume follow s a logarithmic pattern along intersection distribution In order to determine what the spatial distribu tion looks like the ArcGIS 9 .3 histogram tool was used to look at the data. The histogram tool displays a measure of the frequency distribution. The crash rate descriptive statistics of the histogram are found below in Figure 3 17 Figure 3 17 Crash Rate Descriptive statistics The histogram has a large positive skew of 3.4679 with a mean of .52. The kurtosis of the dataset was 18.817. A normal dataset has a kurtosis 4 of around 3 Since it is clear that this dataset is non normal it must be transforme d to normal bell shaped distribution. The crash rate variable was transformed logarithmically to make its distribution normal for regression analysis. (3 2 ) Log Transformation is often used when the data has a positively skewed di stribution and there are high values. The log transformation makes variance of the data range more constant by doing this. After the log transformation the histogram was reexamined for its normalcy. The results are found in Figure 3 18 3 The Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. (Deza and Deza 2009) 4 Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case. PAGE 48 48 Figure 3 18 Normalized Crash Rate Descriptive statistics The Skew is much nearer to zero. Also our kurtosis of 2.76 is much closer to three. Our mean and median are also similar. These results exhibit the aspects of a normal dataset. A logarithmic transformation was also performed on traffic volume explanatory variable for similar reasons. This creates a linear relationship to crash rate allowing our results to be interpreted clearly. The before and after statistics of this trans formation can be seen in Figure 3 19 an d 3 20 Figure 3 19 Traffic Volume Descriptive Statistics Figure 3 20 Normalized Traffic Volume Descriptive Statistics Figure 3 21 shows the spatial clustering exhibited by the crash rates. Multiple areas of high positive z scores indicate a large clustering of high similar values at a 0.05 statistically significant level. PAGE 49 49 Figure 3 21. Spatial Clustering of Crash rates Spatial clustering shows an interesting relationship. Spatial regression methods are used to analyze these relationships because it captures spatial dependency, meaning the spatial component is also a factor in the regression. The method of spatial regression selected is geographic weighted regression; this local version of spatial regression generates parameters disaggregated by sp atial units of analysis. This allows for the assessment of spatial heterogeneity in estimated relationships. This is usefully are likely to be similar. This s patial regr ession estimation model will output variables strength of correlation to accident count. We can use this to deduce whether this variable is a significant factor in a ccident count at intersections. PAGE 50 50 Assumptions of the Study This study assumes that the rel ationships held between intersections are based on a Euclidean distance. This study also assumes the relationship between crash rate and traffic volume is linear for the distribution witnessed in the dataset. Research method Ordinary least squares Ordinary least squares (OLS) regression is a common starting point for linear regression Identifying and measuring relationships allows for a better understand ing of what i s taking place. Also OLS shows preliminary relationships that exist between indepen dent variables and the dependent variable where This is mainly the reason Ordinary least squares regression method is the first step we must take when modeling the data. OLS provides a global model of the variables we are trying to understand (ESRI 2009) After running OLS the general strength and significance of each variable is. OLS also tell s whether each variable is a significant factor in the model. OLS gives the basic information need ed to move on to geographically weighted regression. Ge ographically W eighed Regression Once OLS complete geographically weighted regression ( GWR ) is the next step in the analysis of the data. GWR is one of several spatial regression techniques, increasingly used in geography and other disciplines. GWR provides a local model of the variable or process you are trying to understand/predict by fitting a regression equation to every feature in the dataset. GWR constructs these separate equations by incorporating the dependent and explanatory variables of features falling within the bandwidth of each target feature. (ESRI 2009) PAGE 51 51 GWR is the significant analysis in this study. Through GWR we will answer the questions that this stud y raises and show relationships of intersection crash rates to intersection form factors. GWR is the analysis method of choice because of the tendencies of the data. Basic regression models assume that observations are independent of each other This is not always the case with spatial data. Near things tend to be more related then distant things. (Tobler 1970) Not only might the variables in the model exhibit spatial dependence (that is, nearby locations will have similar val ues) can be observed if the residuals from the basic regression are plotted on a map where commonly the residuals in neighboring spatial units will have a similar ma gnitude and sign. (Charlton 2009) These characteristics have negative implications on the variables that have possible spatial relationships. Geographically weighted regression does not assume the data is spatially homogenous. It takes into account that the relationships being modeled are spatially heterogeneous. T he relationship of nearness differ s as opposed to being the same everywhere in the model. The results of the GWR will reveal the relationships of intersection form factors to crash account and how they vary across space PAGE 52 52 CHAPTER 4 RESEARCH FINDINGS The findings below show the output of the ordinary least square regression and geographically weighted regression. The results of the OLS show the global relationships of intersection form to crash rate Comparison to the OLS model helps to clarify the significance in using a GWR model for this type of analysis. The relationships of each e xplanatory variable will be displayed using a coefficient map and coefficient variation raster to illustrate the relationships further. The coefficients maps are interpreted as follow s: A negative coefficient lowers the crash rate by the respective amount per one unit of the explanatory variable. A positive coefficient raises the crash rate by the respective coefficient per one unit of the explanatory variable. The r aster coefficient surface shows the regional variation of the explanatory variable R egional variation illustrates the change in the of the coefficient variables over the data space. Ordinary least squares Ordinary Least Squares (OLS) regression is the first model used to analyze the relationships between the intersection features and crash rates. OLS creates a single regression equation that represents the relationship. The relationships we are modeling wil l reveal whether the relationships are strong positively, negatively or whether there is no relationship at all. A strong positive relationship will denote the number of crashes at intersection go down as the observed variable goes up. PAGE 53 53 Figure 4 1 O rdinary Least Square Regression Results To assess out models performance we look at the Multiple R Squared and the Adjusted R Squared. Values range from 0 1, higher values indicate more accurate models. We can see that for our multiple R squared we get a re sult of 0.42 The chosen variables account for 42 % of the variation in the dependent variable crash rate. The Adjusted R Squared value of 0.42 represents model complexity as it relates to the data. The Summary of the OLS re sults are found below in Tabl e 4 1 PAGE 54 54 Table 4 1 OLS Results Variable Coefficient Std Error t Statistic Probability Robust_SE Robus t_t Robust_Pr VIF[1] Intercept 0.997591 0.195574 5.100843 0.000001* 0.194614 5.126001 0.000001* Intersection Legs 0.202754 0.023408 8.661564 0.000000* 0.023941 8.469032 0.000000* 1.174717 Traffic Signals 0.667918 0.030405 21.967123 0.000000 0.034862 19.159167 0.000000* 1.137924 Traffic Calming 0.088019 0.028714 3.065306 0.002202* 0.027569 3.192694 0.001436* 1.023737 Corners 0.007750 0.044919 0.172542 0.863011 0.045018 0.172165 0.863308 1.594663 Curbs 0.090124 0.132507 0.680144 0.496449 0.134491 0.670107 0.502826 1.077899 Sidewalks 0.154196 0.042125 3.660402 0.000269* 0.045421 3.394821 0.000710* 1.469729 Percent Slope 0.005279 0.003787 1.393827 0.163462 0.003923 1.345406 0.178583 1.082866 Bridge 0.198736 0.147899 1.343722 0.179127 0.140483 1.414658 0.157262 1.019422 Park 0.098880 0.041413 2.387658 0.016988* 0.038115 2.594262 0.009507* 1.020377 Lane Width 0.015061 0.000903 16.684694 0.000000* 0.000980 15.366648 0.000000* 1.344479 Number of lanes 0.028595 0.018422 1.552196 0.120711 0.022522 1.269677 0.204282 1.144119 Traffic Volume 0.000078 0.000002 47.250741 0.000000 0.000002 36.747557 0.000000* 1.185923 Table 4 2 OLS Diagnostics Number of Observations: 3922 Numb er of Variables: 13 Degrees of Freedom: 3909 Ak aike's Information Criterion (AIC) [2] 8675.40818 Multiple R Squared [2] 0.425375 Adjusted R Squared [2] 0.423611 Joint F Statistic [3] 241.141745 Prob( >F), ( 12,3909) degrees of freedom 0.000000* Joint Wald Statistic[4] 2135.128270 Prob( >chi sq uared), ( 12) degrees of freedom 0.000000* Koenker (BP) Statistic [5] 308.128852 Prob( >chi sq uared), ( 12) degrees of freedom 0.000000* Jarque Bera Statistic [6] 213.534112 Prob( >chi s quared ), ( 2) degrees of freedom 0.000000* PAGE 55 55 Explanatory Variable A ssessment Each variable is assessed for its correlation and significance. The coefficient for each variable reflects the strength and direction of the relationship it holds with the dependent variable (crash rate) When the sign of the coefficient is negative it shares a negative relationship, this signifies that the independent variable is reducing the crash rate ( e.g. a 0.66 decrease in crash rate is witnessed whenever traffic Signal is no t present at an intersection) The Coefficient represents the expected change in the dependent variable for every one unit of change in the indepen dent variable. The explanatory variables significance is tested within the model using a T test, where the null hypothesis is the coefficient is equal to zero and not helping mode l. The smaller the probability or robust probability the more likely that the coefficient is not zero is high. An explanatory variable that is statistically significant is important to the model and signifies a relationship with the dependent variable. In tersection l egs : T his variable proves to share a significant positive relationship with crash rate As segment count increases the observed crash r ate increases. A coefficient of 0.20 shows that the increasing complexity of intersection legs raises crash c ounts. A VIF of 1.17 shows that there is no redundancy in this variable. Traffic s ignal : This variable proves to have s i gnificant negative relationship crash rate This is interpreted as meaning when t raffic signals are present lower crash rates are witnessed. A coefficient of 0.66 is the strongest relationship in this study and proves to be the prominent variable affecting crash counts at intersections in OLS regression. A VIF of 1.17 shows that there is no redundancy in this variable. Traffic calming : This variable proves to have significant negative relationship with crash rate. A coefficient of 0.8 shows a moderate decrease in crash rate, when traffic PAGE 56 56 calming devices are observed at intersections. A VIF of 1.02 shows that there is no redunda ncy in this variable. Corners present : Non significant negative relationship T here seems to be no relevant relationship between traffic corners devices and crash rates A VIF of 1.59 verifies this variable is not redundant. This explanatory variable will be removed from the geographically weighted regression. Curbs present : Non significant negative relationship there seems to be no relationship between traffic curbs devices and crash counts. This explanatory variable will be removed from the geographically weighted regression. Sidewalk present : Sidewalks exhibit a s ignificant positive relationship with crash rate A coefficient of 0.12 tells us as sidewalks are witness at intersections a larger crash rate will be observed. A VIF of 1.46 verifies this variable is not redundant. Percent Slope : Non significant positive relationship as it failed the T test. T here seems to be no relationship between the slope gradient and crash counts at intersections. This explanatory variable will be removed from the geographically weighted regression. Bridge Intersection : Bridge intersections exhibit Non s ignificant negative relationsh ip. The Probability and Robust probability of 0.155253 and 0.135205 prove to be too high for significance. This explanatory variable will be removed from the geographically weighted regression. Park Intersection : Significant positive relationship A coeffi cient of 0.09 shows that p arks intersections are related with higher crash rates. A VIF of 1.46 verifies this variable is not redundant. PAGE 57 57 Lane width : S ignificant slight positive relationship coefficient of .014 shows that wider the lane width the larger the crash rate. Number of lanes : Non significant negative relationship. There seems to be no relationship be tween number of lanes and Crash rate. This explanatory variable will be removed from the geographically weighted regression. Traffic Volume : S ignificant negative relationship A coefficient 0.000078 proves a correlation with traffic volume at intersection with crash counts. As traffic volume goes up crash count is reduced There are certain phenomenon witnessed with traffic volume that is discu ssed refer to literature on traffic volume for better understanding of traffic volumes. Model significance T he Koenker (BP) statistic of 308.128852 and Joint Wald Statistic of 2135.128270 exhibit overall model significance. The null hypothesis for these t ests is that the explanatory variables in the model are not effective. Stationarity Assessment The Koen ker (BP) Statistic is also used to assess Stationarity. It is important to determine whether the explanatory variables behave the same every where in the study. When the same correlations between the explanatory variables and independent variables are witness ed everywhere in the study area the model exhibits stationarity. When the model is consistent in data space, the variation in the relationship between predicted values and each explanatory variable does not change with changes in explanatory variable magnitudes (there is no h eteroscedasticity in the model). (ESRI 2011) The null hypothesis for this test is that the model is stationary. A p value of smaller that 0.05 indicates significant heteroscedasticity and nonstationarity. PAGE 58 58 The p value for the Koenker (BP) Statistic is 0.00000 so our model exhibits nonstationarity. Models that exhibit nonstationarit y prove to be good candidates for geographically weighted regression. Model Bias Model bias The Jarque Bera Statistic is used to assess whether the model is biased. A model is defined as being biased when the observed depende nt values minus the estimated values are not normally distributed T hese are known as residuals. When the p v alue is less than 0.05 for a 95% confidence interval the residuals are not normally distributed. This can mean that the model is misspecified and one or more key variables are m issing from the model. A significant Jarque Bera statistic is observed in the OLS model results Further analysis of the residuals using a histogram is show n in Table 4 2 Figure 4 2. OLS Residual Histogram PAGE 59 59 Figure 4 3. Spatial Autocorrelation of OLS Residuals The histogram of residuals reveals a near normal distribution. A positive skew of 0.55 and kurtosis of 3.2 are not too far off of what we would expect from a normal distribution. Also referring back to that strong heteroscedasticity witnessed in the stationarity assessment it is not surpri sing to see a small bias. Due to limitations of data key variables that may contribute to model strength are missing and this also contributes to the small model bias we are seeing. After running spatial autocorrelation ( see Figure 4 3 ) we see that the res iduals are clustered further emphasizing that fact high heteroscedasticity exists along with some variable misspecification. This is an expected result when the final R squared is 0.42. PAGE 60 60 Geogr aphically W eight ed R egression Geographically weighted regression (GWR) is the second and final model used to analyze the relationships exhibited by our explanatory variables The results of the ordinary least squares regression showed the data exhibited strong heteroscedasticity. GWR provides a local model of the varia ble relation process. It fits a local regression equation to every feature in the dataset. It does this by incorporating the dependent and explanatory variables of features that lie within the bandwidth 1 of each target feature. This accommodates the spatia l characteristics of the intersection data much better than Ordinary least square regression. The analysis will be able to model the relationship of crash rate to our intersection form variables spatially. Table 4 3 GWR Results Output Table VarName Var iable Neighbors 140 ResidualSquares 575.068345 EffectiveNumber 306.568381 Sigma 0.627079 AIC 3574.863381 R 2 0.644784 R 2 Adjusted 0.570564 To assess the performance of the geographically weighted regression we look at the Adjusted R Squared and AIC value to see how well our model preformed. As we see from Table 4 3 t he adjusted R Squared increased to.57 from .42 indicating this model has increased in complexity from OLS. In OLS our R Squared was 42% and by 1 Bandwidth or number of neighbors used for each local estimation and is perhaps the most important parameter for geographically weighted regression. It co ntrols the degree of smoothing in the model. Typically, you will let the program choose a bandwidth or neighbor value for you by selecting either aicc (the corrected A kaike information criterion) or cross validation for the bandwidth method parameter. Both of these options try to identify an optimal fixed distance or optimal adaptive number of neighbors. Since the criteria for "optimal" are different for aicc than for c ross v alidation it is common to get a different optimal value. You may a lso provide an exact fixed distance or a particular number of neighbors by selecting bandwidth parameter for the bandwidth method.( E sri, 2011) PAGE 61 61 modeling our variables spatially across our study area the R Squared has increased to 64 percent. Previously OLS reported an Akaike's Information Criterion (AIC) of 8675.4 The result for GWR is down to 3574.8. This allows for the models to be compared, the lower numbe r of 3574.8 is much lower and therefore GWR is a much better model for the relationship of the variables. Residual Squares record shown in Table 4 3 is the sum of the square residuals, t he smaller this measure is the closer the fit of the GWR model to the observed data. The effective number record in shown Table 4 3 is a tradeoff between the variance of the fitted values and the bias of the coefficient estimates and is related to the choice of bandwidth. The effective number is used to compute a number of d iagnostic measures. (ESRI 2009) Finally the s igma is the estimated standard deviation for the residuals smaller v alues of this number is preferred PAGE 62 62 Figure 4 4. Geographically weighted Regression Results Standard Deviations of Residuals Figure 4 5. Spatial autocorrelation of GWR residuals Another output of GWR is a map of residuals. It is important to quickly test for spatial clustering that we run a spatial autocorrelatio n In Figure 4 5 can see that the residuals are not spatially clustered. Local R 2 The Lo cal Residual S quared shown below in Figure 4 6 shows us how well the model predicts the outcomes in each of the observations included in the local model. It is a number from 0 1 denoting weakness to strength respectively. The model does poorer in the more dense portions of central Portland. High model accuracy is pretty much witnessed in the area surrounding the city center. PAGE 63 63 Figure 4 6. GWR Local R 2 GWR Variable Analysis GWR outputs variable coefficients to show the strength and direction for each observation. GWR also creates a coefficient variability surface of each explanatory variable. This surface shows how the variables relationships vary across space; in effect testing how consistent is stationarity bet ween the explanatory and depende nt variable Each variable is analyzed with its Coe fficient t his way it is shown where each variable varies spatially and its significance to crash rate. PAGE 64 64 Figure 4 7. Sidewalk Coefficients GWR PAGE 65 65 Figure 4 8. Coefficient Variation surface Sidewalks The Figures 4 7 and 4 8 show the Coefficient map and coefficient variation surface for Sidewalks. Figure 4 9 shows the distribution of the coefficients. The distribution of coefficient map for sidewalks suggests high variation. The coefficients vary from a value of 1.17 and 2 this is a large spread meaning that in some areas sidewalks can influence crash rates positively or negatively. Further analysis of the large spread shows that there are large standard of errors on the records with large positive effects. These are areas where the model failed to perfor m well. The Sidewalk coefficient confirms that Sidewalks relationship with crash count varies highly through a large portion of the network. Because of its v ariation and large range is it hard to discern whether sidewalks has a strong relationship with cra sh can counts positively or negatively. This variable PAGE 66 66 has a general trend of having a negative coefficient meaning a reducing effect on crash count. But overall high standard errors hinder the validity of this trend. Figure 4 9. Sidewalk Coefficient Histogram Figure 4 1 0. Traffic Signal Coefficients GWR PAGE 67 67 Figure 4 1 1. Traffic Signal Coefficient Variation surface Traffic Signals The Figures 4 10 and 4 11 show the Coefficient map and coefficient variation surface for Traffic Signals. Figure 4 12 shows the distribution of the coefficients. The distribution of the coefficient map for traffic signals suggests low variation. Traffic count has a coefficient distribution of 2.1543 to 0 15 this spread shows an overall negative direction. This means tha t traffic signals in most cases reduces the crash rates witnessed throughout the city of Portland. The stand error distribution range is low meaning that these coefficients are a reliable measure of correlat ion to the depende nt variable of crash count. The coefficient Variation surface is fairly consistent to showing low traffic signal coefficient variability over the network. From this analysis we can deduce that Traffic Signals a re consistent factor in reducing crash rate by a large amount. PAGE 68 68 Figure 4 1 2. Traffic Signal Coefficient Histogram Figure 4 1 3. Lane Width Coefficient GWR PAGE 69 69 Figure 4 1 4. Lane Width Coefficient Variation surface Lane Width The Figures 4 13 and 4 1 4 show the Coefficient map and coefficient variation surface for Lane Width. Figure 4 15 shows the distribution of the coefficients. The distribution of the coefficient map for travel signals shows a weak relationship with the dependent variable. The Spread of the distribution is 0.025 to 0.051 with most of the observations lying near the middle of that range. The coefficient variation surface shows us that there is a large variation in the lane width coefficient variable within the center of the city. Less variation in this variable is witness in the city periphery suggesting th at measuring lane may exhibit a stronger relationship to crash rate outside the dense city center. The standard error for lane width exhibited a small variation with a high frequency at the .006 mark. These results are fairly trustworthy when taking the PAGE 70 70 lo cal R Squared into account but still show a weak relationship and high variability with crash rate throughout the city of Portland. Figure 4 1 5. Lane Width Coefficient Histogram Figure 4 1 6. Traffic Calming Coefficient GWR PAGE 71 71 Figure 4 1 7. Traffic Calming Coefficient Variation surface Traffic Calming The Figures 4 16 and 4 17 show the Coefficient map and coefficient variation surface for Traffic Calming. Figure 4 18 shows the distribution of the coefficients. The distribution of the coefficient map for traffic signals shows moderate spread of values from 1.2655 to 0.68 this spread is misleading Most of the observations lie illustrates a negative direction meaning that traffic calming has a reducing effect on crash rate. Standard Errors seem rather high. When looking further into this issue the traffic calming variable seems only be represented in the areas where low crash rate are witnessed. This tells us that traffic calming devices are clustered in areas tha t do no This may be a definition issue where traffic calming devices are either not presents in the city core or they are just not PAGE 72 72 part of the database for the pedestrian districts. The traffic calming variation surface s hows consistent model stationarity and low variation over the locations where traffic calming devices are witnessed. Traffic calming supposedly reduces crashes but the model does not show this correlation well I t is hard to discern whether the data or the model does not lend its self well to the analysis. Figure 4 1 8. Traffic calming Coefficient Histogram Figure 4 1 9. Intersection Leg Coefficient Variation surface PAGE 73 73 Figure 4 2 0. Intersection Leg Coefficient Variation surface Intersection Legs The Figures 4 19 and 4 20 show the Coefficient map and coefficient variation surface for Intersection Legs. Figure 4 21 shows the distribution of the coefficients. The distribution of the coefficient map for shows a moderate positive correlation with traff ic count. The spread of the distribution is from 0.37 to .99. This means as intersection legs increase and the intersection becomes more complex a rise in crash rate is witnessed. Although most of the observations lie with a positive correlation the GWR m odel shows us that for certain areas this does not remain true. In some cases higher amounts of intersection l egs can lead to lower crash rate. The standard error is low indicating that observations modeled are trustworthy. The c oefficient variation surfac e shows us that the intersection leg variable is subject to many variations throughout the network. It exhibits stationarity in the areas where high traffic volume is witnessed. PAGE 74 74 From this we can conclude that as the amount i ntersection l egs increase so d oes the crash rate. Figure 4 2 1. Intersection Legs Coefficient Histogram Figure 4 2 2. Traffic Volume Coefficient surface PAGE 75 75 Figure 4 2 3. Traffic Volume Coefficient surface Traffic Volume Th e Figures 4 22 and 4 23 show the c oefficient map and coefficient variation surface for Traffic Volume. Figure 4 24 shows the distribution of the coefficients. The Distribution of the coefficients for traffic volume suggests a really weak negative correlation with crash rate. The spread of the observations is 0.0002 to 0.000013. The direction suggests that as traffic column increases we see a decrease in crash rate. This is an expected result because of after about 20,000vpd 2 the relationship that crash rate increases with Traffic volume does not hold true. As traffic volume increases past this level the crash rate witnessed regresses very quickly. The coefficient standard errors are low and thus the results reliable. The c oefficient variation surface shows that traffic volume exhibits stationarity in areas w here traffic volume is most dense. This is 2 Vehicles per day Average Vehicles per day observed entering the intersection. PAGE 76 76 expected because there is a large density variation in the traffic volumes witnessed and as traffic disperses through the city volume decreases rapidly. Figure 4 24 Traffic Volume Coefficient Histogram PAGE 77 77 CHAPTER 5 DISCUSSION The primary objective of this study is to analyze the relationships between traffic intersection and intersection form factors in Portland Oregon using spatial regression. The results show that GWR does provide significant and useful results. It also proves that using GWR is significantly better at modeling i ntersection crashes than a global regression method. The GWR model results show a visual and statistical ly accurate relationship between intersection form and crashes. The results of the model can help shape decisions concerning intersection design and policy. This chapter discusses the findings from the result maps of GWR and how the variables r elate. Then the study looks at any external factors that may be weakening the model It also discusses the shortcomings of the spatial regression techniqu e. T he impact of geographic weighted regression in intersection analysis is also discussed Figure 5 1 Model performance vs. OLS PAGE 78 78 Ordinary Least Squares In doing the preliminary analysis it is discovered how weak using a global regression model like Ordinary Least Squares (OLS) is in modeling the relationship between traffic intersection crashes and in tersection form. Figure 5 1 shows where the GWR model performed better than the OLS model. Since the model does not account for the inherent spatial relationships that exists in a transportation network it fails to produce relevant results in the direction and strength of correlations that exists between variables. Each obser ved intersection is an important and unique instance in the transportation network that using a global model to explain what is going on becomes irrelevant for our analysis. Many of th e OLS variables failed to exhibit significance. Corners, curbs percent slope, bridges and number of lanes correlates with crash rate as expected, but did not affect the model as expected. Better variable specification and a larger dataset may show significance in future analysis but until more data is obtained these variables prove to be inconclusive. For the variables that exhibited significance ; traffic signals, traffic calming devices, intersection legs, sidewalks, lane width and traffic volume t he results followed expectations. Traffic signals shared the largest crash count with crash rate. Traffic volume relationship is not presented well because of its irregular relationship with crash rate. The larger traffic volumes mask the relationship that might be expected from the traffic volumes ranging from 0 to 20,000 Vpd Geographically Weighted Regression This study shows that t he geographically weighted regression model s the relationships between crash rate at intersections and intersection form fa ctors in a meaningful and conclusive manner. The witnessed relationships mak e sense on an PAGE 79 79 engineering level and expected results appear in many cases. The reason behind o bservation. The local model mirrors more accurately what we naturally see as relationships that exist in transportation networks. A n observation by observation model taken into spatial context can be manipulated to reveal or predict effects that maybe the result of future intersection form implementation. Also it is worth mentioning that the results of the GWR model are independent of time because the data is continuous This which ge ts weaker as the time in between observations gets larger and the external factors create variations that cannot be accounted for (Levinson and Chen 2006) We will look at traffic signals for an example of the uses of this ana lysis. I t is apparent that traffic signals have the propensity to reduce cra sh rates over the greater Portland area. These results are reinforced through the spatial stationarity 1 that this variable exhibits over the range of the data. It is widely know n that traffic signals are a key factor in traffic safety management at intersections. T he spatial regression results correlate with the traffic safety management studies To take it a step further the GWR model models the strength of each traffic signal s impact on the crash rate at the local level. In effect this study can directly model how strong an impact will be witness ed to a location if a traffic signal is applied to that area. Weaknesses in the GWR model Firstly GWR uses neighbors on a Euclidean distance measurement. Neighboring intersections do not relate accurately on a transportation network using Euclidean distance, although we see from the model that we get conclusive results, these may be 1 Stationarity: the mean, vari ance and autocorrelation structure do not change over time and space. PAGE 80 80 further imp roved by a more accurate distance measure. Transportation network phenomenon is another area that weakens the model; throughout Portland there are bridges that funnel huge amounts of traffic. These bridges affect the intersection relationships making for l ower a R 2 in the areas near bridges. This could be mitigated somewhat by using a distance to nearest bridge explanatory variable to analyze their effect on observations that are near them. is just of a single t ype, alternating grid pattern. It is not known if transportation network was of another type, for example Radial ringed 2 or contour forming 3 street patterns would affect the relationships in this model. The definition of nearness changes in each street pat tern There is much to be gained from analyzing intersection using spatial regression techniques. The b en algorithm that engineers can use on site to measure what is happening at intersections are significant. and a external factors. The continuousness of the data can diminish some of the effects of a and Limitations of the Study It should be m entioned first that d ue to the limitation of data, it is not possible to test all the potential explanatory variables for the ideal regression model. This is a deficiency of this analysis. Missing landuse at intersection could be an important form 2 Radial ringed street pattern: A Street pattern of loops or rings that are surrounded by successively larger ones. Usually found in conjunctions with larger radial patterns. Radial ring s incorporate the elements of radial and ring/concentric designs (Defense Science Board 1996) 3 Contour forming street pattern: A Street pattern where pronounced relief influences construction of roadways along lines of elev ation. Primary streets run parallel to contour lines, with intersection roads connecting them. (Defense Science Board 1996) PAGE 81 81 variable that may affect intersection crash rate. Visibility may also be a factor in intersection crash rate. This variable added to the model would most like have a large effect in increasing its accuracy. Errors in the data also can affect the model since traff ic volume is arduous to measure at the intersection level city wide. Areas where the traffic volume is calculated for some intersections may deviate from what is actually happening. These weaknesses do not invalidate the results of GWR but they reduce its potential by a noticeable amount. In many cases Intersections do no travel directions, landuse variations, weather all play a part in making the rule of nearness difficult to apply. Some intersections that are near each other may exhibit no relationships because of this. It is impossible to separate all factors of the traffic network. Each traffic system affects others and therefore is related to any model involving traffic analysis. Because of the characteristics of traffic network data it is difficult to do an accurately model intersection crash rate s using just intersection form features. To effectively model crash rate all the factors that c ontribute crash rate should be included into the model. This is not the case due to data limitations. This situation should be taken into consideration when viewing the regression results. This study is an exploratory use of the using spatial regression te chniques to model the effects on crash count. Conclusion Before and after studies are the p rimary way of analy zing of the effect of intersection form factors on crashes at intersections. With this method there are limitations that exist affect the decisio n making process. This study implement ed an PAGE 82 82 alternative measure spatial regression to understand the relationship between intersections form factors and traffic crashes I t was revealed that through g eographically weighted regression (GWR) it is possible to measure that relationship in accurate and visual ly insightful manner. This study also proves GWR is a much more accurate method of analysis when compared to global linear regression. This method of measurement may be useful in support ing the intersection design decision s of the future. Suggestions for Future Research In future research it is imperative to include addition al variables relating to crash rate T redication model ing would be the next step in this research. Predicting intersection crash rates from un observed explanatory variables would be an interesting study to undertake. More data and mitigation of model design limitations would be required to produce accurate and practical prediction result s Also incorporating network specific data analysis is the next step in improving the accuracy of the model Modeling the relationships of intersection on traffic network at a network specific level will go a long way ; developing an adaptive distance method for analysis of intersections. Like crash reduction factors, i ntersection form reduction factors could be developed from a geographically weighted regression model. This could help bring a new purpose to regression mo deling at intersection by building a database of the effect of intersection for m factors in varying situations PAGE 83 83 REFERENCES AASHTO. AASHTO Strategic Highway Safety Plan. Washington, DC: American Association of State Highway and Transportation O fficials, 2004. Beneficial Designs Inc. Designing Sidewalks and Trails for Access Part II of II: Best Practices Design Guide. Federal Highway Admininstration, 2001. Charlton, Martin. Geographically Weighted Regression White Paper. Maynooth, Co Kildare: National Centre for Geocomputation, 2009. Choi, Eun Ha. Crash Factors in Intersection Related Crashes: An On Scene Perspective. Washington, DC: Mathematical Analysis Division, National Center for Statistics and Analysis 2010. Defen se Science Board. Field Manual No. 3 06 of Combined Arms operations in urban terrain. Fort Benning, Georgia: Headquarters Department of the Army, October 1996. Deza, Marie Michel, and Elena Deza. Encyclopedia of Distances. Springer, 2009. ESRI. ArcGIS Reso urce Center. April 27, 2011. http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/Interpreting_OLS_r esults/005p00000030000000/ (accessed October 11, 2011). How GWR Regression works. January 28, 2009. http://webhelp.esri.com/arcgisdesktop/9.3/in dex.cfm?TopicName=How%20GWR %20Regression%20works (accessed October 9, 2011). How OLS regression works. January 28, 2009. http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=How%20OLS %20regression%20works (accessed October 9, 2011). Federal Hig hway Administration. "Intersection Safety Issue Briefs." FHWA Safety. November 2009. http://safety.fhwa.dot.gov/intersection/resources/#fhwasa10005 (accessed October 1, 2011). "Safety at Unsignalized Intersections." FHWA Safety. n.d. http://safety.fhwa. dot.gov/intersection/unsignalized/presentations/unsig_pps_041 409/long.cfm (accessed October 2, 2011). Fitzpatrick, Kay, Mark D. Wooldridge, and Joseph D. Blaschke. Urban Intersection Design Guide. College Station: Texas Transportation Institute, 2005, 4 4. PAGE 84 84 Highway Safety Manual. Highway Safety Manual. Washington, D.C: American Association of State Highway and Transportation Officials, 2010. Hovey, Peter, and Mashrur (Ronnie) Chowdhury. Development of Crash Reduction Factors. Columbus: Ohio Department of Tra nsportation, 2005. Institute of Transportation Engineers. Designing Walkable Urban Thoroughfares: A Context Sensitive Approach. Washington, DC: Institute of Transportation Engineers, 2010 Institute of Transportation Engineers. Toolbox on Intersection Saf ety and Design. Washington, DC: Institute of Transportation Engineers, 2004. Joksch, Hans C., and Lidia P. Kostyniuk. Modeling Intersection Crash Counts and Traffic Volume. Ann Arbor: University of Michigan Transportation Reasearch Institute, 1998. Levinso n, David, and Wei Chen. "Traffic Management System Performance Using Regression Analysis." California Path Program Institute Of Transportation Studies 2006: 4. MassHighway DOT. "Crash Rate Information." MassHighway DOT. 2011. http://www.mhd.state.ma.us/do wnloads/footprint/roads/procedures09.pdf (accessed October 4, 2011). National Highway Traff ic Safety Administration. "Fata lity Analysis Reporting System Encyclopedia ." 2009. New York City Department of Transportation. Downtown Brooklyn Traffic Calming Pr oject. New York: Arup Services New York Ltd, 2003. Oregon Metro Council. "Transit Oriented Development Program." http://library.oregonmetro.gov. May 2011. http://library.oregonmetro.gov/files//tod_strat_plan_execsum.pdf (accessed October 6, 2011). Orski, C Kenneth. "The "Smart Growth" Debate Continues." Innovation Briefs Vol. 14, no. No. 3 (2003): 1. Rodegerdts, Lee, Brandon Nevers, and Bruce Robinson. Signalized Intersections: Informational Guide. Portland: Kittelson & Associates, Inc., 2004. Schrank, Dav id, Tim Lomax, and Bill Eisele. Urban Mobility Report. College Station: Texas Transportation Institute, 2011. PAGE 85 85 Shen, Joan, and Albert Gan. "Development of Crash Reduction Factors." Transportation Research Record: Journal of the Transportation Research Board (Transportation Research Board of the National Academies) 1840, no. Paper No. 03 4345 (2007): 50 56. Tarko, A., S. Eranky, and K. Sinha. Methodological Considerations in the Development and Use of Crash Reduction Factors. Washington D.C.: Transportation R esearch Board, 1998. Tobler, W.R. "A Computer Model Simulating Urban Growth in the Detroit Region." Economic Geography Volume 46 (June 1970): 237 240. U.S Census Bureau American FactFinder. 2010. http://factfinder2.census.gov/faces/nav/jsf/pages/index.xh tml (accessed September 20, 2011). PAGE 86 86 BIOGRAPHICAL SKETCH Reginald Pierre Jean was born in Nyack, New York in 1986. Majored and graduated in Geography at the University of Florida in 2008. This is where he took up an interest in geospatial relationships. Solving spatial problems is on e of h is passions. 