Women’s Issues in Transportation: Summary of the 4th International Conference, Volume 2: Technical Papers (2011)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

12 Spatial Variation in Motor Vehicle Crashes by Gender in the Houston, Texas, Metropolitan Area Ned Levine, Ned Levine & Associates This study examines spatial variation in motor vehicle crashes by gender within the Houston, Texas, metro- politan area. Examination of data on 252,240 crashes that occurred in the Houston metropolitan area between 1999 and 2001 showed that substantial behavioral dif- ferences between male and female drivers contributed to the crashes. Males had more severe crashes than females and showed riskier driving behavior for every crash type. Crash risk varied throughout the metropolitan area, however, being much higher in the central city than in the suburbs. Because male drivers were more likely to be involved in crashes in the central city than female drivers, part of the gender differential in crashes appears to be the result of men driving in riskier locations. A negative binomial regression model, estimated with the Markov Chain Monte Carlo method, was tested on road seg- ments and showed gender differentials controlling for the volume-to-capacity ratio, the distance from downtown, and functional road classification. The general pattern of women making more frequent but shorter trips was asso- ciated with driving to less risky destinations. It is argued that lack of information on driver residences prevents a more detailed analysis of crash risk and that exposure to crashes needs to be understood in terms of behavior and not just relative to travel distance. This paper examines gender differences in motor vehicle crashes within the Houston, Texas, met-ropolitan area with respect to spatial location. In particular, the study shows that part of the differential in crash risk between women and men is due to differ- ences in the spatial location of the crashes, most likely the result of different driving patterns. It has long been known that there are substantial dif- ferences in crash likelihood between women and men, and that, whether the total number of crashes or crash rates (relative to population or to travel exposure) are examined, men far exceed women in the number and severity of crashes. Gender is the second strongest pre- dictor of crash likelihood, after age. For example, the National Safety Council showed that in 2003, men incurred more deaths from unintentional injuries for all age groups from 0 to 82 (National Safety Council 2007a, pp. 16–17). In terms of fatalities caused by motor vehicle crashes, men exceeded women by a ratio of 2.2 to 1 in 2003 (National Safety Council 2007a, p. 20). The National High- way Traffic Safety Administration (NHTSA) documented that men accounted for 68% of all motor vehicle fatalities between 1996 and 2005, with female fatalities decreasing by 0.7% per year while male fatalities were increasing by 0.8% per year over the period (NHTSA 2007a). On a per capita basis, males had higher motor vehicle fatality rates per 100,000 population for every age group from 1 through 85 and above from 1950 through 2005 (U.S. Department of Health and Human Services 2008). This held for every ethnic group documented. In 2007, the fatality rate per 100,000 persons was higher for males than for females in every age group (NHTSA 2007b). fActoRs Affecting gendeR diffeRences in cRAshes Driving exposure Some differences are due to differential driving exposure. Three simple measures of exposure are found in the lit-

13SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER erature. First, there is the number of driver’s licenses issued for men and women as a simple indicator of abil- ity to drive. Licensing, however, is more or less balanced by gender within the United States (Federal Highway Administration 2006). Second, there are differences in aggregate driving dis- tance, usually measured as vehicle miles traveled (VMT) or vehicle kilometers traveled (VKT). Historically, men have driven more than women, which partly explains the gender differentials in crashes. In 2001, for example, the National Household Travel Survey indicated that men traveled by personal vehicle an average of 39 mi per day while women traveled an average of 31 mi per day, a ratio of 1.25 to 1 (Bureau of Transportation Statistics 2004). Nevertheless, the differential by gender in driv- ing has been decreasing over time, and while still not at equal levels, is starting to balance out (National Safety Council 2000, p. 93). Not surprisingly, some of the gen- der differences in crashes have decreased as this driving differential has narrowed (Kostyniuk et al. 2000). Third, there are differences in individual trip length. In theory, longer trips should be associated with greater crash risk, all other things being equal, and some sup- port for this has been found (Moellering 1974). Unfortu- nately, there is no information that is publically available for identifying trip length by drivers involved in crashes, nor even information released that could allow synthetic trips from the driver residence to the crash location to be constructed. In Texas, as in most other states, the loca- tion of the residence of a driver involved in a crash is not provided in publically accessible databases. Although this information is collected in the crash report, it is not released to the public, researchers, or local government agencies. Consequently, trip length cannot be used as a baseline for measuring crash risk. Risky Driving behavior By far the strongest factor accounting for the large male- to-female ratios in severe crashes is riskier driving behavior by men (or, more accurately, a proportion of men showing risky behavior that is greater than the proportion of women showing risky behavior). For example, in 1999, the National Safety Council estimated that the ratio of fatalities per 1 bil- lion vehicle miles driven for men to women was 1.5, although for all crashes, the ratio was 0.85. In other words, men were involved in more severe crashes and women were involved in less severe crashes (National Safety Council 2000, p. 93). This result has been shown for individual states (Michigan Department of State Police 2007). Even among older driv- ers (age 70 or older), males exceed females in fatalities by a ratio of 2 to 1 (Baker et al. 2003). Kim (2000) found that in Hawaii, a higher propor- tion of males involved in crashes were killed compared with women, who, in turn, were injured proportionately more. Examining risk factors, he found that men sig- nificantly exceeded women in crashes involving driving while intoxicated (DwI), speeding, driving at nighttime, and being involved in head-on collisions. Also, men were less likely to have used a seat belt. On the other hand, women were more involved in crashes at intersections and in failing to yield the right of way. Kostyniuk et al. (2000) examined crashes in Michi- gan between 1987 and 1994 and found that, while cer- tain risky driving behavior had increased among women drivers (e.g., following too closely, speeding), other behaviors decreased (e.g., DwI). Men showed higher risk in driving than women for all risky behaviors. Of those women who showed an increase in risky behavior, most were younger women. The differential in risk applies to specific types of crashes as well. For example, in a study of Baltimore, Maryland, from 2000 to 2002, women were involved in fewer pedestrian crashes overall and, when involved, exhibited fewer risk-taking behaviors such as consuming alcohol or violating traffic laws (Clifton et al. 2005). In other words, in general, male drivers take more risks than female drivers, resulting in higher fatality rates and severe injury rates (Social Issues Research Centre 2007). Other Factors Affecting Gender Differences in Crashes Although risky driving behavior is the dominant factor, there are other factors that affect gender differences in crashes. First, women are less likely to drive on freeways and more likely to drive on arterial roads than men. Because freeways have a much lower crash risk than arterial roads, women are exposing themselves to higher risk. This behavior would run counter to the general ten- dency of males taking more risks; however, when crashes occur on freeways, they tend to be more severe, on aver- age, than crashes on arterials. The differences in driving patterns between men and women constitute a second factor. A large number of studies has shown that women travel shorter distances than men, on average, but make more trips (Giuliano 1979; Gordon et al. 1989; Hanson and Johnston 1985; Madden 1981; Michelson 1983; Nobis and Lenz 2005; Pickup 1985; Rosenbloom 2000; Rosenbloom and Burns 1993; Rutherford and wekerle 1989; Skinner and Borlaug 1980; wachs 1997). This behavior would be expected to result in fewer crashes because women are less likely to drive in high-risk areas. Levine et al. (1995a, 1995b) showed that crash risk increased substantially toward the center of downtown Honolulu. Driving trips that are more local would be less likely to encounter the high-risk roads of the central city.

14 wOMEN’S ISSUES IN TRANSPORTATION, VOLUME 2 Therefore, two hypotheses are proposed to partially explain differences in crash likelihoods between men and women: 1. There are spatial differences in the crash likeli- hoods of men and women. 2. Men are more likely than women to be involved in crashes in areas at high risk for crashes, implying an untested hypothesis that men drive more to risky envi- ronments than women. Methodology This study examines gender differentials in crash risk by spatial location within the Houston metropolitan region, an eight-county area that surrounds the City of Houston and that encompassed a population of around 5 million in 2000. Between 1999 and 2001, there were 252,241 serious crashes in the eight-county region, an average of 84,080 a year. In these crashes, 1,882 persons were killed and 281,914 persons were injured. The crashes accounted for 26% of all serious crashes in Texas during that period com- pared with the region’s 22% share of the state’s population and 21% share of the state’s VMT (Levine 2009). The likelihood of a driver in the region being involved in a fatal or injury crash in the region was 36% higher than the Texas average and 149% higher than the U.S. average. The region led the state of Texas in virtually every type of crash and led the nation in alcohol-related fatalities per capita (NHTSA 2008; Houston Chronicle 2009).1 Data Sources The data were compiled by the Crash Records Bureau of the Texas Department of Public Safety, the agency that was vested at the time with compiling crash information for every jurisdiction in Texas (Texas Department of Public Safety 2007). The agency collected data on crashes involv- ing fatalities, injuries, and serious property damage (defined as one or more vehicles being towed from the crash scene). These data represent the most severe crashes, as nonserious property-damage-only crashes are not included. Because of delays in releasing information, data were obtained only for crashes that occurred between 1999 and 2001. Driver 1 In the Texas crash report, fault is not determined by the investigating police officer, as it is in some other states 1 Special compilation by the National Highway Traffic Safety Administration, Region 6. (see Kim 2000). This is a function of the courts. Police officers are trained, however, to list vehicles in the order in which responsibility for the crash is assumed to lie. with one exception, the first driver listed (Unit 1 or Driver 1) is generally the individual seen as most respon- sible for causing the crash. Additional information on behavioral factors associ- ated with the crash (called contributing factors) is also listed. By analyzing these contributing factors for Driver 1, the causes of the crash can be assessed. For example, 82% of DwI crashes, 97% of speeding crashes, 93% of following-too-closely crashes, and 74% of failure-to-stop crashes were attributed to Driver 1. On the other hand, only 32% of failure-to-yield crashes were attributed to Driver 1.2 Thus, an analysis of the factors associated with Driver 1 provides a reasonably accurate picture of crashes associated with DwI, speeding, failure to stop, and following too closely, but not of crashes associated with failure to yield. Characteristics of the vehicle of the driver were listed on the form, including the driver’s gender, age, and race. Gender was recorded for Driver 1 in 239,946 of the 252,241 crash records. Spatial Location For the crash location, the data were geocoded according to a methodology that was developed initially in Hono- lulu (Levine and Kim 1999; Levine et al. 1995a, 1995b). Approximately 82% of the crashes were geocoded, with accuracy being around 91%. Of the 252,241 crash records, 206,577 had spatial locations assigned. Male-to-Female Crash Ratios without understanding both the trip origin and the trip distance, it is difficult to analyze the extent to which crashes reflect driving exposure. Consequently, the approach used by Kim (2000) was used, namely, to analyze the ratio of male-to-female crashes for different geographical levels. Establishing a baseline ratio for all crashes allows comparisons of risk by males relative to females as well as comparisons by location. In doing this, it is assumed that behavioral differences in risk taken by males and females are independent of spatial location. 2 Of the 49,542 failure-to-yield crashes, 34,315 were assigned to Driver 2. For those crashes, Driver 1 was attributed with speeding in 1,142 of the cases and also with failure to yield in 394 of the cases, failure to stop in 228 of the cases, and making a passing error in 147 of the cases.

15SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER Spatial Analysis Spatial analysis was conducted for three geographical levels: 1. The metropolitan area by individual crashes. The entire database was used. 2. By distance from downtown Houston. A series of 40 one-mi bands was overlaid on the study area, cen- tered on downtown Houston, and crashes within each band were calibrated. All crashes were analyzed, as were crashes by severity. 3. By individual segments on major roadways. A modeling network was obtained from the Houston– Galveston Area Council, the metropolitan planning organization for the Houston area. The modeling net- work has 10,911 segments, including all major roads (freeways, principal arterials), most minor arterials, and some collector roads. The data had information on functional road classification, traffic volume, number of lanes, segment length, VMT, roadway capacity, and the volume-to-capacity (V–C) ratio. The network includes the vast majority of the region’s VMT. Crashes that occurred on or very close to the modeled road segments were allocated to the nearest road segment.3 The direct distance of the segment midpoint to downtown Houston in miles was calculated. Results Gender Differences for the Metropolitan Area Severity of Injury Of the 239,946 crashes for which the gender of Driver 1 was known, 152,719 (or 64%) were by males. Further- more, consistent with other studies, males were involved in a higher proportion of the most severe crashes—those involving fatalities (79%)—and of crashes involving incapacitating injuries (68%), probable injuries (63%), possible injuries (61%), and serious property damage only (66%). Using the National Safety Council methodology for monetizing the comprehensive costs of crashes for the year 2000 (National Safety Council 2007b), it was esti- mated that the average cost per crash involving a male Driver 1 was $44,119, while the average cost per crash 3 The geocoding assigned crashes to the nearest intersection, regard- less of whether they actually occurred in an intersection or not (43% had). The crashes were then assigned to the midpoint of the segment, most of which were one block long. Because all intersections link two to four road segments, there is a slight local bias in the allocation, as a crash is assigned to the segment to which it is closest (i.e., the shortest segment). involving a female Driver 1 was $29,623 (both in year 2000 dollars).4 These results are partly consistent with prior research. The higher proportion of males being involved in serious crashes is consistent. The higher proportion of males involved in less serious injury crashes is not consistent, however, nor is the higher proportion of males involved in property-damage-only crashes. As mentioned above, this database only included the most serious property damage crashes, so that the general conclusions might apply if a full record were available. The excess of less serious injuries by males is differ- ent from the national data and studies conducted else- where. Houston has a severe traffic safety problem in general and crash rates are among the worst for met- ropolitan areas in the country. Risky Driving Behavior Again, consistent with other studies, males were more involved in crashes involving risky driving behavior. Table 1 presents the numbers and ratios of male-to- female crashes for different types of behaviors docu- mented on the “contributing factors” field of the Texas crash report. The data are for Driver 1. For all contributing factors documented, males exceeded females on every single type, including the use of cell phones. For this latter factor, data were only col- lected in 2001 and, because the numbers are small, con- clusions are uncertain. For all crashes, the ratio of male to female crashes was 1.75 to 1. Unfortunately, estimates of VMT by gender are unknown for the Houston met- ropolitan area. If VMT by gender does follow the 2001 national rate, however, then it would be expected that this ratio should be 1.25 to 1 (Bureau of Transportation Statistics 2004). Consequently, two chi-square tests of the observed frequencies relative to expected frequencies were conducted (Kanji 1993, p. 69): first, whether the ratio differed from the regional average of 1.75 to 1, and, second, whether the ratio differed from an expected ratio of 1.25 to 1 based on the national estimate of driving exposure. Factors with ratios significantly higher than the regional average include DwI, speeding, driving in the wrong direction, passing errors, making a bad turn or start, and poor signaling. At the other end, factors with lower ratios than the regional average include failure to yield the right-of-way, following too closely, and failure to stop at a traffic light or stop sign (slightly below the 4 The National Safety Council estimates both economic (direct) and comprehensive (lifetime) costs. This paper considers only the compre- hensive costs. For the year 2000, these were fatality ($3.1 million), incapacitating injury ($159,449), probable injury ($41,027), possible injury ($19,528), and property damage only ($6,400).

16 WOMEN’S ISSUES IN TRANSPORTATION, VOLUME 2 average). All ratios were significantly different from both the regional average and what was expected on the basis of the national exposure rate, with two exceptions. First, the ratio for failure to stop at traffic lights or stop signs was not different from the regional average, although it was significantly higher than the ratio that would be expected if national driving exposure ratios held. Second, cell phone use was not different from the ratio expected if the national driving exposure ratios held, but was significantly lower than the regional average. None- theless, the data indicate that with these two exceptions, men were more likely to be involved in crashes than would be expected based on national exposure. Further, for the most dangerous types of driving behavior—DWI, speeding, and driving in the wrong direction—men far exceeded women. Figure 1 shows Driver 1 by gender for all crashes in 5-year age groups up to age 85 or older. For every behavioral factor listed, with only one exception, males exceeded females in every age group up to age 85 or older (analysis not shown). The exception was for the group age 80 to 84 years on failure-to-stop crashes, where women slightly exceeded men (ratio = 0.94). Gender Differences in Crash Risk by Distance from Downtown Houston Some of these differences can be explained by spatial variation in crashes by males and crashes by females. Crash risk is much higher in the central city than in the suburbs in Houston as in other cities (Levine et al. TABLE 1 Behavioral Factors Associated with Crashes for Driver 1 Driver 1 Contributing Factor Male Female Male/Female Ratio p to Averagea p to 1.25a All crashes 152,719 87,227 1.75 — *** Speeding 59,999 29,968 2.00 *** *** Failure to yield right of way 8,535 7,126 1.20 *** ** Failure to stop at stop sign or traffic light 12,101 7,101 1.70 NS *** Driving while intoxicated 11,541 2,499 4.62 *** *** Following too closely 3,779 2,348 1.61 ** *** Passing error 1,562 712 2.19 *** *** Bad turn or start 907 440 2.06 ** *** Driving the wrong way 614 257 2.39 *** *** Cell phone useb 114 95 1.20 ** NS Poor signaling 54 27 2.00 NS * a c2 test of difference between observed and expected frequencies (Kanji 1993, p. 69): — = not applicable; NS = not significant. b For 2001 only. * p £ .05, **p £ .01, ***p £ .001. 30,000 25,000 20,000 15,000 10,000 N um be r o f C ra sh es Age Group 5,000 <15 20–24 30–34 Males Females 40–44 50–54 60–64 70–74 80–84 0 FIGURE 1 Gender differences in all crashes in Houston, by age group: 1999–2001.

17SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER 1995a). To examine this, 40 one-mile-wide bands were overlaid in a geographic information system on the geo- coded crash data, and the annual number of crashes in each band was calculated. Figure 2 shows the number of fatal crashes per mile as a function of distance from downtown Houston, while Figure 3 shows the number of injury and serious prop- erty damage crashes per mile. Since the area of each band increases with distance, the raw numbers are somewhat misleading. Even though fatal crashes and, to a lesser extent, serious property-damage-only crashes are more dispersed, the majority of fatal, injury, and serious prop- erty damage crashes did occur centrally. For example, 12% of fatalities and 18% of injuries occurred within a 100 80 60 40 20 0 N um be r o f C ra sh es p er M ile Distance from Downtown Houston 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 3-mi rate 1-mi rate N um be r o f C ra sh es p er M ile Distance from Downtown Houston 1 10,000 8,000 6,000 4,000 2,000 0 3 5 7 9 11 13 Injury crashes (1-mi and 3-mi rates) Serious PDO crashes (1-mi and 3-mi rates) 1-mi rate 3-mi rate 1-mi rate 3-mi rate 15 17 19 21 23 25 27 29 31 33 35 37 39 FIGURe 2 Fatal crashes per mile, by distance from downtown Houston: 1999–2001. FIGURe 3 Injury and serious property damage crashes per mile, by distance from downtown Houston: 1999–2001. (Note: PDO = property damage only.)

18 wOMEN’S ISSUES IN TRANSPORTATION, VOLUME 2 5-mi radius of downtown Houston, and 31% of fatali- ties and 47% of injuries occurred within a 10-mi radius (out of a 40-mi radius for the region). To estimate VMT, the same bands were overlaid on the modeling network and the daily VMT within each band was also calculated. Using these calculations, crash risk was calculated as annual crashes per 100 million VMT per band.5 Relating crashes to VMT eliminates the bias of increasing area in each sequential band moving away from downtown Houston. Figure 4 shows the vari- ation in crash risk by distance from downtown Houston; the dashed line is the 1-mi rate, while the solid line is a moving 3-mi spatial average. As seen, crash risk is much higher in downtown Houston than in suburban areas. Crash Risk by Distance from Downtown Houston For the region, crash risk was estimated at 167 crashes per 100 million VMT.6 For downtown Houston, crash risk averaged almost 300 crashes per 100 million VMT. It dropped off rapidly until about 17 mi from the city center (the suburbs that have been built since the 1980s), 5 The crashes were annualized by dividing by three (for the 1999 to 2001 data). The daily VMT estimated by the Houston–Galveston Area Council was converted into annual VMT by multiplying by 365. Finally, for each band, crash risk was calculated by dividing the annual number of crashes by the annual VMT and multiplying the result by 100 million. 6 The regional crash risk ratio includes all crashes in the region but only VMT estimated from the modeling network. The index is there- fore upwardly biased. where it maintained a relatively stable rate of about 150 crashes per 100 million VMT for the rest of the region. In other words, crash risk in the central city, particularly in downtown Houston, was about double the risk of that in the suburbs. To examine the severity of crashes by location, the crashes in each band were monetized using the National Safety Council methodology and related to VMT (National Safety Council 2007b). Figure 5 shows the annual cost of crashes (in year 2000 dollars) per 100 million VMT by distance from downtown Houston. As seen, the costs in the central city and in the far suburbs are much higher than in the new suburbs. Gender Differences in Crashes by Distance from Downtown Houston Gender differences in crashes by location appear to mir- ror this trend. For each distance band, the ratio of male Driver 1 to female Driver 1 was calculated. Figure 6 shows the variation in this index by distance from down- town Houston. Again, the dashed line is the 1-mi ratio and the solid line is a moving 3-mi average. In downtown Houston, the ratio was close to 1.9 (compared with the regional average of 1.75) but dropped to a low of 1.5 at about 20 mi out (the newer suburbs), whereupon it increased again to the edge of the region. It is very clear that there is variation of about 25% in the ratio of male-to-female crashes by Driver 1. It also appears that this ratio follows the spatial trend of crash risk to some extent. The increase in male-to-female 300 250 200 150 100 50 0 Se rio us C ra sh es p er 1 00 M illi on V M T 1-mi rate Distance from Downtown Houston 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 3-mi rate FIGURe 4 Annual crash risk, by distance from downtown Houston: 1999–2001.

19SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER crashes at the more suburban and rural parts of the area are, however, a function of other factors (probably increased speeds and an absolute predominance of adult males over adult females in three of the seven suburban counties). Gender Differences by Road Segments There were substantial differences in male-to-female ratios for different road classes. Table 2 presents the crash risk for each functional road class and the number and ratio of male-to-female crashes. As seen, the crash risk for the modeled network is lower than the regional average, mostly the result of not including crash and VMT data for non-network segments. Freeways had, by far, the lowest crash risk, and minor arterials had the highest (excluding the category “other,” for which the numbers are low). The ratio of male-to-female crashes was significantly higher on the freeway segments and significantly lower on the principal and minor arterial segments. $15,000,000 $10,000,000 $5,000,000Co st p er 1 00 M illi on V M T (ye a r 20 00 d ol la rs ) 1-mi rate Distance from Downtown Houston 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 3-mi rate 3-mi rate 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 M al e- to -F e m a le C ra sh R at io 1-mi rate Distance from Downtown Houston 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 3-mi rate FIGURe 5 Annual cost of crashes per 100 million VMT, by distance from downtown Houston: 1999–2001. FIGURe 6 Ratio of male crashes to female crashes in Houston for Driver 1: 1999–2001.

20 WOMEN’S ISSUES IN TRANSPORTATION, VOLUME 2 In other words, these data indicate that while men are more likely to be involved in crashes on all road types, women are proportionately more likely to be involved in crashes on principal or minor arterial roads and much less likely to be involved in crashes on freeways. This is consistent with the general travel patterns of women making shorter, but more frequent trips than men. Free- ways are designed for longer trips, particularly to the central city. Because principal arterials have a higher crash risk than freeways, women are exposed to higher risk by their road choices. Still, the increased risk is small compared with the variation within the metropolitan area discussed above, namely, that men appear to drive to the central city more often than women. Negative Binomial Regression Model with Spatial Location To examine the interaction between roadway character- istics, spatial location relative to downtown Houston, and crashes, two multivariate models were developed to predict (a) the crash risk and (b) the male-to-female crash ratio for Driver 1.7 The models were applied to the road segments of the modeling network. The model has two properties that apply to these data. First, it has a Poisson mean, which is appropriate for highly skewed data such as motor vehicle crashes (Cam- eron and Trivedi 1998). Second, it allows for extreme dispersion in the degree of skewness and is modeled by a Gamma function (Cameron and Trivedi 1998; Lord 2006). This type of Poisson–Gamma model is known as a negative binomial. Because the dependent variables are ratios (crashes relative to VMT and male crashes relative to female crashes), the formulation used is that of Besag et al. (1995). The dependent variable, Yi, is modeled as a Pois- son function of the mean, µi: 7 It is not possible to use the male-to-female crash ratio to predict crash risk (or vice versa), as there would be extreme multicollinearity. Yi  Poisson (µi) (1) In turn, the mean of the Poisson is modeled as µi  nili (2) where ni is an exposure measure and li is the rate (or risk). For the crash risk model, the exposure variable is VMT and the rate variable is crash risk. In the case of the male-to-female crash ratios, the exposure variable is the number of female crashes and the rate is the male-to- female crash ratio. The rate is further structured as follows (Cameron and Trivedi 1998; Lord 2006): li  exp(b0  S(bkCk)  xi) (3) where b0 = constant, Xk = one of k variables, bk = coefficient of variable Xk, and xi = error term distributed as a Gamma function with a mean equal to 1 and a variance equal to 1/a, where a >0. With the exposure term, the full model is estimated as a log-linear function: Yi  bi * exp[b0  S(bkXk )] * xi (4) ln(Yi)  ln(ni)  b0  b1X1  b2X2  . . .  bkXk  ln(xi) (5) In the case of crash risk, the term on the left is the num- ber of crashes while the terms on the right include traf- fic volume multiplied by a function of other variables (which are linear predictors but in an exponential form). In the case of the male-to-female crash ratio, the term on the left is the number of male crashes and the terms on the right include the number of female crashes—the exposure variable, multiplied by a linear combination of TABLE 2 Functional Road Classes Associated with Crashes for Driver 1 Driver 1 Road Class Crash Risk Male Female Male/Female Ratioa All network crashes 120.8 30,216 17,166 1.76 Freeway 50.0 6,879 3,430 2.01*** Principal arterial 99.6 6,813 4,141 1.65*** Minor arterial 221.9 14,056 8,228 1.71* Collector 140.2 2,002 1,118 1.79NS Other 3,405.6 466 249 1.87 NS Note: Annual number of crashes. a c2 test of difference between observed and expected frequencies (Kanji 1993, p. 69): NS = not significant. * p £ .05, **p £ .01, ***p £ .001.

21SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER additional factors in exponential form. Note that there is no coefficient of the exposure variable (i.e., it is 1.0) because it is the denominator of the rate or ratio. This particular equation was estimated by a process called a Markov Chain Monte Carlo (MCMC) simula- tion (Besag et al. 1995; Denison et al. 2002). Although it could have been estimated with maximum likelihoods, the MCMC simulation was used because it produces an actual sampling distribution, which might be non- normal. The implementation of the function is part of CrimeStat IV, which is currently under development (Levine in press). The function is estimated with two algorithms. First, the model itself is estimated by a sequential set of samples drawn from equations that approximate the model using the actual data (the MCMC part of the algorithm). Because of potential bias in the initial selection, the first 10,000 samples are dropped (the “burn in” period). The actual estimates come from an additional 90,000 samples. Second, to speed up calculation because of a large num- ber of records (10,911 road segments), a block sampling methodology was adopted. A series of 30 samples of approximately 400 cases each was drawn and the MCMC algorithm was run on the sample cases. The final estimates are based on the mean of the 30 samples. Significance is usually tested by examining the 2.5th and 97.5th percen- tiles of the distribution, producing an approximate 95% confidence interval (Guo et al. 2010). Predictors of Crash Risk Table 3 presents the results of the model for predicting crash risk.8 In addition to the V–C ratio and distance to downtown, functional road classifications were included. Two models were tested: one that included all functional road types and one with only freeway and collector road segments included. The 95% confidence interval is shown but significance is also presented for the 99% confidence interval. In the second (reduced form) model, there were four variables that were significantly corre- lated with crash risk. The first is the V–C ratio. This indicates that on road segments in which the volume is very high relative to the capacity of the road, crash risk is much higher. That is, more congested roadway segments are associated with more crashes. This result has been 8 The Akaike information criterion (AIC) and the Bayesian infor- mation criterion (BIC) are log likelihoods adjusted for degrees of freedom. The Monte Carlo error (MC error) is an error estimate for the simulation. A common practice is to accept the simulation if the ratio of the MC error to the standard error is less than 5%. The Gelman–Rubin (G–R) statistic is another indicator of convergence in the simulation if the ratio is less than 1.2. TABLE 3 Predictors of Crash Risk, by Road Segment Full 95% Confidence Reduced 95% Confidence Model Interval Model Interval Coefficient 2.5% 97.5% Coefficient 2.5% 97.5% Exposure: VMT 1.0 — — 1.0 — — Linear predictor Intercept 5.559** 7.16 3.64 4.998** 5.71 4.28 V–C ratio 1.310** 0.44 2.20 1.308** 0.44 2.22 Distance to downtown (mi) 0.053 0.07 0.03 0.053** 0.07 0.03 Freeway 1.532 0.55 3.41 1.056* 0.16 2.06 Principal arterial 0.962 1.07 2.73 — — — Minor arterial 0.282 1.66 1.94 — — — Collector 0.408 2.38 1.34 1.112** 1.81 0.37 Note: N = 10,911 road segments; dependent variable = annual crashes 1999–2001; — = not applicable. Full Model Reduced Model N 10,911 10,911 Degrees of freedom 10,903 10,905 Number of iterations 100,000 100,000 Number of “burn in” iterations 10,000 10,000 Number of samples 30 30 Average sample size 397.3 400.6 Log likelihood 28,962.2 28,866.4 Likelihood ratio 65,763.0 68,278.8 p-value of likelihood ratio .0001 .0001 AIC 57,940.4 57,744.7 BIC–Schwarz criterion 57,998.7 57,788.5 Dispersion multiplier 0.20 0.19 Inverse dispersion multiplier 5.08 5.21 *p £ .05, **p £ .01.

22 WOMEN’S ISSUES IN TRANSPORTATION, VOLUME 2 frequently found in the literature (Frantzeskakis and Ior- danis 1987; Zhou and Sisiopiku 1997). Second, the closer to downtown Houston (in miles), the greater is the crash risk on the segment. The reason probably reflects a number of factors associated with adjacency to the central city: convergence of freeways and major arterials, the greater likelihood of a road- way intersecting a higher-capacity road, shorter blocks between intersecting roadways, more commercial drive- ways providing a greater number of conflict points, and greater numbers of pedestrians and bicyclists. The result is consistent with higher crash risk in the central city, as shown in Figure 1 above. Third, when VMT, the V–C ratio, and distance from downtown are controlled for, there are more crashes on freeway segments, contrary to the simple tables, and fewer crashes on collector road segments. It is probable that there are effects associated with freeways that are not the result of the existing variables in the equation. One of these is the high volume of truck traffic that uses the freeways and the potential crashes that can occur from that use. Houston has the second largest port in the United States and generates a large amount of local and intercity truck traffic. Much of the truck traffic, in turn, is routed to the freeways. During the period of 1999 to 2001, there were 15,369 crashes involving commercial motor vehicles, about half of which occurred on freeway segments (Levine 2009). In addition, the Houston area has a weak arterial system in which many principal arte- rial roads are discontinuous. This tends to force traffic to the freeways, thereby adding to the congestion. The entry and exit ramps tend to have a high number of crashes, an effect that is not necessarily captured by the V–C ratio. There may be other effects associated with the design of freeways segments. More research is clearly needed on this point. The lower number of crashes occurring on collector road segments is, however, probably due to the lack of conflict points with major traffic volumes. Therefore, independent of the VMT, there are more crashes when the roadway segments are congested, when the segments are closer to downtown Houston, and when the segments are on freeways. Conversely, when these variables are controlled for, crashes are less frequent when the roadway segments are collector roads. Predictors of Male-to-Female Crash Ratios Table 4 presents the results of the best model predicting the male-to-female crash ratio. In addition to the V–C ratio and distance to downtown, functional road clas- sifications were included. Two models were tested: one TABLE 4 Predictors of Crashes for Male and Female Drivers, by Road Segment Full 95% Confidence Reduced 95% Confidence Model Interval Model Interval Coefficient 2.5% 97.5% Coefficient 2.5% 97.5% Exposure: Female crashes 1.0 — — 1.0 — — Linear predictor Intercept 1.713** 1.007 2.573 1.526** 1.228 1.832 V–C ratio 1.293** 0.901 1.829 1.340** 0.971 1.714 Distance to downtown (mi) –0.026** –0.035 –0.014 –0.023** –0.031 –0.014 Freeway 0.688 –0.266 1.749 0.871** 0.453 1.318 Principal arterial 0.231 –0.692 1.204 — — — Minor arterial –0.199 –1.070 0.708 — — — Collector –0.669 –1.576 0.279 –0.602** –0.926 –0.269 Note: N = 10,911 road segments; dependent variable = male crashes 1999–2001; — = not applicable. Full Model Reduced Model N 10,911 10,911 Degrees of freedom 10,903 10,905 Number of iterations 100,000 100,000 Number of “burn in” iterations 10,000 10,000 Number of samples 30 30 Average sample size 398.2 401.5 Log likelihood –34,657.7 –34,770.7 Likelihood ratio 7,282.6 7,421.5 p-value of likelihood ratio .0001 .0001 AIC 69,331.4 69,553.5 BIC–Schwarz criterion 69,389.8 69,597.3 Dispersion multiplier 0.78 0.78 Inverse dispersion multiplier 1.29 1.28 *p £ .05, **p £ .01.

23SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER that included all functional road types and one with only freeway and collector road segments included. The same variables that predict crash risk also predict the male-to-female crash ratio. First, there is a sizeable correlation with the V–C ratio. Second, there is a sizeable correlation with closeness to downtown Houston. Third, there is a positive correlation with freeway segments. Fourth, in addition, there is a negative relationship with collector roads. On roadway segments that are congested, closer to downtown Houston, and on freeways, there are more male crashes relative to female crashes. Conversely, on roadway segments that are less congested and further from downtown and on collector roads, there are fewer male crashes relative to female crashes. In other words, while there is much overlap in their spatial location, male crashes and female crashes are occurring in slightly different locations, with male crashes being more centrally located while female crashes are more peripherally located. Further, male crashes are more likely to occur on roadways segments that have higher crash risk. In short, some of the differentials in crashes between men and women are the result of the risk associated with trip destinations. Predictors of Male-to-Female Crash Ratios for Different Driver Behaviors Male-to-female ratios were tested with specific crash types involving speeding, DwI, failure to stop, failure to yield, and following too closely (analysis not shown). The results confirmed the model presented above, although the coefficients varied slightly. For example, the coeffi- cient for the V–C ratio was stronger for DwI and speed- ing crashes than for the other behaviors. The coefficient for the distance-to-downtown variable was stronger for speeding crashes than for other types but was not sig- nificant for crashes caused by following too closely. The coefficient for freeways was strongest for DwI crashes and speeding crashes, respectively, but not significant for failure-to-stop crashes. The coefficient for collector roads was not significant for failure-to-stop crashes. The general results held, however. That is, crashes involving male drivers occurred in slightly different locations from those involving female drivers, regardless of the behavior involved. conclusion Overall, there is no question that proportionately more males exhibit riskier driving behavior than females. This is true in the Houston area as in most other areas that have been studied. what has been shown here, however, is that males also are more likely to have crashes in areas that have higher risk associated with them, namely, in downtown Houston and in the central city more gener- ally. The general gender differences in trip patterns that have been documented (i.e., women make more frequent, but shorter, trips) is consistent with driving in areas that differ in terms of safety. Local trips, particularly in the suburbs, occur in safer environments than long-distance commuter trips to the central city. This is partly a by- product of the congestion that occurs in the central city because of the concentration of employment and the convergence of roads. From a policy perspective, there are a few implica- tions. First, in spite of large behavioral differences between male drivers and female drivers in terms of risky driving, law enforcement efforts cannot discriminate on the basis of gender. Even though males are more likely to show aggressive and dangerous driving behavior than females, officers have to respond to the behavior of the driver, not to the driver’s gender. The same would be true of characteristics associated with dangerous driving, such as youth (young drivers have much higher crash likelihoods than older drivers) or driving a pickup truck (e.g., 35% of all crashes in Houston involve at least one pickup truck). Enforcement has to be even handed and directed at specific behavior, not at characteristics of the individual. This is an obvious point, but one that bears repeating. Second, the lack of information on where drivers live prevents a more detailed intra-urban analysis of trip length in relation to crashes and thereby precludes a more precise measure of driving exposure from being used. Further, if such information were available, pre- ventive actions could be aimed at neighborhoods or communities where a disproportionate number of driv- ers who have been involved in serious crashes reside. Unfortunately, in Texas and in most other states, the agency authorized to compile and release crash informa- tion (either the state police or the state department of transportation) does not release information on the loca- tion of drivers’ residences. This makes it very difficult to identify neighborhoods with higher driving risk or even to analyze the length of a trip that ends in a crash. The National Highway Traffic Safety Administration and the Federal Highway Administration should seriously con- sider requiring states to provide residence information on drivers involved in crashes in order to further safety goals. Third, exposure to crashes needs to be understood in a broader context. Simply measuring the VMT of a cohort of drivers or even the trip length for individual drivers involved in crashes (should this information be made available) begs the question of what risks drivers are taking. Short trips that are home-based, as many women appear to make, are much less risky than longer trips to

24 wOMEN’S ISSUES IN TRANSPORTATION, VOLUME 2 the central city. The two types of trips are not identical, even if their distance may be the same. One occurs in a safer environment while the other is in a much riskier environment. Similarly, risky behavior on the part of a driver is a much more critical predictor of crash likelihood than dis- tance, per se. For example, a driver who has been drink- ing, who drives at nighttime, who travels with passengers who are also drunk, who speeds, and who travels on less well-lit roads has a much riskier trip than a single driver making a daytime trip who stays in the local area, who has not been drinking, and who does not speed, even if the distance covered by both trips is equal. This should be obvious. Risk has to be understood as a complex interac- tion of driving exposure, the behavior of the driver, the driving conditions affecting the trip, and the destination of the trip. Future research needs to develop better measures of driving exposure than heretofore have been used. AcknowledgMents The data used in this study were geocoded by the Houston– Galveston Area Council. The author thanks the agency for providing the data and the modeling network and, in par- ticular, Alan Clark, Director of Transportation, and Jeff Kaufman, Manager, Traffic Safety Planning Program. RefeRences Baker, T. K., T. Falb, R. Voas, and J. Lacey. 2003. Older women Drivers: Fatal Crashes in Good Conditions. Jour- nal of Safety Research, Vol. 34, pp. 399–405. Besag, J., P. Green, D. Higdon, and K. Mengersen. 1995. Bayesian Computation and Stochastic Systems (with dis- cussion). Statistical Science, Vol. 10, pp. 3–66. Bureau of Transportation Statistics. 2004. Figure 5-13: Aver- age Daily Trips and Miles by Gender and Mode: 2001. In 2001 National Household Travel Survey Data (CD- ROM). Bureau of Transportation Statistics, washington, D.C. Cameron, A. C., and P. K. Trivedi. 1998. Regression Analysis of Count Data. Cambridge University Press, Cambridge, United Kingdom. Clifton, K. J., C. Burnier, and K. K. Fults. 2005. women’s Involvement in Pedestrian–Vehicle Crashes. In Conference Proceedings 35: Research on Women’s Issues in Trans- portation: Report of a Conference; Volume 2: Technical Papers, Transportation Research Board of the National Academies, washington, D.C., pp. 155–162. Denison, D. G. T., C. C. Holmes, B. K. Mallick, and A. F. M. Smith. 2002. Bayesian Methods for Nonlinear Classifica- tion and Regression. John wiley & Sons, Ltd: Chichester, Sussex, United Kingdom. Federal Highway Administration. 2006. Driver Licensing. In Highway Statistics 2006. Federal Highway Adminis- tration, U.S. Department of Transportation, washing- ton, D.C. http://wwwcf.fhwa.dot.gov/policy/ohim/hs06/ driver_licensing.htm. Frantzeskakis, J. M., and D. I. Iordanis. 1987. Volume-to- Capacity Ratio and Traffic Accidents on Interurban Four- Lane Highways in Greece. In Transportation Research Record 1112, TRB, National Research Council, washing- ton, D.C., pp. 29–38. Giuliano, G. 1979. Public Transportation and the Travel Needs of women. Traffic Quarterly, Vol. 33, No. 4, pp. 607–616. Gordon, P., A. Kumar, and H. w. Richardson. 1989. Gender Differences in Metropolitan Travel Behavior. Regional Studies, Vol. 23, No. 6, pp. 499–510. Guo, F., X. wang, and M. A. Abdel-Aty. 2010. Modeling Sig- nalized Intersection Safety with Corridor-Level Spatial Correlations. Accident Analysis & Prevention, Vol. 42, No. 1, pp. 84–92. Hanson, S., and I. Johnston. 1985. Gender Differences in work-Trip Length: Explanations and Implications. Urban Geography, Vol. 6, pp. 193–219. Houston Chronicle. 2009. Deaths by DwI—A ‘Pandemic.’ Houston, Tex. June 10, p. A1. Kanji, G. K. 1993. 100 Statistical Tests. Sage Publications, Thousand Oaks, Calif. Kim, K. 2000. Differences Between Male and Female Involve- ment in Motor Vehicle Collisions in Hawaii, 1986–1993. In Women’s Travel Issues: Proceedings from the Second National Conference, October 1996, FHwA, U.S. Depart- ment of Transportation, washington, D.C., pp. 518–528. http://www.fhwa.dot.gov/ohim/womens/chap27.pdf. Kostyniuk, L. P., L. J. Molnar, and D. w. Eby. 2000. Are women Taking More Risks while Driving? A Look at Michigan Drivers. In Women’s Travel Issues: Proceedings from the Second National Conference, October 1996, FHwA, U.S. Department of Transportation, washington, D.C., pp. 502–516. http://www.fhwa.dot.gov/ohim/wom ens/chap26.pdf. Levine, N. 2009. A Motor Vehicle Safety Planning Support System: The Houston Experience. In Planning Support Systems: Best Practice and New Methods (S. Geertman and J. Stillwell, eds.) Springer Publishers, New York, pp. 93–111. Levine, N. In press. CrimeStat IV: A Spatial Statistics Program for the Analysis of Crime Incident Locations. Ned Levine & Associates, Houston, Tex., and National Institute of Justice, washington, D.C. Version 3.3 available at http:// www.icpsr.umich.edu/crimestat. Levine, N., and K. E. Kim. 1999. The Spatial Location of Motor Vehicle Accidents: A Methodology for Geocoding Intersections. Computers, Environment, and Urban Sys- tems, Vol. 22, No. 6, pp. 557–576. Levine, N., K. E. Kim, and L. H. Nitz. 1995a. Spatial Analysis of Honolulu Motor Vehicle Crashes: I. Spatial Patterns.

25SPATIAL VARIATION IN MOTOR VEHICLE CRASHES BY GENDER Accident Analysis & Prevention, Vol. 27, No. 5, pp. 663– 674. Levine, N., K. E. Kim, and L. H. Nitz. 1995b. Spatial Analy- sis of Honolulu Motor Vehicle Crashes: II. Generators of Crashes. Accident Analysis & Prevention, Vol. 27, No. 5, pp. 675–685. Lord, D. 2006. Modeling Motor Vehicle Crashes Using Pois- son-Gamma Models: Examining the Effects of Low Sam- ple Mean Values and Small Sample Size on the Estimation of the Fixed Dispersion Parameter. Accident Analysis and Prevention, Vol. 38, pp. 751–766. Madden, J. F. 1981. why women work Closer to Home. Urban Studies Vol. 18, pp. 181–194. Michelson, w. 1983. The Impact of Changing Women’s Roles on Transportation Needs and Usage. Report DOT-I-83- 01. U.S. Department of Transportation, washington, D.C. Michigan Department of State Police. 2007. 2007 Michigan Traffic Crash Facts. Michigan Office of Highway Safety Planning, Lansing, Mich. http://www.michigantraf- ficcrashfacts.org/doc/2007/2007MTCF_vol1.pdf. Moellering, H. 1974. The Journey to Death: A Spatial Analy- sis of Fatal Traffic Crashes in Michigan. Department of Geography, University of Michigan, Ann Arbor. National Highway Traffic Safety Administration. 2007a. Com- parison of Crash Fatalities by Gender and Year from 1996 to 2005. Traffic Safety Facts. Report DOT HS 810 780. National Highway Traffic Safety Administration, U.S. Department of Transportation, washington, D.C. http:// www-nrd.nhtsa.dot.gov/Pubs/810780.PDF. National Highway Traffic Safety Administration. 2007b. Table 56: Persons Killed or Injured and Fatality and Injury Rates per 100,000 Population by Age and Sex. Traffic Safety Facts: 2007. Report DOT HS 811 002. National Highway Traffic Safety Administration, U.S. Department of Trans- portation, washington, D.C. National Highway Traffic Safety Administration. 2008. Alco- hol-Impaired Driving. Traffic Safety Facts: 2006 Data. DOT HS 810 801. National Highway Traffic Safety Administration, U.S. Department of Transportation, washington, DC, pp. 1–6. National Safety Council. 2000. Injury Facts: 2000 Edition. National Safety Council, Itasaca, Ill. National Safety Council. 2007a. Injury Facts: 2007 Edition. National Safety Council, Itasaca, Ill. National Safety Council. 2007b. Estimating the Costs of Unin- tentional Injuries. National Safety Council, Itasaca, Ill. http://www.nsc.org/news_resources/injury_and_death_ statistics/Pages/EstimatingtheCostsofUnintentionalInju ries.aspx. Nobis, C., and B. Lenz. 2005. Gender Differences in Travel Pat- terns: Role of Employment Status and Household Struc- ture. In Conference Proceedings 35: Research on Women’s Issues in Transportation: Report of a Conference; Volume 2: Technical Papers, Transportation Research Board of the National Academies, washington, D.C., pp. 114–123. Pickup, L. 1985. women’s Travel Needs in a Period of Rising Female Employment, Transportation and Mobility in an Era of Transition. In Transportation and Mobility in an Era of Transition (G. R. M. Jansen, P. Nijkamp, and C. J. Ruijgrok, eds.), Elsevier Science Publishing Company, Amsterdam, Netherlands, pp. 97–113. Rosenbloom, S. 2000. Trends in women’s Travel Patterns. In Women’s Travel Issues: Proceedings from the Second National Conference, October 1996, FHwA, U.S. Depart- ment of Transportation, washington, D.C., pp. 16–34. http://www.fhwa.dot.gov/ohim/womens/chap2.pdf. Rosenbloom, S., and E. Burns. 1993. Gender Differences in Commuter Travel in Tucson: Implications of the Travel Demand Management Programs. In Transportation Research Record 1404, TRB, National Research Council, washington, D.C., pp. 82–90. Rutherford, B., and G. wekerle. 1989. Single Parents in the Suburbs: Journey-to-work and Access to Transportation. Journal of Specialized Transportation Planning and Prac- tice, Vol. 3, No. 3, pp. 277–294. Skinner, L., and K. Borlaug. 1980. Shopping Trips: who Makes Them and when. In Women’s Travel Issues: Research Needs and Priorities.Conference Proceedings and Papers (S. Rosenbloom, ed.), U.S. Government Printing Office, washington, D.C., pp. 105–126. Social Issues Research Centre. 2007. Sex Differences in Driving and Insurance Risk: An Analysis of the Social and Psy- chological Differences Between Men and Women That Are Relevant to Their Driving Behaviour. Social Issues Research Centre, Oxford, United Kingdom. http://www. sirc.org/publik/driving.pdf. Texas Department of Public Safety. 2007. Crash Records Bureau. Department of Public Safety, State of Texas, Aus- tin. http://www.txdps.state.tx.us/administration/driver_ licensing_control/arb.htm. U.S. Department of Health and Human Services. 2008. Table 43: Death Rates for Motor Vehicle–Related Injuries, by Sex, Race, Hispanic Origin, and Age: United States, Selected Years 1950–2005. In Health, United States, 2008, Centers for Disease Control and Prevention and National Center for Health Statistics, U.S. Department of Health and Human Services, washington, D.C., pp. 250–253. http://www.cdc.gov/nchs/hus.htm. wachs, M. 1997. The Gender Gap: How Men and women Developed Different Travel Patterns. ITS Review, Vol. 20, No. 2, pp. 1–2. Zhou, M., and V. P. Sisiopiku. 1997. Relationship Between Volume-to-Capacity Ratios and Accident Rates. In Trans- portation Research Record 1581, TRB, National Research Council, washington, D.C., pp. 47–52.