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category: literaturenote citekey: nolanddolowerincomeareas2013 title: Do lower income areas have more pedestrian casualties? authors: "Noland, Robert B.; Klein, Nicholas J.; Tulach, Nicholas K." year: 2013 date: 2013-00-00 2013 doi: 10.1016/j.aap.2013.06.009 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2013.06.009" zotero_key: U3JNG858 zotero_storage: WVEUEPXJ collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Noland, Robert B."
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Accident Analysis and Prevention
journal homepage: www.elsevier.com/locate/aap
Do lower income areas have more pedestrian casualties?
Robert B. Noland∗, Nicholas J. Klein, Nicholas K. Tulach
Alan M. Voorhees Transportation Center, Edward J. Bloustein School of Planning and Public Policy, Rutgers University, New Brunswick, NJ 08901, USA
a r t i c l e i n f o
Article history: Received 6 February 2010 Received in revised form 31 May 2013 Accepted 5 June 2013
Keywords: Road safety Pedestrians Negative binomial models Bayesian analysis Deprivation Low income Car ownership
a b s t r a c t
Pedestrian and motor vehicle casualties are analyzed for the State of New Jersey with the objective of determining how the income of an area may be associated with casualties. We develop a maximumlikelihood negative binomial model to examine how various spatially defined variables, including road, income, and vehicle ownership, may be associated with casualties using census block-group level data. Due to suspected spatial correlation in the data we also employ a conditional autoregressive Bayesian model using Markov Chain Monte Carlo simulation, implemented with Crimestat software. Results suggest that spatial correlation is an issue as some variables are not statistically significant in the spatial model. We find that both pedestrian and motor vehicle casualties are greater in lower income block groups. Both are also associated with less household vehicle ownership, which is not surprising for pedestrian casualties, but is a surprising result for motor vehicle casualties. Controls for various road categories provide expected relationships. Individual level data is further examined to determine relationships between the location of a crash victim and their residence zip code, and this largely confirms a residual effect associated with both lower income individuals and lower income areas.
© 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Pedestrian fatalities and injuries in New Jersey constitute a large fraction of total vehicle crashes and disproportionately occur in lower income communities. About 20% of crash fatalities in New Jersey are pedestrians resulting in roughly 150 pedestrian fatalities and roughly ten times as many pedestrian injuries each year. About 29% of pedestrian fatalities and 41% of pedestrian injuries occur in the lowest income quartile Census block groups. By comparison, about 16% of motor vehicle fatalities and 20% of motor vehicle injuries occur in these block groups. Notably, while the proportion of crashes that involve a pedestrian are higher than in other states, the total casualty rate in New Jersey is one ofthe lowest of any state. One probable reason for this disparity is that New Jersey is more urbanized than other states. An unknown question is why pedestrian casualties are more likely in lower income neighborhoods; the analysis presented here seeks to examine why this is the case.
Recent research has established that spatial analysis techniques can help to explain associations between area-based factors and road crashes. This includes a spatial analysis of crashes in Honolulu, Hawaii, and an analysis for all of England (Levine et al., 1995; Noland and Quddus, 2004). These and other analyses find that total fatalities or injuries are associated with land use characteristics, road types, and area-based demographic factors. Commercial land
One issue with area-based analysis of crash data is that there may be spatial correlation. In general, we would expect that a given spatial unit would be affected by characteristics of neighboring units. Omission of spatial correlation, if it exists, may lead to biased estimates. Because crash data is non-normally distributed (i.e., zero counts in some units), count data models are typically used and accounting for spatial correlation in these models requires a more complex estimation approach. We use the Crimestat v4.0 (Levine, 2010) software package to estimate these models.2
Our primary objective in this analysis is to examine the spatial factors associated with pedestrian casualties with a focus on understanding why lower income areas tend to suffermore crashes. As a comparative analysis we also examine motor-vehicle only casualties to determine whether there are distinct differences in associations. This is an ecological analysis of area-based factors and their association with casualties; we make no judgment on how these factors affect individual crashes. Disaggregate data is
uses frequently have more pedestrian-related crashes (Kim et al., 2006; Lightstone et al., 2001). Larger roads are associated withmore crashes, possibly representing larger traffic flows. More deprived areas also tend to have more crashes, and in particular, those that injure pedestrians (Graham and Glaister, 2003; Loukaitou-Sideris et al., 2007).
∗ Corresponding author. Tel.: +1 848 932 2859. E-mail address: rnoland@rutgers.edu (R.B. Noland).
2 Crimestat is freely available at http://www.icpsr.umich.edu/CrimeStat/ download.html. Version 4 is currently in beta testing and was kindly provided by Ned Levine.
also analyzed based on the zip code of the victim's residence, which provides a proxy for the victim's socio-economic status. Various cross-tabulations of crash location with residence location are examined to disentangle whether low income areas or low income individuals are more likely to be associated with more pedestrian casualties.
2. Data
For this analysis, we combined data from four primary sources, Plan4Safety3 crash data, 2000 US Census data, the Longitudinal Employer-Household Dynamics Data for 2008, and GIS layers obtained from the state of New Jersey.
We include pedestrian and motor vehicle crash data from 2003 to 2007 extracted from the Plan4Safety database which is a comprehensive database of crashes that have taken place in New Jersey, based on police reports. We extracted records for casualties to pedestrian and motor vehicle occupants (driver and passenger) where the person involved was "killed", "incapacitated", or sustained a "moderate injury".4 We also included records that listed pedestrians with "complaint of pain", or "null" values where there was another pedestrian involved that had a "moderate injury" or worse. The resulting crash database includes 8144 pedestrian casualties and 82,477 motor vehicle casualties. There may be some recorded injuries that were very minor or non-existent and would represent poor reporting by the police, especially for crashes with multiple pedestrians, thus for completeness we include all recorded pedestrians as injured. After extracting the data from the Plan4Safety database, we geo-coded the records using geolocation information from the Plan4Safety database and aggregated the counts of casualties to census block groups. The data contained the residence zip code of the victims, and we also geo-coded the crashes to the zip code area in which the crash occurred.
We obtained basic demographic data for block groups in New Jersey from the 2000 US Census Summary File 3. We excluded any block groups with zero resident population (43 in total) which reduces the total pedestrian casualties by 27 (0.3%) to 8117 casualties and motor vehicle casualties by 692 (0.8%) to 81,785 casualties.5 The final database includes 6460 block groups. Employment data at place of work was derived from the Census Longitudinal Employer-Household Dynamics data for 2008.6 This is distinct from other employment measures that measure the employed population within a given spatial unit. Measuring employment where people actually work is important as these are often areas where there is more pedestrian activity.
We obtained GIS road layers from the New Jersey Department of Transportation (NJDOT). For each block group, we calculated road density per square mile by functional class. We included the following functional classes: freeways and turnpikes, US highways (generally the largest arterial roads), New Jersey state highways (also relatively large arterials), two categories of county roads (500 and 600 designations, with 500 being higher category roads), and ramps and jughandles.
Jughandles appear to be a road engineering innovation originally unique to New Jersey. These are designed to avoid cross-traffic turns (left turns) and involve an off-ramp that loops around so that vehicles cross the main arterial flow at a right angle with a traffic signal. The rationale is to minimize vehicle conflicts by reducing cross-traffic turning crashes, while also improving operations via the elimination of dedicated cross-traffic (left)turn signals (Jagannathan, 2006).7
3. Hypotheses
Previous spatial analyses have generally found an association between the income level of an area and both pedestrian and vehicle casualties (Graham et al., 2005; Graham and Glaister, 2003; LaScala et al., 2000; Loukaitou-Sideris et al., 2007; Noland and Quddus, 2004). Thus we can hypothesize that lower income areas will be associated with more pedestrian casualties. One of our objectives is to understand why this is the case, therefore we also hypothesize that lower rates of vehicle ownership are associated with more pedestrian casualties, and that this will fully capture the effect of area-based income. Furthermore, we hypothesize that the effect of vehicle ownwership and income will have different associations with motor-vehicle passenger casualties.
Additional evaluated hypotheses include the impact of population and employment density, both proxies for land use and urban form. Previous research has suggested that population density is associated with reductions in pedestrian casualties while employment density is associated with increases (Ewing and Dumbaugh, 2009; Noland and Quddus, 2004). Road network density variables are also examined and it is hypothesized that more roads with higher speed traffic (i.e., those of a higher functional classification) will be associated with more pedestrian casualties.
The dataset also includes the zip code residence of many of the victims. Using this information, we compare the income level of each victim's residential neighborhood with the income level of the area where the crash occurred. We also include how many victims were in a crash in their home zip code area. Our hypothesis is that area-based income is associated with more casualties and that individual income is not. Individual income can vary substantially within a zip code and this is a limitation of this analysis. However, if one accepts area-based income as a proxy for individual income then this hypothesis can be tested and determine whether lower income areas are inherently more risky or whether lower income individuals take more risks.
4. Modeling approach and estimation methods
Our analysis uses a negative binomial model because crash data, and in particular pedestrian casualties, are rare events that are typically Poisson distributed. Estimation methods that assume normality cannot be used since crash outcomes are non-negative discrete counts with some dependent variables being equalto zero. In our dataset, 48% of the block groups have zero pedestrian casualties and 10% have zero counts of motor vehicle casualties. We tested our dependent variables and residuals and could not reject the hypothesis that these were not normally distributed. In addition, further tests on per capita rates were found to be non-normal necessitating use of a count estimation method.
Due to over-dispersion in the data, negative binomialmodels are used in place of Poisson regressions. The Poisson model assumes that the mean is equal to the standard deviation; this does not typically hold in empirical settings. Tests of over-dispersion for our models found that negative binomial regression was required.
3 The Plan4Safety database is maintained by Rutgers University Center for Advanced Infrastructure and Transportation. More detailed information on the Plan4Safety database is available online at http://plan4safety.rutgers.edu/ plan4safety/login.aspx.
4 The data coded bicyclists as pedestrians within the pedestrian tab. These were removed from the dataset.
5 Population was used as an off-set variable in our models. This represents an exposure measure and the zero population block-groups were elimated to avoid estimation problems.
6 Available at http://lehd.ces.census.gov/.
7 Further information on jughandle design is available at http://www.state.nj.us/ transportation/eng/documents/RDM/sec6.shtm (accessed 01.08.12).
Given that our data is spatial we tested for spatial autocorrelation using Moran's I (Anselin and Bera, 1998). This is defined as,
$$I = \frac{N}{\sum{i} \sum{j} w{ij}} \frac{\sum{i} \sum{j} w{ij} (X{i} - \bar{X})(X{j} - \bar{X})}{\sum{i} (X{i} - \bar{X})^{2}}$$
The variable X is typically the dependent variable, where i and j are subscripts for each spatial unit, X¯ is the mean, and wij is the spatial weights matrix, in our case we define this based on the centroid distances between the N block groups.
The Moran's I test reveals that there is spatial correlation in the data for pedestrian casualties and motor vehicle casualties. Thus we implement a more complex modeling procedure to account for spatial autocorrelation in a negative binomial model. The method of Besag et al. (1991) which defines a conditional autoregressive method of dealing with spatial correlation in a count model is used, and this is estimated using a Bayesian approach. This is a Bayesian hierarchical model and follows Bayes' Law whereby,
$$p(\theta|y) \propto p(y|\theta)p(\theta)$$
This sets the posterior distribution, p(-|y) proportional to the likelihood, p(y|-) times the prior distribution, p(-
The conditional autoregressive (CAR) negative binomial model (also known as a Poisson-gamma-CAR model) is defined as follows, based on Levine et al. (2010):
$$y_i | \lambda_i \sim Poisson(\lambda_i)$$
where
$$\lambda_i = \exp(x_i^T \beta + \varepsilon_i + \phi_i)$$
In this formulation yi is the dependent variable (casualties) and i is the mean of the Poisson distribution, with a matrix of independent variables x and coefficients ˇ. The error term ε is equal to 1 plus the inverse of the dispersion parameter and this follows a gamma distribution. The CAR model adds the spatial random effect, ϕi and includes a spatial weights matrix. We use a negative exponential decay function, based on distance between block group centroids with a decay parameter of -0.5 miles. Priors for the distribution are non-informative in our estimates, and are based on the default values in Crimestat. We set priors for the ˇ parameters based on maximum likelihood estimates, which provides a good starting point for the algorithm.
Estimation of this model is implemented via a Markov Chain Monte Carlo (MCMC) simulation using the Metropolis–Hasting algorithm (Levine, 2010; Levine et al., 2010). This is a very data intensive simulation approach that has been implemented in Crimestat starting with version 3.3.
Initial tests with the MCMC model found that a significant burnin time was needed to achieve convergence. For our models we therefore sample 100,000 simulations with a burn-in of 20,000, which are not included in the final estimate. Crimestat provides output for the Gelman–Rubin (G–R) convergence diagnostic and the Monte Carlo (MC) simulation error. When the former is below 1.2, convergence is considered good, while for the MC error, its ratio with the standard error of the parameter should be below about 0.05 (Levine et al., 2010). These criteria were generally met once 100,000 iterations were run.
Our analysis strategy begins by estimating the maximum likelihood models which do not include a spatial correction. We also examine the correlation structure of the independent variables and the variance inflation factor to determine the best set of theoretically justified variables to include. Final models are then estimated using the Bayesian negative binomial CAR model. We estimated models both with and without population as an offset(or exposure) variable. This constrains population to be equalto one. As one of our theoretically important variables is population density, we were concerned that this may be correlated with population. However, the correlation coefficient was low (R = 0.118) and models without the offset gave very similar results.8
5. Maximum-likelihood analysis results
Our initial intention was to estimate a model similar to that of Noland and Quddus (2004) which was based on road casualties for all of England. This previous work specified land use variables (populationandemploymentdensity anddummy variables for land use types), road characteristics (per square meter of area), demographic characteristics (age of population and a deprivation index), and various proxies for traffic flow.
The data for New Jersey is naturally quite different and we were unable to fully specify a similarmodel.We initially includedpercent of land use devoted to specific activities, such as industrial, commercial and residential activity. These variables, however, were highly correlated with other more significant variables, such as density variables, and with each other, and thus we removed them from the analysis.
We estimated both pedestrian and motor-vehicle casualty models to allow for a comparison of the effects of income. These are discussed in turn below. One goal of evaluating both models was to examine whether rates of zero-vehicle households (which are associated with lower income areas) may affect pedestrian casualties, while we would not expect a similar relationship for motor-vehicle casualties.
5.1. Pedestrian casualty models
Our initial negative binomial maximum-likelihood results are presented in Table 1. Models 1–3 show estimates for pedestrian casualties; resident population is used as the offset or exposure variable in these estimates. Model 1 includes a full set of variables and all are found to be statistically significant. Income is consistently significant with a negative sign indicating that areas with increased income have fewer pedestrian casualties and conversely lower income areas have more pedestrian casualties. Those areas with a higher fraction of households with no vehicles also have a higher level of pedestrian casualties. These block groups tend to also be lower income areas and the correlation coefficient between income and percent of households with no vehicle is −0.449. The Variance Inflation Factor (VIF) was calculated and all are below the normal cut-off of 2. We estimated two additional models, one without income and one without the percent of households with no vehicles (models 2 and 3), to determine if any correlation between these two variables affects model estimates. In both models, the coefficient value for the variable not omitted increases, especially in model 3 for the income variable, suggesting that the lack of vehicle ownership in lower income areas is a potential cause of higher pedestrian casualties. This is presumably because more people must walk to destinations or to access public transit.
Population density is negative and statistically significant in all models, but the coefficient is much smaller in model 3. Population density is somewhat correlated with the percent of households
8 We also explored using the amount of employmentin a block-group as an offset. However, employment was highly correlated with employment density (R = 0.668) and estimated models resulted in a reversal of the signs of both the population density and employment density parameters, with relatively high z-statistics. This suggests that the collinearity may be driving this result and leading to invalid inference on these two key variables ofinterest. Similar effects were found with estimates that used the sum of population and employment as an offset.
Table 1 Maximum likelihood estimates of negative binomial models: pedestrian and motor-vehicle casualties.
| Dependent variable | Pedestrian casualties (1) Coef. |
Pedestrian casualties (2) Coef. |
Pedestrian casualties (3) Coef. |
Motor-vehicle casualties (4) Coef. |
Motor-vehicle casualties (5) Coef. |
Motor-vehicle casualties (6) Coef. |
|---|---|---|---|---|---|---|
| Offset is ln(population) | ||||||
| ln(% HH with no vehicle) | 0.317*** | 0.383*** | 0.0924*** | 0.155*** | ||
| ln(HH income) | −0.238*** | −0.557*** | −0.208*** | −0.292*** | ||
| ln(population density) | −0.167*** | −0.164*** | −0.0723*** | −0.583*** | −0.604*** | −0.552*** |
| ln(employment density) | 0.228*** | 0.227*** | 0.250*** | 0.113*** | 0.123*** | 0.116*** |
| ln(US highways/sqmile) | 0.222*** | 0.243*** | 0.202*** | 0.485*** | 0.491*** | 0.486*** |
| ln(NJ state hwy/sqmile) | 0.172*** | 0.177*** | 0.158*** | 0.430*** | 0.425*** | 0.431*** |
| ln(county 500 hwy/sqmile) | 0.220*** | 0.216*** | 0.230*** | 0.275*** | 0.266*** | 0.279*** |
| ln(county 600 hwy/sqmile) | 0.204*** | 0.200*** | 0.211*** | 0.206*** | 0.200*** | 0.208*** |
| ln(ramps and jughandles/sqm) | 0.116*** | 0.142*** | 0.133*** | |||
| ln(freeways-turnpikes/sqm) | 0.650*** | 0.675*** | 0.653*** | |||
| Constant | −5.488*** | −8.230*** | −2.275*** | 0.818*** | −1.444*** | 1.650*** |
| N | 6460 | 6460 | 6460 | 6460 | 6460 | 6460 |
| 2 | 0.0704 | 0.0673 | 0.0612 | 0.124 | 0.121 | 0.123 |
| Log-likelihood | −9407.6 | −9439.0 | −9500.7 | −20,648.0 | −20,721.6 | −20,671.8 |
| Alpha | 0.919 | 0.937 | 1.019 | 0.631 | 0.648 | 0.637 |
Note: n.s.: not significant.
with no vehicle, with a correlation coefficient of 0.55, so removal of this variable may be causing this reduction in value, although this is not apparentin the equivalent motor-vehicle casualty model (model 6). Other results in the literature generally have found that areas with higher population density tend to have lower pedestrian fatalities, although our measure is total casualties, not fatalities. A recent review by Ewing and Dumbaugh (2009) concludes that higher density and less sprawling areas are generally safer for pedestrians. Employment density, on the other hand, is positive and statistically significant, a result found in other studies as well.
All the road density variables are statistically significant and positive. Coefficient values do not show any clear pattern, such as higher road classes having larger effects. US highways have a slightly higher coefficient value than NJ highways, and higher classified county roads (500) have a slightly larger effect than 600 county roads, but these effects are small. Ramps and jughandles have a positive association with pedestrian casualties, but as will be shown, this effect is diminished in the spatial models.
Jagannathan (2006) compared conventional intersections with jughandle intersections. Their conclusion was thatjughandle intersections had fewer crashes, including fewer fatal and injury crashes than traditional intersections. Their comparative analysis also foundmorepedestrians involvedinaccidents at conventionalintersections relative to jughandles. Our study is not strictly comparable, as we include jughandle mileage within all ramp mileage. Their study did not control for other factors, except by trying to have similar traffic characteristics for the sample of intersections analyzed. In any case, it would not be surprising that jughandles reduce some types of vehicle to vehicle collisions, but the geometry of crossing through them as a pedestrian is clearly more complex, and most have inadequate pedestrian facilities, all of which would affect both pedestrian usage and risk.
We also estimated these models without the offset variable and these are shown in Table 2. Our concern is that the use of population as an offset might be interacting with our population density variable, despite their low correlation (0.118). The coefficient on population density is lower in the pedestrian casualty models and
Table 2 Maximum likelihood estimates of negative binomial models: pedestrian and motor-vehicle casualties, no off-set variable.
| Dependent variable | Pedestrian casualties (1) Coef. |
Pedestrian casualties (2) Coef. |
Pedestrian casualties (3) Coef. |
Motor-vehicle casualties (4) Coef. |
Motor-vehicle casualties (5) Coef. |
Motor-vehicle casualties (6) Coef. |
|---|---|---|---|---|---|---|
| ln(% HH with no vehicle) | 0.313*** | 0.348*** | 0.119*** | 0.132*** | ||
| ln(HH income) | −0.127*** | −0.416*** | −0.0456** | −0.153*** | ||
| ln(population density) | −0.100*** | −0.101*** | −0.00316 | −0.535*** | −0.533*** | −0.500*** |
| ln(employment density) | 0.194*** | 0.194*** | 0.216*** | 0.0908*** | 0.0902*** | 0.0972*** |
| ln(US highways/sqmile) | 0.266*** | 0.275*** | 0.250*** | 0.510*** | 0.517*** | 0.504*** |
| ln(NJ state hwy/sqmile) | 0.169*** | 0.169*** | 0.161*** | 0.398*** | 0.400*** | 0.399*** |
| ln(county 500 hwy/sqmile) | 0.216*** | 0.213*** | 0.228*** | 0.300*** | 0.300*** | 0.303*** |
| ln(county 600 hwy/sqmile) | 0.162*** | 0.159*** | 0.170*** | 0.170*** | 0.169*** | 0.174*** |
| ln(ramps and jughandles/sqm) | 0.0381 | 0.0546 | 0.0493 | |||
| ln(freeways-turnpikes/sqm) | 0.584*** | 0.586*** | 0.587*** | |||
| Constant | 0.117 | −1.336*** | 2.972*** | 5.892*** | 5.360*** | 6.975*** |
| N | 6460 | 6460 | 6460 | 6460 | 6460 | 6460 |
| 2 | 0.0648 | 0.0637 | 0.054 | 0.0789 | 0.0788 | 0.0774 |
| Log-likelihood | −9308.5 | −9319.7 | −9416.2 | −21,103.6 | −21,105.7 | −21,136.9 |
| Alpha | 0.867 | 0.875 | 0.972 | 0.767 | 0.767 | 0.776 |
Note: n.s.: not significant.
*p < 0.10.
**p < 0.05. *** p < 0.01.
*p < 0.10.
** p < 0.05. *** p < 0.01.
Table 3 Bayesian model output – pedestrian casualties.
| Pedestrian casualties (1) | Pedestrian casualties (2) | Pedestrian casualties (3) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | ||||
| 2.5% | 97.5% | 2.5% | 97.5% | 2.5% | 97.5% | |||||||
| Variable | ||||||||||||
| Exposure: ln(population) | ||||||||||||
| Intercept | −1.943 | −4.104 | 0.495 | 1.201 | −3.385 | −4.334 | −2.693 | 1.024 | 0.972 | −2.282 | 3.575 | 1.272 |
| ln(% HH with no vehicle) | 0.300 | 0.177 | 0.420 | 1.037 | 0.350 | 0.212 | 0.458 | 1.006 | ||||
| ln(HH income) | −0.138 | −0.339 | 0.039 | 1.190 | −0.438 | −0.698 | −0.239 | 1.259 | ||||
| ln(population density) | −0.078 | −0.174 | 0.020 | 1.028 | −0.096 | −0.222 | −0.001 | 1.022 | 0.017 | −0.104 | 0.111 | 1.076 |
| ln(employment density) | 0.200 | 0.138 | 0.266 | 1.006 | 0.196 | 0.112 | 0.262 | 1.005 | 0.230 | 0.141 | 0.291 | 1.007 |
| ln(US highways/sqmile) | 0.290 | 0.050 | 0.527 | 1.001 | 0.265 | −0.052 | 0.512 | 1.001 | 0.260 | −0.052 | 0.510 | 1.001 |
| ln(NJ state hwy/sqmile) | 0.151 | −0.032 | 0.336 | 1.001 | 0.190 | −0.054 | 0.377 | 1.000 | 0.170 | −0.058 | 0.373 | 1.001 |
| ln(county 500 hwy/sqmile) | 0.200 | 0.008 | 0.391 | 1.001 | 0.200 | −0.054 | 0.395 | 1.000 | 0.220 | −0.033 | 0.412 | 1.001 |
| ln(county 600 hwy/sqmile) | 0.180 | 0.042 | 0.313 | 1.001 | 0.169 | −0.007 | 0.304 | 1.001 | 0.170 | −0.012 | 0.303 | 1.001 |
| ln(ramps and jughandles/sqm) | 0.052 | −0.180 | 0.286 | 1.002 | 0.023 | −0.279 | 0.254 | 1.001 | 0.058 | −0.254 | 0.297 | 1.003 |
| Model Stats | ||||||||||||
| N | 6460 | 6460 | 6460 | |||||||||
| Average sample size | 809.6 | 799.84 | 800.24 | |||||||||
| Log likelihood | −9268 | −9284 | −9384 |
Note: All models were run with 100,000 iterations, 20,000 "burn-in" iterations and 25 samples.
is insignificant in model 3. The changes are much less in the motorvehicle casualty models. The density of jughandles and ramps also becomes insignificant, but in general, other coefficient values are relatively robust. This latter result is actually confirmed in our spatial analysis, discussed below.
5.2. Motor-vehicle casualty models
To understand whether there is some distinct factor associated with lower income areas and pedestrian casualties, we also examine motor-vehicle casualties (excluding pedestrian casualties from our total count). These results are also shown in Table 1 with an offset and Table 2 without the offset (models 4–6). In general, the statistical significance of all variables is the same as in the pedestrian casualty models. The magnitudes of the parameter estimates show some distinct differences.
The estimate for income is similar to the pedestrian model, suggesting that lower income areas also are associated with more motor-vehicle casualties. Those areas with a larger fraction of households with no vehicles also have more motor-vehicle casualties; this is a surprising result as obviously those without vehicles are probably not involved with these crashes. While the coefficient is statistically significant, the value is about 30–40% less than in the pedestrian casualty model; thus, while there is still a positive effect, it is smaller.
Population density shows a larger negative effect than in the pedestrian casualty models. This may be largely because areas that are denser in population will tend to have slower traffic speeds. This parameter is also more robust in the models without the offset variable (Table 2). Employment density has a much smaller positive effect than in the pedestrian casualty models.
The road density variables all show positive and significant effects. In these models we include the density of freeways and turnpikes as opposed to ramp and jughandle density. This was largely because these variables were correlated (correlation coefficient is 0.537) and showed some interaction in preliminary models that we estimated. Theoretically it makes more sense to include motorway density as this is where motor-vehicles have the largest share of their mileage. In these models we do see more of a pattern where higher functional classifications tend to be associated with more motor-vehicle casualties. This may partly be due to more vehicle mileage occurring on the higher order roads. This result is also apparent in the model without an offset variable.
We calculated Moran's I for both dependent variables to determine whether there is potential spatial correlation in the data. The test was statistically significant in both cases, thus this leads us to conduct a Bayesian estimation of a negative binomial conditional auto regressive model (Besag et al., 1991).
6. Bayesian analysis results
Several studies have used Bayesian inference methods to correct for spatial correlation in negative binomial count models (Aguero-Valverde and Jovanis, 2006; Levine, 2011; Quddus, 2008). We used Crimestat to estimate a Bayesian negative binomial conditional auto regressive model (Besag, 1974; Levine et al., 2010) implemented with a Markov Chain Monte Carlo (MCMC) simulation.
The advantage of Bayesian analysis with spatial count data is that it provides a correction for spatial autocorrelation giving us greater confidence in our estimates. But more fundamentally, Bayesian analysis produces a distribution of parameter estimates, which delivers more information for the analyst. The interpretation of results thus allows us to specify the probability that the parameter estimate falls within a certain range, known as a credible interval, as opposed to confidence intervals in classical statistics. Confidence intervals only allow us to claim that multiple experiments will lead to the same result a given percent ofthe time, 95% ofthe time in the case of 95% confidence intervals, not that the parameter estimate is within the 95% confidence interval for a given estimate. Bayesian analysis, on the other hand, generates what is known as a credible interval; therefore, a 95% credible interval means that there is a 95% probability that the estimate lies within the interval. Bayesian analysis thus provides a much more intuitive interpretation of the results and greater insights (O'Hagan and Luce, 2003). One can also specify prior information; as discussed previously we use uninformed priors for the distribution and our maximum likelihood estimates as prior coefficients.
The Bayesian negative binomial CAR results are shown in Table 3 for the pedestrian casualty models and Table 5 for the motorvehicle models (Tables 4 and 6 show the same models, but without an offset variable). The tables display the model coefficient (mean) and the 95% credible interval. The G–R statistic which signifies
Table 4 Bayesian model output – pedestrian casualties, no off-set.
| Pedestrian casualties (1) | Pedestrian casualties (2) | Pedestrian casualties (3) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | ||||
| 2.5% | 97.5% | 2.5% | 97.5% | 2.5% | 97.5% | |||||||
| Intercept | 0.166 | −2.112 | 2.565 | 1.210 | −1.402 | −2.105 | −1.205 | 1.020 | 3.297 | 0.841 | 5.945 | 1.212 |
| ln(% HH with no vehicle) | 0.315 | 0.192 | 0.438 | 1.051 | 0.362 | 0.252 | 0.472 | 1.006 | ||||
| ln(HH income) | −0.150 | −0.349 | 0.040 | 1.210 | −0.461 | −0.670 | −0.267 | 1.206 | ||||
| ln(population density) | −0.081 | −0.175 | 0.014 | 1.021 | −0.105 | −0.200 | −0.008 | 1.020 | 0.012 | −0.077 | 0.100 | 1.052 |
| ln(employment density) | 0.193 | 0.130 | 0.257 | 1.006 | 0.195 | 0.130 | 0.260 | 1.005 | 0.217 | 0.153 | 0.282 | 1.005 |
| ln(US highways/sqmile) | 0.255 | 0.014 | 0.501 | 1.001 | 0.308 | 0.061 | 0.560 | 1.000 | 0.241 | −0.004 | 0.493 | 1.001 |
| ln(NJ state hwy/sqmile) | 0.169 | −0.014 | 0.354 | 1.001 | 0.180 | −0.010 | 0.371 | 1.001 | 0.166 | −0.024 | 0.357 | 1.001 |
| ln(county 500 hwy/sqmile) | 0.209 | 0.018 | 0.402 | 1.000 | 0.227 | 0.031 | 0.426 | 1.000 | 0.236 | 0.039 | 0.435 | 1.001 |
| ln(county 600 hwy/sqmile) | 0.163 | 0.028 | 0.298 | 1.001 | 0.176 | 0.040 | 0.313 | 1.001 | 0.178 | 0.040 | 0.317 | 1.001 |
| ln(ramps and jughandles/sqm) | 0.067 | −0.159 | 0.297 | 1.001 | 0.108 | −0.127 | 0.346 | 1.000 | 0.068 | −0.174 | 0.313 | 1.002 |
| Model Stats | ||||||||||||
| N | 6460 | 6460 | 6460 | |||||||||
| Average sample size | 805.6 | 796.68 | 801.08 | |||||||||
| Log likelihood | −9316 | −9327 | −9423 |
Note: All models were run with 100,000 iterations, 20,000 "burn-in" iterations and 25 samples.
Table 5 Bayesian model output – motor vehicle casualties.
| Motor-vehicle casualties (4) | Motor-vehicle casualties (5) | Motor-vehicle casualties (6) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Model Coef. | interval | 95% credible | Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | ||||
| 2.5% | 97.5% | 2.5% | 97.5% | 2.5% | 97.5% | |||||||
| Variable | ||||||||||||
| Exposure: ln(population) | ||||||||||||
| Intercept | 3.350 | 1.618 | 5.117 | 1.101 | 3.432 | 2.991 | 3.879 | 1.008 | 4.821 | 3.229 | 6.565 | 1.089 |
| ln(% HH with no vehicle) | 0.140 | 0.060 | 0.230 | 1.028 | 0.135 | 0.063 | 0.208 | 1.003 | ||||
| ln(HH income) | −0.010 | −0.143 | 0.151 | 1.100 | −0.135 | −0.272 | −0.009 | 1.087 | ||||
| ln(population density) | −0.536 | −0.599 | −0.473 | 1.008 | −0.530 | −0.595 | −0.467 | 1.008 | −0.500 | −0.559 | −0.442 | 1.023 |
| ln(employment density) | 0.090 | 0.047 | 0.136 | 1.003 | 0.086 | 0.042 | 0.130 | 1.002 | 0.100 | 0.056 | 0.145 | 1.003 |
| ln(US highways/sqmile) | 0.500 | 0.321 | 0.678 | 1.001 | 0.515 | 0.343 | 0.695 | 1.000 | 0.480 | 0.305 | 0.661 | 1.001 |
| ln(NJ state hwy/sqmile) | 0.400 | 0.270 | 0.531 | 1.000 | 0.409 | 0.280 | 0.542 | 1.000 | 0.396 | 0.269 | 0.527 | 1.001 |
| ln(county 500 hwy/sqmile) | 0.300 | 0.156 | 0.457 | 1.000 | 0.292 | 0.145 | 0.443 | 1.000 | 0.295 | 0.148 | 0.445 | 1.000 |
| ln(county 600 hwy/sqmile) | 0.170 | 0.072 | 0.275 | 1.001 | 0.161 | 0.059 | 0.264 | 1.000 | 0.179 | 0.077 | 0.281 | 1.000 |
| ln(freeways-turnpikes/sqm) | 0.590 | 0.440 | 0.742 | 1.001 | 0.589 | 0.443 | 0.742 | 1.000 | 0.583 | 0.437 | 0.735 | 1.001 |
| Model Stats | ||||||||||||
| N | 6460 | 6460 | 6460 | |||||||||
| Average sample size | 807.4 | 805.84 | 813.2 | |||||||||
| Log likelihood | −20,912 | −20,914 | −20,944 |
Note: All models were run with 100,000 iterations, 20,000 "burn-in" iterations and 25 samples.
Table 6 Bayesian model output–motor vehicle casualties, no off-set.
| Motor-vehicle casualties (4) | Motor-vehicle casualties (5) | Motor-vehicle casualties (6) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | Model Coef. | 95% credible interval |
G–R Stat | ||||
| 2.5% | 97.5% | 2.5% | 97.5% | 2.5% | 97.5% | |||||||
| Intercept | 5.805 | 4.059 | 7.744 | 1.135 | 5.237 | 4.790 | 5.689 | 1.008 | 6.838 | 5.138 | 8.583 | 1.108 |
| ln(% HH with no vehicle) | 0.134 | 0.047 | 0.219 | 1.039 | 0.135 | 0.062 | 0.208 | 1.003 | ||||
| ln(HH income) | −0.041 | −0.203 | 0.104 | 1.133 | −0.138 | −0.275 | −0.005 | 1.106 | ||||
| ln(population density) | −0.534 | −0.598 | −0.469 | 1.013 | −0.522 | −0.587 | −0.458 | 1.008 | −0.510 | −0.571 | −0.450 | 1.028 |
| ln(employment density) | 0.089 | 0.044 | 0.134 | 1.003 | 0.093 | 0.049 | 0.138 | 1.002 | 0.101 | 0.056 | 0.146 | 1.003 |
| ln(US highways/sqmile) | 0.484 | 0.310 | 0.665 | 1.001 | 0.505 | 0.331 | 0.686 | 1.000 | 0.508 | 0.331 | 0.693 | 1.001 |
| ln(NJ state hwy/sqmile) | 0.399 | 0.271 | 0.530 | 1.001 | 0.395 | 0.265 | 0.529 | 1.000 | 0.420 | 0.289 | 0.555 | 1.001 |
| ln(county 500 hwy/sqmile) | 0.271 | 0.125 | 0.420 | 1.001 | 0.284 | 0.136 | 0.435 | 1.000 | 0.331 | 0.183 | 0.484 | 1.000 |
| ln(county 600 hwy/sqmile) | 0.183 | 0.082 | 0.285 | 1.001 | 0.173 | 0.071 | 0.277 | 1.000 | 0.179 | 0.076 | 0.282 | 1.000 |
| ln(freeways-turnpikes/sqm) | 0.564 | 0.421 | 0.714 | 1.001 | 0.611 | 0.461 | 0.767 | 1.000 | 0.613 | 0.467 | 0.765 | 1.001 |
| Model Stats | ||||||||||||
| N | 6460 | 6460 | 6460 | |||||||||
| Average sample size | 806.44 | 802.72 | 803.52 | |||||||||
| Log likelihood | −21,109 | −21,108 | −21,140 |
Note: All models were run with 100,000 iterations, 20,000 "burn-in" iterations and 25 samples.
Table 7 Relationship between residence area of pedestrian fatality and crash location, by zip code income quintile.
| Income quintile of area where crash occurred |
Total | Percent of total crashes of pedestrians from lower income areas |
Percent of crashes in same income quintile as pedestrian's home |
Crashes in victim's own zip code |
Percent in victim's own zip code |
|||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||||||
| Income quintile of pedestrian's home | ||||||||||
| 1 | 120 | 17 | 15 | 9 | 2 | 163 | 33.40% | 73.62% | 84 | 51.53% |
| 2 | 13 | 83 | 11 | 13 | 5 | 125 | 25.61% | 66.40% | 70 | 56.00% |
| 3 | 6 | 5 | 51 | 8 | 4 | 74 | 15.16% | 68.92% | 38 | 51.35% |
| 4 | 6 | 7 | 3 | 55 | 5 | 76 | 15.57% | 72.37% | 43 | 56.58% |
| 5 | 2 | 4 | 3 | 4 | 37 | 50 | 10.25% | 74.00% | 28 | 56.00% |
| Total | 147 | 116 | 83 | 89 | 53 | 488 | 263 | 53.89% | ||
| % total crashes occurring in quintile |
30.1% | 23.8% | 17.0% | 18.2% | 10.9% |
Income quintiles are defined as follows: 1: <\$44,444; 2: \$44,445–54,114; 3: \$54,116–64,850; 4: \$64,851–79,762; 5: \$79,763 and above.
model convergence is also shown; all are below 1.2, with only a few exceptions, suggesting good convergence.
Recall that this estimation technique is explicitly controlling for spatial effects using a negative exponential decay function. So block groups near each other will affectthe incidence of crashes in nearby block groups. This may represent similar unmeasured spatial characteristics or some effect of how traffic flow is correlated between block groups.
Many results are similar to our maximum likelihood estimates, with a few notable differences. As previously, we see in the pedestrian casualty model that block groups with a larger percent of households with no vehicle consistently have more pedestrian casualties. Lower income areas also have more pedestrian casualties, however when vehicle ownership in the area is controlled for (model 1)the income variable partially spans zero within the credible interval. This suggests that while income effects are for the most part distinct from the level of vehicle ownership in the area, there are some block groups where income does not matter. Because the 95% credible interval represents the probability that the coefficient lies within the interval, in some cases the coefficient is positive; we can say with 80% certainty (based on the 80th credible interval for the income coefficient, −0.261 to −0.020) that it is always negative. In model 3, which excludes household vehicle ownership, the 95% credible interval on income is always negative. These results suggest some interaction between percent of households owning a vehicle and the income of the area; the former variable tends to be more robust and clearly plays a role in pedestrian casualties probably because of more people walking instead of driving in these neighborhoods. This result is the same in the model without an offset (Table 4).
Results for the motor-vehicle crash model (Table 5) show less of an impact of income on casualties. The credible interval in model 4 largely spans zero while the percent of households with no vehicle is positive, although with a smaller effect than for pedestrians. The indeterminate effect of income in this model is distinct from the finding in the maximum likelihood model (Table 1, model 4). When household vehicle ownership is omitted (model 6), income is negative in Table 5. Thus, this result seems to suggest a stronger connection between vehicle ownership and the income level of the block group compared with the pedestrian casualty model.
Population density is negative in all cases except when percent of households with no vehicle is excluded in the pedestrian model, and consistently negative in the motor-vehicle model (both with and without the offset). The maximum likelihood estimates are similar in that population density, while significant in Table 1, model 3, had a much smaller coefficient size. This is a good example of the additional information that a Bayesian analysis can provide, as it suggests a much stronger effect from the correlation between the income of an area and the population density.
Results for employment density in the Bayesian models show a consistent positive effect that higher employment density leads to more pedestrian and motor-vehicle casualties. Again, this was also found in the maximum likelihood estimates and both with and without the offset.
The road category variables are for the most part positive in both models with one exception. Ramps and jughandles very clearly span zero in the 95% credible interval, as opposed to the statistical significance found in the maximum likelihood model of pedestrian casualties (with the offset). This suggests no obvious positive or negative effect on pedestrian casualties. It is likely that the actual impact is very context specific and is in this case affected by the spatial adjustments of the CAR model. The credible intervals on the other road variables show a large degree of overlap in coefficient values so it is not possible to argue that different road functional
Table 8 Relationship between residence area of pedestrian injury and crash location, by zip code income quintile.
| Income quintile of area where crash occurred |
Total | Percent of total crashes of pedestrians from lower income areas |
Percent of crashes in same income quintile as pedestrian's home |
Crashes in victim's own zip code |
Percent in victim's own zip code |
|||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||||||
| Income quintile of pedestrian's home | ||||||||||
| 1 | 2243 | 174 | 93 | 48 | 37 | 2595 | 24.84% | 86.44% | 1590 | 61.27% |
| 2 | 151 | 900 | 82 | 60 | 18 | 1211 | 22.72% | 74.32% | 785 | 64.82% |
| 3 | 69 | 73 | 680 | 60 | 33 | 915 | 19.64% | 74.32% | 613 | 66.99% |
| 4 | 40 | 56 | 55 | 542 | 54 | 747 | 19.77% | 72.56% | 499 | 66.80% |
| 5 | 22 | 30 | 35 | 43 | 384 | 514 | 13.03% | 74.71% | 319 | 62.06% |
| Total | 2525 | 1233 | 945 | 753 | 526 | 5982 | 63.62% | |||
| % total crashes occurring in quintile |
42.2% | 20.6% | 15.8% | 12.6% | 8.8% |
Table 9 Relationship between residence area of motor-vehicle fatality and crash location, by zip code income quintile.
| Income quintile of area where crash occurred |
Total | Percent of total crashes of drivers from lower income areas |
Percent of crashes in same income quintile as driver's home |
Crashes in victim's own zip code |
Percent in victim's own zip code |
|||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||||||
| Income quintile of pedestrian's home | ||||||||||
| 1 | 369 | 190 | 109 | 84 | 28 | 780 | 27.01% | 47.31% | 196 | 25.13% |
| 2 | 105 | 345 | 123 | 114 | 25 | 712 | 24.65% | 48.46% | 174 | 24.44% |
| 3 | 70 | 94 | 254 | 113 | 50 | 581 | 20.12% | 43.72% | 130 | 22.38% |
| 4 | 41 | 76 | 89 | 243 | 77 | 526 | 18.21% | 46.20% | 129 | 24.52% |
| 5 | 23 | 28 | 49 | 60 | 129 | 289 | 10.01% | 44.64% | 65 | 22.49% |
| Total | 608 | 733 | 624 | 614 | 309 | 2888 | 694 | 24.03% | ||
| % total crashes occurring in quintile |
21.1% | 25.4% | 21.6% | 21.3% | 10.7% |
Income quintiles are defined as follows: 1: <\$44,444; 2: \$44,445–54,114; 3: \$54,116–64,850; 4: \$64,851–79,762; 5: \$79,763 and above.
classes have different effects either on pedestrian or motor-vehicle casualties.
7. Analysis of victim residence location versus crash location
Results of our individual level analysis are shown in Tables 7 and 8 as cross-tabulations of the residence and casualty location income quintiles for both pedestrian fatalities and injuries. Tables 9 and 10 show results for motor-vehicle crashes. The tables are a cross-tabulation of zip code income quintiles (20%oftotal New Jersey zip code areas are in each quintile). The lowest income zip code areas are grouped in quintile 1 up to the highest income zip code areas in quintile 5. The columns represent the quintile where the casualty occurred while the rows represent the income quintile of where each victim lives. Thus, the diagonal represents those casualties that were in the same income quintile as where the victim lives (although not necessarily where they live). The percent of fatalities or injuries in the income-equivalent quintile are calculated and shown in a labeled column on the right side of the table. The percent of fatalities or injuries that occurred in the victim's home zip code area are also presented in a separate right-hand column. The bottom row shows the percent of fatalities or injuries in each quintile. This analysis includes only victims who live in New Jersey, excluding victims from other states.
Table 7 shows pedestrian fatalities and shows that more fatalities occur in the lower income quintiles (30.1%) and those that are victims tend to be from lower income areas (33.4%) versus a much smaller percent (10.25%) from higher income zip codes. For pedestrian injuries (Table 8) proportionally more injuries occur in lower income areas (42.2%) but the difference between the income quintiles of the victim are much less for the first four quintiles. The table also displays the percent of crashes that fall along the diagonal, i.e., those where the crash is reported in a zip code area that has the same income range as where the victim lives. For pedestrian fatalities (Table 7) there is no clear pattern while for pedestrian injuries (Table 8), there is a somewhat greater chance that a person from the lowest income zip code is a victim in a low income area. The final column displays the percent who are victims in the zip code area where they live. The majority of pedestrian injuries in all cases are victims near where they live, though somewhat less for pedestrian fatalities. This may suggest that pedestrians are more at risk in areas they are unfamiliar with.
Overall, these results for pedestrian fatalities and injuries suggest that lower income areas are at greater risk, for both fatalities and injuries. There is also a slight difference based on the individual home zip code, with those from lower income areas being at greater risk of being killed, but less evidence of this for pedestrian injury crashes. The pattern in terms of whether people are victims near their home appears constant regardless of the income quintile of the zip code; there is evidence, however, that lower income individuals are more likely victims in zip codes of the same income quintile. This may be because they are more likely to walk, supporting our multivariate analysis that those areas with less household car ownership may have more pedestrian casualties.
For comparison, Tables 9 and 10 provide results for the same analysis for motor-vehicle fatalities and injuries. These results do not provide evidence that lower income areas are at greater risk, although the highest income zip codes have the lowest proportion of both fatalities and injuries. Those who reside in lower income zip codes, however, appear to be at greater risk of both fatalities and injuries and it is not apparent that there is any pattern in how these occur in zip codes of the same income level. Fatalities and injuries in motor-vehicles are less likely to occur in one's home zip code, compared to pedestrian crashes.
Table 10 Relationship between residence area of motor-vehicle injury and crash location, by zip code income quintile.
| Income quintile of area where crash occurred |
Total | Percent of total crashes of drivers from lower income areas |
Percent of crashes in same income quintile as driver's home |
Crashes in victim's own zip code |
Percent in victim's own zip code |
|||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||||||
| Income quintile of pedestrian's home | ||||||||||
| 1 | 12,375 | 3915 | 2861 | 1930 | 1064 | 22,145 24.84% | 55.88% | 6607 | 29.84% | |
| 2 | 3378 | 10,229 | 3182 | 2510 | 955 | 20,254 22.72% | 50.50% | 6002 | 29.63% | |
| 3 | 2053 | 2689 | 8090 | 2963 | 1715 | 17,510 19.64% | 46.20% | 5122 | 29.25% | |
| 4 | 1577 | 2173 | 2774 | 8303 | 2798 | 17,625 19.77% | 47.11% | 5040 | 28.60% | |
| 5 | 690 | 760 | 1442 | 2384 | 6339 | 11,615 13.03% | 54.58% | 3526 | 30.36% | |
| Total | 20,073 | 19,766 | 18,349 | 18,090 | 12,871 | 89,149 | 26,297 | 29.50% | ||
| % total crashes occurring in quintile |
22.5% | 22.2% | 20.6% | 20.3% | 14.4% |
This individual level analysis to some extent supports the multivariate spatial analysis in thatthe income of areas and our proxy for personal income suggest that lower income areas and those who have lower incomes are more likely to be pedestrian fatalities, with a smaller difference in injury occurrence. Lower income individuals are also at greater risk as motor-vehicle drivers and occupants, with less evidence that lower income areas are associated with motorvehicle risk. One caveat of this analysis is that it does not control for other factors, and in particular there is no control for exposure or the details of the road network.
8. Conclusions
The main question this paper has tried to address is whether lower income areas tend to have more pedestrian casualties. The answer is clearlynot definitive, as other factors appear toplay a role, based on our spatial regression analysis. Motor-vehicle casualties, for the most part, follow a similar pattern to pedestrian casualties. The level of household vehicle ownership within an area appears to be an important factor in both cases, and while intuitively this is appealing for its relationship to pedestrian casualties, it is not clear why this is a factor in motor-vehicle casualties.
Other control variables appear to have expected effects, such as higher population density tending to reduce casualties, and higher employment density tending to increase casualties. Population density appears to also be somewhat correlated with the income of an area. Road variables, with the exception of ramps and jughandles, all have a positive and statistically significant effect, although there seems to be no pattern of effect associated with the functional class of road, especially as shownintheBayesiananalysis where the credible intervals all overlap.
The conditional autoregressive model to control for spatial correlation provides minor differences in results. One of the main differences is that when we account for spatial autocorrelation, the statistical significance of ramp and jughandle density disappears. In addition,the Bayesian approach provides amore intuitively appealing interpretation of results, as it provides ranges of parameter estimates within a given credible interval. We also examined models with and without population as an offset variable. Results are generally comparable on our key variables of interest, and while there are some minor differences in results, these tend not to change our overall conclusions and the models appear robust to inclusion or exclusion of the offset variable.
Finally, our disaggregate analysis of fatalities and injuries for both pedestrians and motor-vehicle crashes was intended to determine more clearly whether lower income individuals are more at risk or whether there is something inherent about lower income areas that leads to more risk. Our results suggest that for pedestrian crashes it is both the area that causes greater risk, and the likely income level (or quintile) of the victim (especially for fatalities). For motor-vehicle casualties, the income of the area matters less, although the highest income areas have relatively fewer fatalities and injuries. The income quintile of the motor-vehicle victim appears to matter with lower income individuals being at greater risk. This disaggregate analysis saysnothing abouthow incomemay play a role in both area-based risk and individual risk. Presumably individual income levels are representing various socio-economic factors that are not controlled for, while area-based income may represent deficiencies in how pedestrian infrastructure is provided. While our results support the hypothesis that lower income areas have more pedestrian casualties, this is clearly still an area for further study to understand the precise mechanisms at play.
Acknowledgements
We acknowledge the assistance of Sarah Weissman formerly from Rutgers Center for Advanced Infrastructure and Transportation for explaining the Plan4Safety data. Patrick Brennan and Bahareh Sehatzedeh provided valuable assistance in early stages of this research. Partial funding was provided by the Region 2 University Transportation Research Center. All remaining errors and omissions are the responsibility of the authors.
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