VALERIAN KWIGIZILE, PH. D., P.E.

ENELIKO MULOKOZI

XUECAI XU, PH. D., F.E.

HUALIANG (HARRY) TENG, PH. D.

CAIWEN MA, PH.D.

Western Michigan University

1903 W. Michigan Avenue

Kalamazoo, MI 49008-5316

Phone: (269) 276-3218

Fax: (269) 276-3211

Email: Valerian.Kwigizile@wmich.edu

University of Nevada Las Vegas

Las Vegas, NV

Huazhong

University of Science and Technology

Wuhan, China

University of Nevada Las Vegas

Las Vegas, NV

Department of Transportation Engineering

Daliang Jiaotong University

Dalian, China

**KEYWORDS:** corner clearance, urban intersection safety

### Abstract

Corner clearance is defined as the distance between the corner of an intersection of two roadways and the first driveway. Vehicles turning into a driveway adjacent to an intersection or vehicles merging into the mainline from such a driveway may pose a safety hazard to other traffic. Adequate corner clearance is important to effectively separate conflict points and allow drivers enough time to make safe maneuvers. Although previous studies have investigated and identified factors influencing crash frequency at intersections, corner clearance has not been well studied. In this study, we used crash count data collected from all signalized intersections of major roadways in the cities of Las Vegas and North Las Vegas, Nevada, to investigate the impact of corner clearance on crash frequency. We estimated and compared results from four models: Poisson, Negative Binomial, and Zero-Inflated (Poisson and Negative Binomial). Model comparison test results indicated that the Zero-Inflated Negative Binomial was the best fitted model for the data at hand. As expected, it was revealed that longer corner clearance tends to reduce the number of crashes occurring at an urban intersection. In addition to corner clearance, the results indicated that landuse type, entering volume, number of left-turn lanes, as well as number of through lanes, have significant impact on the number of crashes occurring at an intersection. Sensitivity results revealed that adequate corner clearances have greater potential of improving safety at signalized intersections when compared to other factors considered in this study.

### Background and Motivation

Corner clearance is defined as the distance between the corner of an intersection of two roadways and the first driveway. Vehicles turning into a driveway adjacent to an intersection or vehicles merging into the mainline from a driveway may pose a safety hazard to other traffic. Adequate corner clearance is important to effectively separate conflict points and allow drivers enough time to make safe maneuvers. Although many studies (e.g., Oh et al. 2004; Guo et al. 2009; Wang and Abdel-Aty 2007; Poch and Mannering 2007; and Kumara and Chin 2010) have investigated the impact of roadway and traffic characteristics on intersection safety, corner clearance has not been fully investigated. Most studies have primarily evaluated the impact of corner clearance on other intersection performance aspects, while treating the impact of corner clearance on intersection safety as secondary. For example, McCoy and Heimann (1990) evaluated the impact of corner clearance on saturation flow rates at signalized intersections in Lincoln, Nebraska. Similarly, Long and Gan (2007) developed a model for minimum driveway corner clearances at signalized intersections by considering saturation flow rates. Long and Gan (1993) and Gluck et al. (1999) focused on how to specify the corner clearance criteria for practical implementation. Although the above studies did not explicitly address the impact of corner clearance on safety of signalized intersections, their findings suggested the importance of corner clearance as well as driveway density at signalized intersections. For example, a finding by Long and Gan (1997) that corner clearance has significant impact on saturation flow rates implies that this could lead to some types of crashes, such as rear-end crashes due to interruption of traffic flow resulting from vehicles entering and/or exiting driveways.

Very often, roadway designers ask themselves which design feature has greater potential to improve safety at a signalized intersection. Although it is clear that longer corner clearances may result in improved safety of a signalized intersection, quantification of their impacts is lacking in the literature. Also, the relative impact of corner clearances on safety of signalized intersections is not well documented. As a result, the main objective of this study is to investigate the impact of corner clearance and other variables on the number of crashes occurring at urban signalized intersections. Data from signalized intersections in the Las Vegas and North Las Vegas urban areas were used to conduct the analyses. Count models were developed to investigate the impact of corner clearance and other variables on the number of crashes occurring at such intersections.

### Literature on Modeling Intersection Safety

Proper design of roadway features around signalized intersection can result in increased intersection safety. To achieve such a good design, safety studies are required to identify high risk factors related to these features. Guo et al. (2009) utilized five full Bayesian models on 170 signalized intersections of Orange and Hillsborough counties in central Florida to show that intersections in close proximity along a corridor are correlated and proper signal coordination has significant impact on safety. In addition to spatial correlation between intersections, it was found that Average Daily Traffic (ADT) per through-lane and left-turn traffic, landuse, speed limits, intersection size, and exposure have a significant impact on the safety of signalized intersections. It was also shown that larger intersections are more dangerous than smaller intersections. However, this study did not investigate the impact of corner clearance on signalized intersection safety. Different severity levels of crash incidents at signalized intersections have been studied. Wong et al. (2007) used Poisson and negative binomial regression models on 262 signalized intersections features from Hong Kong to quantify the influence of various factors on fatal and severe injury, and slightly injury crashes. The negative binomial regression model indicated that an increase in curvature and the presence of tram stops significantly increased the incidence of slightly injury crashes. Also, the marginal increase of the incidence of slightly injury crashes diminished under high traffic flow conditions. With the Poisson regression model it was found that the presence of tram stops, the increase in the proportional of commercial vehicles, the increase in the number of pedestrian streams, and the decrease in the average lane width significantly increased the incidence of killed and severe injury crashes. Similar to the study by Guo et al. (2009), this study did not incorporate corner clearance in the models.

Although Poisson and traditional negative binomial regression models are widely used in crash frequency analysis (Yaacob et al, 2011; Zlatoper, 1989; Lord, 2006; Chin and Quddus, 2003; Miaou and Lum, 1993; and Noland and Quddus, 2004), they may lead to biased estimators and invalid statistics when applied to longitudinal crash data. The correlation features in longitudinal data for signalized intersections require a different modeling approach leading to consistent estimates. Wang et al. (2006) applied generalized estimating equations (GEEs) to identify significant factors and their temporal correlation effect on crashes at signalized intersections. Using 208 signalized intersections in central Florida from Brevard and Seminole Counties in suburban areas, they modeled the relationship between crash frequencies and other variables at signalized intersections. Speed limits, traffic volume (ADT), intersection size (indicated by total number of lanes), and intersection within highly populated areas were found to be associated with high crash frequency. Using the same model of GEEs but with different link functions, Wang and Abdel-Aty (2007) investigated the relationship between different patterns of left-turn crash occurrence and intersection features using 197 four-legged signalized intersections from Orange and Hillsborough counties in the central Florida area. Selection of the particular link function in the GEEs for modeling different functions was a function of the number of crashes and the proportion of zero crashes and one crashes recorded. GEEs with binomial logit link function were applied to crash patterns with a higher proportion of zeros and one crashes. Negative binomial link function was used to model crash frequency for patterns with fewer crashes. The modeling results showed that the amount of conflicting flows (traffic volumes), the type of left-turn phasing, crossing distance (indicated by the number of through lanes), and speed limit are significant in influencing the crash occurrence frequency.

Other researchers have used negative binomial and zero-inflated negative binomial regression in modeling crashes at signalized intersections. Using 104 three-legged signalized intersections from Singapore, Kumara, and Chin (2010) indicated that right-turn channelization, acceleration section on the left-turning lane, median railing, and existence of more than a 5% gradient may reduce accident occurrence. Although surprising, the finding that existence of more than a 5% gradient may reduce accident occurrences may be attributed to possible proper signage and extra carefulness by drivers resulting from existence of such steep grade. The same research team indicated that traffic volumes (total and left-turn), an uncontrolled left-turn slip road, signal phases per cycle, existence of horizontal curve, and permissive right-turn phase may increase accident occurrence. Poch and Mannering (2007) used negative binomial regression modeling on 64 intersections from Bellevue in Washington to show that traffic volumes (separated according to traffic movements), number of lanes, sight distance restriction, and speed limit have a negative effect on intersection safety while signal controlled intersections and protected left turn movements have a positive effect on intersection safety. A study by Oh et al. (2004) was aimed at developing macrolevel crash prediction models that can be used to understand and identify effective countermeasures for improving signalized highway intersections and multilane stop-controlled highway intersections in rural areas. The results indicated that traffic flow variables significantly affected the overall safety performance of the intersections regardless of intersection type and that the geometric features of intersections varied across intersection type and also influenced crash type.

There are many issues related with modeling crash counts. Lord and Mannering (2010) provides a detailed review of the key issues associated with crash-frequency data as well as the strengths and weaknesses of the various methodological approaches that researchers have used to address these problems. Among the issues discussed include dispersion (over- or under-), temporal and spatial correlations, endogeneity, low sample mean, underreporting, etc. Different model types designed to handle these issues were also discussed. The authors identified Zero-Inflated models (Poisson or Negative Binomial) as models that can handle datasets that have a large number of zero-crash observations. However, the authors cautioned that the zero-inflated negative binomial can be adversely influenced by the low sample-mean and small sample size bias.

Despite all the efforts to investigate different factors contributing to intersection crash frequencies using different modeling approaches, other important factors have not been included in the previous researches. In this study, investigation of the impact of corner clearance on urban intersection crash occurrence using data from the cities of Las Vegas and North Las Vegas, Nevada, is performed. Crashes considered in the model were those that happened within a 250 ft radius measured from the center of a signalized intersection. Crashes occurring within 250 ft of the intersection have traditionally been considered to be influenced by intersection performance (e.g., Oh et al. 2004; and Ye et al 2009)

### Methodology

When modeling crash counts, Poisson regression analysis or Negative Binomial (NB) regression analysis can be used (Yaacob et al, 2011; Zlatoper, 1989; Lord, 2006; Chin and Quddus, 2003; Miaou and Lum, 1993; and Noland and Quddus, 2004). The choice between the two model types depends on the relationship between the mean and the variance of the data. If the mean is equal to the variance, the data is assumed to follow a Poisson distribution, and hence the Poisson regression analysis can be performed. However, as a result of possible positive correlation between observed accident frequencies, overdispersion may occur (Hilbe, 2011). Accident frequency observations are said to be overdispersed if their variance is greater than their mean. If overdispersion is detected in the data, NB regression analysis should be used. Another issue arising with modeling accident frequencies is presence of sites with zero counts. Hurdle and zero-inflated Poisson or NB regression models are the two foremost methods used to deal with count data (e.g., accident frequencies) having zero counts (Hilbe, 2011). This study explored the suitability of Poisson, NB, and zero-inflated (Poisson and NB) models.

Standard textbooks (e.g., Hilbe 2011; Greene 2012; and Washington et al 2011) present clear derivation of the Poisson, Negative Binomial (NB), and zero-inflated models (Poisson (ZIP) or Negative Binomial (ZINB)). According to Poisson distribution, the probability P(y_{i}) of intersection i having y_{i} crashes in a given time period (usually one year) can be written as:

(1) P(y_{i}) = ((EXP(-λ)⋅λ_{i}^{yi} ) / (y_{i}!))

where λ_{i} denotes the Poisson parameter for intersection i. By definition, λ_{i} is equal to the expected number of crashes in a given time period for intersection i, E[y_{i}]. According to Washington et al. (2011), the expected number of crash occurrences λ_{i}, can be related to a vector of explanatory variables, X i as follows:

(2) λ_{i}=EXP(βX_{i})

where β represents a vector of estimable parameters. Under Poisson assumption, the mean and variance of crashes occurring at an intersection in a year are equal (i.e.,E[y_{i}]=Var[y_{i}],). With N observations, the parameters of the Poisson model can be estimated by maximum likelihood method with a function that can be shown to be as follows:

(3) LL(β) = ΣNi=1 [-EXP(βX_{i}) +y_{i}βX_{i}-In(y_{i}!)]

The Poisson assumption of equal mean and variance of the observed crash occurrences is not always true. To handle the cases where the mean and variance of crashes are not equal, the Poisson model is generalized by introducing an individual, unobserved effect, εi, in the function relating crash occurrences and explanatory variables (equation 2) as follows:

(4) λ_{i}=EXP(βX_{i}+ε_{i})

in which EXP(ε_{i}) is a gamma-distributed error term with mean one and variance α^{2}. With such a modification, the mean λ_{i} becomes a variable that follows binomial distribution. The mean-variance relationship becomes:

(5) Var[y_{i}]=E(y_{i})⋅[1+αE(y_{i})]=E[y_{i}]+αE(y_{i})^{2}

If α is equal to zero, the negative binomial distribution reduces to Poisson distribution. If α is significantly different from zero, the crash data are said to be overdispersed (positive value) or underdispersed (negative value). As stated earlier, overdispersion is a result of possible positive correlation between observed accident frequencies. When α is significantly different from zero, the resulting negative binomial probability distribution is:

(6) P(y_{i})= (Γ((1/α)+y_{i}))/(Γ(1/α)y_{i}!) ((1/α)/((1/α)+λ_{i}))^{1/α} ((λ_{i})/((1/α)+λ_{i}))^{yi}

where Γ(x) is a value of the gamma function, y_{i} is the number of crashes for intersection i and α is an overdispersion parameter. Because crash counts involve intersections with zero observations, possible remedies include the estimation of models such as zero-inflated (ZIP or ZINB) and hurdle models. The zero-inflated models have two parts: a binary part for distinguishing the intersections that will always have zero counts from those that, although they now have zero counts, will not always have zero counts, and a Poisson regression model (for ZIP) or Negative Binomial model (for ZINB), which models the intersections with zero or positive counts. Washington et al, 2011, shows that with the ZINB regression model the probability of an intersection having zero crash counts can be estimated as:

(7) Pr(y_{i}=0)=P_{i}+(1-P_{i}) [(1/α)/(1/α+λ_{i})]^{1/α}

and the probability of having positive crash counts (y = 1, 2, 3,…) can be estimated as:

(8) Pr(y_{i}=y)=(1-P_{i}) [(Γ((1/α)+y) Ψ_{i}^{1/α} (1-Ψ_{i})^{y})/(Γ(1/α)y!)]

in which. Ψ_{i}=(1/α)/(1/α+λ_{i})

It is imperative to test whether using the zero-inflated model is necessary. This can be achieved by conducting the Vuong test (Vuong 1989). Although alternative tests have been developed to improve model selection reliability, the Vuong test is commonly used. The Vuong test is far more conservative than alternative tests such as the distribution-free test and therefore does a better job of protecting against an incorrect decision (Clarke 2007). Given two models, model 1 with P1(yi/x) as the probability of observing y crashes on the basis of variable x, and model 2 with the probability denoted as P2(yi/x), the log ratio of the sum of probabilities for each observation can be computed as:

(9) Φ_{i}=ln((Σ_{i}P_{1}(y_{i}/x_{i}))/(Σ_{i}P_{2}(y_{i}/x_{i})))

and the Vuong test statistic can be computed as:

(10) V=(√N(Φ)) / (SD(Φ_{i}))

in which Φ is the average of the log ratios and SD(Φ_{i}) is the standard deviation of the log ratios. The Vuong test statistic has been proved to follow a normal distribution. Greene (2012) states that if |V| is less than 1.96, then the test does not favor one model over the other. If V is greater than 1.96, model one is favored while if V is less than -1.96, model two is favored. In addition to comparing the models using the Vuong test statistic, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were calculated for each model and compared. Standard statistical software such as Stata (2008) can be used to estimate the models and statistics described above.

To better interpret the results of a count data models, elasticities can be computed. Elasticity of a continuous variable is used to quantify the effect of a small change (1%) in the mean of the variable on the outcome (expected crash occurrences λ_{i}). Elasticity of a k^{th} continuous variable x for observation i(x_{ik}), can be estimated as:

(11) E_{xik}^{λi} = (θλ_{i} / λ_{i}) X (x_{ik}) / δx_{ik} = β_{k}x_{ik}

For indicator variables (which strictly take on values of 0 or 1), such a small change is meaningless. As a result, the "pseudo-elasticity" can be used to accommodate such variables. It shows the difference in the outcome (crash occurrence) with a specific variable taking the value of 1 versus 0. It can be computed as:

(12) E_{xik}^{λi} = (EXP(β_{k})-1) / EXP(β_{k})

### Data Description

Data used in this study were collected from all signalized intersections in the cities of Las Vegas and North Las Vegas, Nevada, in the USA. With the Geographic Information System (GIS) and aerial images from Google Earth, we located the identified signalized intersections. The roadway network map for Las Vegas and North Las Vegas area was used as the base layer in the ArcGIS. The geographic coordinates of each intersection obtained from Google Maps were used to geo-code the intersections to create a GIS layer. The Safety and Traffic Engineering Division of the Nevada Department of Transportation (NDOT) maintains a database of all crashes occurring in the state. From this database, North Las Vegas and Las Vegas crashes were selected. The crash data were mapped with ArcGIS to identify crashes that occurred at signalized intersections. This was accomplished by creating a buffer with a radius of 250 ft around each signalized intersection in Las Vegas and North Las Vegas and counting the number of crashes within that buffer. These crashes were deemed to be influenced by the intersection. Although the 250-ft buffer around an intersection may omit some intersection crashes and/or include some nonintersection crashes, it is commonly used in the United States as it is a nonarbitrary criterion that is easily repeatable and generalizable across jurisdictions (Ye et al. 2009). The number of corner clearances was obtained by counting the number of driveways within the intersection area (a circle with a radius of 250 ft) and the corner clearances were measured as shown in figure 1. For example, the intersection depicted in figure 1 has five corner clearances.

Traffic volume is a very important determinant of crash occurrence at intersections. This data item was obtained from a database maintained by the Southern Nevada Regional Transportation Commission (RTC). For the intersections selected, the RTC database contained complete traffic volume data for year 2004 only. Therefore, this study used crash data for year 2004 only. In addition, landuse type for each intersection was collected.

**FIGURE 1 Corner Clearance Measurements and Counting**

For each approach, functional classification was obtained from the GIS database provided by the Regional Transportation Commission (RTC) of Southern Nevada. From the same database, the number of lanes on both directions and the posted speed limit were also extracted. The number of lanes was confirmed using the Google map. To designate major and minor approaches, the AADT volumes were used. The opposing approaches with the highest sum of AADT were designated major while the ones with the lowest were labeled minor. In addition to AADT data, other roadway attributes were extracted. After cleaning data to remove intersections with incomplete information, only 170 intersections remained. Table 1 presents the descriptive statistics for the selected variables.

Table 1 indicates that on average, over 22 crashes occurred at signalized intersections in Las Vegas and North Las Vegas during 2004.

**Table 1: Descriptive Statistics of all Extracted Variables**

Variable | Average | Std. Dev. | Minimum | Maximum |
---|---|---|---|---|

2004 crash count | 22.71 | 19.89 | 0 | 96 |

Commercial landuse | 0.53 | 0 | 1 | |

No. of lanes on major approach | 4.77 | 1.12 | 1 | 7 |

No. of left turn lanes on major approach | 1.29 | 0.51 | 0 | 4 |

No. of right turn lanes on major approach | 1.01 | 0.1 | 1 | 2 |

No. of lanes on minor approach | 3.15 | 1.56 | 1 | 8 |

No. of left turn lanes on minor approach | 1.2 | 0.44 | 1 | 3 |

No. of right turn lanes on minor approach | 1.03 | 0.17 | 1 | 2 |

No. of corner clearances | 6.24 | 1.79 | 2 | 8 |

Average corner clearance (ft) | 134.85 | 69.28 | 43.63 | 250 |

AADT on major approach | 13241.19 | 29936.59 | 554 | 153896 |

AADT on minor approach | 6315.17 | 14929.43 | 469 | 99890 |

Average speed on major approach | 41.22 | 4.93 | 25 | 50 |

Average speed on minor approach | 33.84 | 7.28 | 15 | 45 |

The results also show that the abutting land on about 53% of the signalized intersections was commercial landuse. On average, major approaches had about five lanes (in both directions) while minor approaches had about three lanes (in both directions). Both major and minor approaches had an average of one left-turn lane and one right-turn lane. Corner clearance for each driveway was measured all averaged to determine the average corner clearance. On average, the observed average corner clearance was 134.85 ft. The average AADT on major approaches was 13,242 vehicles/day while for minor approaches it was 6,316 vehicles/day. There was an average of six corner clearances (equivalent to driveways) at the intersections observed.

The extracted variables were to derive explanatory variables used in the models. Only significant variables were retained and are presented in the next section. In modeling, number of left turn lanes and right turn lanes were combined into one category of "turning lanes" for each approach. The "turning lanes" were used distinctively from "through lanes". Commercial landuse was another significant variable used in modeling. The AADT on minor approach was divided by the AADT on major approach to generate "flow ratio." Average corner clearance was transformed by taking natural logarithm before using it in modeling. Also, the number of corner clearances was used in modeling. Table 2 presents summary statistics for variables used in the model.

### Modeling Results and Discussion

Using commercially available software, Stata (2008), we estimated and compared results from four models: Poisson, Negative Binomial, Zero-Inflated Poisson, and Zero-Inflated Negative Binomial. Table 3 presents the coefficient estimates from these models. As it can be seen, all models (Poisson, Negative Binomial, Zero-Inflated Poisson ZIP) and Zero-Inflated Negative Binomial (ZINB)) produced results consistent with intuition in terms of the impact of the variables on crash count. The models were compared to identify the "best" fitted model. The resulting test statistic of 1,153.64 with a p-value of 0.0000 for the likelihood-ratio test of zero overdispersion (α=0) indicates that the Negative Binomial model is preferred to the Poisson model. Even the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) support this assertion. As shown in figure 2, both the AIC and the BIC for the Negative Binomial model are less than those of the Poisson model, signifying superiority of the Negative Binomial model over the Poisson model. Furthermore, the Vuong test statistics of 2.90 (with p-value of 0.002) and 2.58 (with p-value of 0.004) from the Zero-Inflated Poisson (ZIP) and the Zero-Inflated Negative Binomial (ZINB) models, respectively, indicate that the zero-inflated models (ZIP and ZINB) are preferred to their respective standard models (Poisson and Negative Binomial).

**Table 2: Descriptive Statistics of Modeling Variables**

Variable | Average | Std. Dev. | Minimum | Maximum |
---|---|---|---|---|

Commercial landuse | 0.53 | 0.5 | 0 | 1 |

Flow ratio | 1.3 | 1.55 | 0.05 | 11 |

Natural log. of average corner clearance | 4.97 | 0.35 | 3.78 | 5.75 |

Left turning lanes | 2.49 | 0.74 | 1 | 5 |

Through lanes | 7.95 | 2.18 | 2 | 13 |

Number of corner clearance | 6.25 | 1.79 | 2 | 8 |

**Table 3: Model Estimation Results**

Explanatory Variables | Poisson | Negative Binomial | ZIP | ZINB | ||||
---|---|---|---|---|---|---|---|---|

Coef. | Statistic | Coef. | Statistic | Coef. | Statistic | Coef. | Statistic | |

Regression Part | ||||||||

Commercial kanduse | 0.511 | 14.31 | 0.463 | 3.72 | 0.394 | 11.05 | 0.377 | 3.59 |

Flow (AADT) ratio (minor/major) | 0.065 | 8.33 | 0.074 | 1.9 | 0.062 | 7.84 | 0.063 | 2 |

Natural log. of avg. corner clearance | -0.21 | -6.46 | -0.193 | -1.14 | -0.404 | -9 | -0.509 | -3.26 |

Number of left turning lanes | 0.096 | 4.24 | 0.094 | 1.02 | 0.185 | 7.32 | 0.208 | 2.6 |

Number of through Lanes | 0.147 | 15.49 | 0.147 | 4.28 | 0.11 | 11.35 | 0.112 | 3.8 |

Constant | 2.304 | 13.36 | 2.242 | 2.49 | 3.479 | 12.78 | 3.929 | 4.74 |

Inflation Part |
||||||||

No. of corner clearance | -0.551 | -2.67 | -0.564 | -2.57 | ||||

Natural log. of avg. corner clearance | -0.845 | -1.59 | -0.873 | -1.57 | ||||

Constant | 4.237 | 1.49 | 4.375 | 1.48 | ||||

Auxiliary Statistics |
||||||||

Alpha (α) | 0.528 | 8.07 | 0.338 | 7.61 | ||||

Number of observations | 170 | 170 | 170 | 170 | ||||

Final log-likelihood | -1262.2 | -685.38 | -1101.62 | -665.18 | ||||

Likelihood-ratio test of α=0 (p-value) | - | 1153.64 (0.000) | - | 872.89 (0.000) | ||||

Vuong statistic (p-value) | - | - | 2.90 (0.002) | 2.58 (0.004) |

Comparing the AIC and the BIC for the ZIP and the ZINB indicates that the ZINB has slightly lower values (figure 2), which signifies slight preference of the ZINB over the ZIP. However, the Vuong test statistic for comparing ZINB to ZIP was 0.84, signifying that neither of the two models is preferable over the other for the data at hand. Table 4 presents the model selection results.

**FIGURE 2 Selection of the “Best” Fitted Model**

It should be recalled that the test on alpha (testing equality of mean and variance) indicated that alpha is significantly different from zero, which indicates that Poisson is not the closest estimation of the distribution for the data at hand. Therefore, the Zero-Inflated Negative Binomial (ZINB) model was identified as the "best" fitted model for the data at hand.

The results from the ZINB model estimates (table 3) indicate that increased length of corner clearance leads to decreased crash frequency. This is because a driveway that is far from the intersection allows sufficient distance for drivers exiting the businesses (whether they are familiar or unfamiliar with the area) to perform the desired maneuver. Also, with longer corner clearance, the drivers of through traffic could perceive and respond more quickly and safely to the maneuvers by traffic leaving or entering the adjacent lands because their attention is not already preoccupied by the maneuver they desire to perform at the intersection. In other words, with longer corner clearances, the maneuver needed at the intersection has less influence on decisions by through-traffic drivers and those leaving or entering businesses. Also, shorter corner clearances imply more driveways at intersections, which increase the chance of conflicts to occur between turning and through traffic.

The results also show that an intersection surrounded by commercial landuse is more likely to experience more crashes compared to an intersection surrounded by residential landuse. Reasons for this finding might include the fact that drivers entering or exiting businesses around an intersection may include those who are unfamiliar with the roadway (noncommuters). Such drivers who are unfamiliar with the roadway are more likely to perform unpredictable maneuvers that increase the chance of crash occurrence.

The results also show that signalized intersections with traffic volume on minor street close to the traffic on major street (high ratio) tend to have higher crashes. In previous studies such as Chin and Quddus (2003), traffic flow was also found to be an important predictor of crashes at intersections. Some studies have used total entering traffic volume (e.g., Greibe (2003) and Chin and Quddus (2003)) while others have separated traffic volume on minor street from that on major street (e.g., Lord and Persaud 2000). Other studies have used traffic volume per lane (e.g., Wang et al 2006). The finding in this study indicates that with higher traffic on the minor approach, there is an increased probability of higher conflicts and therefore higher crashes. Although not examined in this study, this could be associated with permitted right-turn and left-turn movements. This study examined the separate impact of turning lanes and through lanes at signalized intersections. Left-turning lanes and right-turning lanes as well as through lanes were counted for each intersection. The modeling results also indicated that crash increases with increase in number of both left-turning lanes and through lanes. However, the number of through lanes has the highest impact on the number of crashes (higher elasticity presented in table 5). With left-turning lanes, vehicles exiting adjacent businesses around the intersection and desiring to make left turn may experience relatively higher difficulty in performing their maneuvers.

Extra care is needed when interpreting the results of the "inflation" part of the model. This is a binary process with a prediction of success being a prediction that the response will certainly be a zero. The negative coefficients associated with both the number of corner clearances and the natural logarithm of corner clearance signify that an increase in these variables reduces the chance of having zero crashes at signalized intersections. In other words, increase in these variables could potentially lead to crash occurrence at intersections.

**Table 4: Model selection results**

Model | Test Statistic | “Best” Model | Vuong Statistic for ZINB vs. ZIP | Conclusion | ||
---|---|---|---|---|---|---|

BIC | AIC | Vuong | ||||

NB |
1407 | 1385 | 2.58 | ZINB | 0.84 | Neither ZINB nor ZIP is superior over the other |

ZINB |
1382 | 1350 | ||||

Poisson |
2555 | 2536 | 2.9 | ZIP | ||

ZIP |
2249 | 2221 |

**Table 5: Estimated Elasticities**

Variable | Elasticity | Std. Err. | z-statistic | p-value |
---|---|---|---|---|

Commercial landuse | 0.07 | 0.02 | 3.75 | 0 |

Flow (AADT) ratio (minor/major) | 0.03 | 0.01 | 2.06 | 0.039 |

Natural log. of avg. corner clearance | -0.83 | 0.26 | -3.22 | 0.001 |

Number of left turning lanes | 0.16 | 0.06 | 2.62 | 0.009 |

Number of through Lanes | 0.29 | 0.08 | 3.81 | 0 |

To better investigate the impact of corner clearance and other variables on the number of crashes occurring at signalized intersections we calculated their elasticities presented in table 4. Elasticity of a continuous variable is used to quantify the effect of a small change (1%) in the mean of the variable on the outcome (expected crash occurrences λ_{i}). Because a small change is meaningless for indicator variables (which strictly take on values of 0 or 1), the "pseudo-elasticity" was calculated. Again, the results indicate that corner clearance is very sensitive to the number of crashes occurring at signalized intersections. There could be an 83% reduction in the number of crashes by increasing the natural logarithm of average corner clearance by 1%. However, an increase of 1% on the number of left-turn lanes would increase the number of crashes by about 16%. Compared to the number of left turn lanes, an increase of 1% in the number of through lanes would result into a 29% increase on the number of crashes. Flow ratio and landuse have the lowest sensitivity to the number of crashes. An intersection being surrounded by commercial landuse would result into a 7% increase on number of crashes while a 1% increase on the flow ratio would result into just 3% increase on the number of crashes. This indicates that intersections with higher traffic volumes on minor approaches (i.e., ratio close to 1) may experience relatively more crashes. Large number of left-turn lanes may be an indication of higher left-turn traffic, making maneuverability more difficult and dangerous.

### Conclusions and Recommendations

Adequate corner clearance is important to effectively separate conflict points and allow drivers enough time to make safe maneuvers. Although most studies have investigated the impact of roadway and traffic characteristics on intersection safety, corner clearance has not been fully investigated. The main objective of this study was to investigate the impact of corner clearance and other variables on the number of crashes occurring at urban signalized intersections. Data from all signalized intersections in the Las Vegas and North Las Vegas urban areas were used to conduct the analyses. This study explored the suitability of Poisson, Negative Binomial (NB), Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models. Statistical tests such as the Vuong test, Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC) were calculated to identify the best model. Also, the accuracy of the Negative Binomial (NB) and the Zero-Inflated Negative Binomial (ZINB) models in predicting crash occurrence was compared by computing the difference between predicted probability and observed probability for each model. With all comparison tests, the ZINB outperformed other models and was selected as the best fitted model for the data at hand. It was revealed that the ZINB is very accurate in predicting zero crash occurrences when compared with the regular NB but their difference fades away for high crash occurrences. To better interpret the results of a count data models, elasticities can be computed.

The results from the ZINB model estimates indicated that increased length of corner clearance leads to decreased crash frequency. This finding is consistent with intuition because shorter corner clearances imply more driveways at intersections, which increase the chance of conflicts to occur between turning and through traffic. The sensitivity results (table 4) indicated that corner clearance is very sensitive to the number of crashes occurring at signalized intersections. The results also showed that an intersection surrounded by commercial landuse is more likely to experience more crashes compared to an intersection surrounded by residential landuse. Reasons for this finding might include the fact that drivers entering or exiting businesses around an intersection may include those who are unfamiliar with the roadway (noncommuters). The results indicated that 65% of the driveways with corner clearance less than 150 ft are from intersections surrounded by commercial landuse and 78% of the driveways with corner clearance less than 100 ft are from intersections surrounded by commercial landuse. The results also showed that signalized intersections with traffic volume on minor street close to the traffic on major street (high flow ratio) tend to have higher crashes. With higher traffic on the minor approach, there is an increased probability of higher conflicts and therefore higher crashes. Although not examined in this study, this could be associated with permitted right-turn and left-turn movements. The modeling results also indicated that, generally, crash increases with increase in number of both left-turning lanes and through lanes. However, the number of through lanes has the highest impact on the number of crashes (higher elasticity presented in table 4). With turning lanes, vehicles leaving or entering businesses around the intersection make their maneuvers from low speed lanes (turning lanes). In addition to confirming the impact of corner clearance on safety of signalized intersections, the findings of this study also reveal the importance of properly designed corner clearances at signalized intersections when compared with other geometrics. For example, compared to the number of left turn lanes at signalized intersections, adequate corner clearances may produce higher safety gains by reducing number of crashes. Such an understanding is important to access managers and roadway designers as they consider potential geometric design parameters with potential to improving safety.

Intersections located on a given urban arterials may share common but unobserved attributes such as similar traffic volume patterns. Such unobserved common attributes may influence statistical inferences. One way to addressing this issue is to develop panel count models. Such modeling consideration is relatively complex especially with zero-inflated models. It is recommended that future research consider incorporate panel structure to address the possible problem of unobserved common attributes.

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