A Safe Location for a Trip? How the Characteristics of an Area Affect Road Accidents—A Case Study from Poznań

Abstract

The frequency of road accidents in specific locations is determined by a number of variables, among which an important role is played not only by common determinants such as inappropriate behavior of road users, but also by external factors characterizing a given location. Taking this into account, the main objective of the study was to answer the question of which variables determine that the intensity of car accidents is higher in certain parts of the city of Poznań compared to other locations. The study was based on source data from the police Accident and Collision Records System (SEWiK). For the purposes of the analysis, two variants of the regression method were used: ordinary least squares (OLS) and geographically weighted regression (GWR). The obtained results made it possible to identify variables that increase the likelihood of a traffic accident in specific parts of the city, and the variables that proved to be statistically significant include the size of the built-up area and the number of traffic lights. The results obtained using the GWR technique indicate that the way in which the analyzed features influence road accidents can vary across the city, which may emphasize the complexity of the analyzed phenomenon. The results can be used by relevant entities (transport traffic planners and many others) to create road safety policies.

1. Introduction

1.1. Road Accidents and Public Health

Road accidents are a serious problem in the context of ensuring sustainable public health, and reducing their impact while increasing the number of road users remains a fundamental goal and global challenge. According to the WHO report “Global Status Report on Road Safety 2023” [1], it is estimated that around 1.2 million people die in road traffic accidents worldwide every year, and as many as 50 million are injured. Such a huge number of casualties directly affects the efficiency of the health service in many countries. For example, in developing countries, accident victims account for a “burden” of 30 to 70% of orthopedic beds. Road accidents are the leading killer for both children and youth aged 5 to 29 years (as of 2019). Particularly relevant in the context of the sustainable social and economic development of societies is the fact that two-thirds of the deaths affect people of working age (18–59 years), which can impact national economies.

It is worth noting that in 2021, there were fewer road fatalities worldwide (1.19 million) compared to 2010 (1.25 million). This may be due, among other things, to the technological development of vehicle safety systems and the tightening of penalties for non-compliance with traffic regulations in many countries. Considering the continuous increase in the number of motor vehicles, the significant development of the road network, and the increase in the world population, this statistic should be considered a positive phenomenon. The measures taken to improve road safety are producing the expected effect. However, in order to implement the provisions of the United Nations Decade [2], which include halving the number of fatalities by 2030, these efforts should be clearly expanded and intensified, especially in the context of the most common factors increasing the risk of accidents: driving under the influence of alcohol, speeding, and the use of helmets (cyclists), seat belts, and car seats (children).

A special group that is particularly vulnerable to the consequences of road accidents are victims who are not traveling on four-wheeled vehicles (pedestrians, cyclists, motorcyclists)—more than half of all fatalities are in this group. Of the remaining groups, the following are of particular importance: people traveling on four-wheeled vehicles (approx. 30% of fatalities) and public transportation and truck users (approx. 20% of fatalities). It should also be noted that more and more victims are people using new forms of transportation (e.g., electric scooters). The increase in the demand for mobility and urban development will lead to overloading of the motorized transport systems in many countries, which will most likely lead to an increase in the number of fatalities in the first group.

It is also clear that mortality is also related to the economic status and geographical location of a country. The vast majority of victims (9 out of 10) are in countries with low or medium GDP. Nearly 30% of all road accident deaths occur in Southeast Asia, while the percentage is by far the lowest in Europe—5% of all road accident deaths. It is worth noting that the number of deaths in Europe decreased by 36% between 2010 and 2021. At the other end of the spectrum is Africa, where, unlike the other continents, the number of deaths has increased by 17%. The difference between these two regions may be due to the fact that, in general, European countries put safety and people at the center of their mobility systems, and legislation is based on these factors.

Taking the above into account, it seems extremely important to identify the objective factors determining the occurrence of events (road accidents) leading to serious injury or death of the injured persons. Identifying these factors and then trying to eliminate them can bring many benefits, from minimizing the number of victims to having a positive impact on the economies of many countries. In summary, on a global scale, identifying the determinants that reduce the likelihood of traffic accidents in countries/regions with low traffic accident mortality (Europe) and then trying to implement these rules and solutions in countries that clearly need changes in this area (e.g., Africa) can have a positive effect. These solutions could serve as a guide for many responsible parties, such as legislators and planners, and their application in specific locations could contribute to the realization of the aforementioned United Nations Decade goals.

1.2. Factors Determining Accidents—Literature Review

Considering the huge impact of road accidents on public health, this phenomenon has been the subject of many scientific studies for many years [3,4,5]. With the continuous development of the automotive industry, the number of people injured in accidents is also increasing, which has led to a growing interest in improving the safety conditions for road users. Consequently, the issue of identifying factors contributing to road accidents has gained importance in recent years, as confirmed by the extensive literature on the subject. Some of the first pioneering studies whose primary objective was to identify the causes of road accidents date back to the second half of the 20th century, which is connected to the development of this form of transport [6,7,8].

According to the existing literature, it can be seen that the real causes of accidents fall into two groups, namely, human and environmental, and the indicators belonging to the first group are clearly more important [9]. In the aforementioned study covering 450 accidents, 77% of them were attributable to human error (driver, pedestrian, or passenger). Within this group, the most significant element was the driver, who was responsible for the majority of accidents, and the main cause was speeding and careless driving. The factors belonging to the second group (environmental) were of marginal significance in the study in question and accounted for a small proportion of all incidents, e.g., in the case of weather conditions, it was only 8.4%. The relationship presented in this way can be seen in many other studies that present the human factor as the main cause of road accidents.

Within these studies, it is clear that one of the main determinants is driving under the influence of alcohol or other intoxicating substances [10,11,12,13]. Due to the never-ending interest of young people in drugs, this problem may become more significant in the coming years. The second important factor is the behavior of the driver themselves. Excessive speeding, overtaking in the wrong places, falling asleep at the wheel, or using electronic devices while driving are other determinants that are taken into account in contemporary research [14,15,16]. According to current knowledge, the occurrence of these factors can also be directly related to the characteristics of the driver. Research has confirmed that both the age and gender of the driver can determine the number of accidents. In general, drivers with more years of experience have a significantly lower accident rate [17]. Despite the fact that men and women spend a comparable amount of time on the road, almost twice as many men are involved in road accidents [18].

In reference to the previous division of characteristics, many works also consider external factors that do not belong to the group of human determinants. These studies most often take weather conditions into account, and the variables that are analyzed include temperature and humidity [19], precipitation [20], and the occurrence of other adverse phenomena such as fog [21]. Many studies on this topic take a broader perspective and examine the spectrum of climate change rather than a single selected issue [22,23,24]. The conclusions of this research are ambiguous, so caution should be exercised when interpreting them. However, the results from the studies usually indicate that the number of accidents can be positively influenced by the reduction in the number of frosty days due to global warming, while in some parts of the world, the increased amount of rainfall can have a negative impact on safety. Furthermore, characteristics within this group are related to the seasons as well as time periods during the day [25,26,27]. The results are also ambiguous, and the number of accidents in individual months is comparable to a slight increase in intensity during the summer months and a lower frequency at night due to traffic intensity, which can be a determining factor in the occurrence of accidents [28].

The variables mentioned seem to be sufficiently verified in the literature on the subject, and their impact on the number and frequency of accidents is clear. To the best of my knowledge, however, there is a lack of definitive studies within Polish cities in the literature on the subject that would indicate the locational determinants of road accidents. Regarding the term location, I define variables that determine that within a specific area of research, individual locations are characterized by a significantly higher frequency of events compared to other “quieter” places. In the context of the fact that, according to forecasts, by 2050 almost 70% of the Earth’s population will live in cities, it seems crucial to find the characteristics that are significant within urban agglomerations because the probability of road accidents in these places due to greater traffic intensity will most likely be increased. These findings make it possible to identify places potentially exposed to road accidents earlier. Gaining this knowledge would result in a reduction of victims.

Therefore, the main objective of the study was to analyze the spatial determinants affecting the number of road accidents. The analysis was carried out in one of the largest Polish urban centers—the city of Poznań. The research included identifying the variables determining the frequency of accidents in specific parts of the city defined by the boundaries of cadastral districts. In order to achieve the set purpose, statistical methods were used, including Moran’s global statistics, ordinary least square regression, and geographically weighted regression. The analyzed parts of the city differ in size, road network density, building area, length of footpaths and cycle paths, the number of pedestrian crossings, and other characteristics.

2. Materials and Methods

2.1. Characteristics of the Research Area

For the purposes of this study, an area located within the administrative boundaries of the city of Poznań, which is situated in the western part of Poland, was selected for analysis (Figure 1). The city is the capital of the Wielkopolskie Voivodeship and is the socio-economic center of the Poznań agglomeration, which shapes the dynamics of development not only of Poznań but also of neighboring administrative units directly related to it. In terms of size, Poznań is ranked eighth among the largest Polish cities with an area of 262 km². Structurally, the city is divided into 40 cadastral districts, which differ in terms of land use and surface area. The largest district, Kobylepole, covers an area of 13.78 km², while the smallest, Daszewice, only 0.06 km² (Figure 1). Considering the configuration of the conducted study, cadastral districts are a key element because it is for these units that the characteristics determining the frequency of road accidents have been determined.

According to data from the Central Statistical Office, the city’s population in June 2024 was 536,818. Detailed information about population are presented in

Table 1. Population statistics.

Population—Total	Population by Gender	Demographic Structure
536,818	Women—286,333 Men—250,485	Pre-working age—69,859 Working age—336,968 Post-working age—129,991

.

In terms of population, it should be emphasized that, contrary to the general trends in the whole country, the population of Poznań has been clearly increasing in recent years (in 2021 it was 529,410 people (an increase of 1.5%)). In contrast, during the same period of time, the population of the whole country decreased by almost 300,000 people. Unfortunately, this trend may not be reflected in the future. This is due, among other things, to the worrying forecasts made on the basis of the National Census by the Central Statistical Office. According to the latest forecast, developed in 2022, the population of Poland will decrease by 17.5% by 2060, and Poznań will be one of the most depopulating Polish cities with a population decline of 22% in the same period.

The transportation sector plays one of the key roles in the city’s economic system. It can be divided into two categories: private and public transportation. According to the report “Transport in Poznań” [29], the number of all registered cars in Poznań in 2023 amounted to almost 561,000 (a number greater than the total population of the city). The vast majority were, of course, passenger cars (78.5%), which resulted in 820 such vehicles per 1000 inhabitants. Over the years, it is clear that passenger cars have been gaining popularity among residents. In 2017, there were about 360,000 registered cars, and in 2023, there were already 440,000. Other forms of transportation such as trucks, motorcycles, and scooters maintained a comparable number of vehicles over time without a clear growth.

However, public transportation seems to be a key element of the transportation system. In total, 251.7 million passengers used buses and trams in 2023, and after a significant drop in 2020 (173 million) due to the COVID-19 pandemic, this figure is returning to pre-pandemic levels. The length of the tram routes within the city limits is 72.7 km, and that of all bus routes is 356.0 km. These values are constantly increasing, which may indicate that the government is aware that there is a real need to develop this form of transport. The system is complemented by 10 buffer parking lots, which offer a total of 1238 parking spaces. Since 2021, there have also been 4 Park&Ride parking lots available, which guarantee 337 parking spaces. This is especially important for people from neighboring municipalities who commute to work in the city center. This type of infrastructure allows for free travel, without wasting time in traffic jams, especially during rush hours.

2.2. Research Material

In this study, I used data on traffic accidents from the police’s Accident and Collision Records System (SEWiK). These data were collected and aggregated by the Motor Transport Institute—Polish Road Safety Observatory, which makes it available for road transport monitoring. From the point of view of the analysis carried out, it is extremely important that the database in question contains a range of detailed information about individual accidents. This includes information about the exact location, time of the incident, type of accident, participants, and any casualties. After taking the time criterion into account, as I wanted to identify the contemporary conditions of road accidents, all incidents that took place within the city in 2023 were included in the analysis. As a result, the selected data set contained a total of 537 road accidents on the basis of which the analysis was carried out. The vast majority of incidents took place in the central or western parts of the city in districts such as Łazarz, Jeżyce, Poznań, or Wilda (Figure 2).

Undoubtedly, the highest number of accidents involved interactions between vehicles (mostly passenger cars) and pedestrians, cyclists, and other road users. Incidents of this kind accounted for 56% of all accidents. Collisions involving only motor vehicles (cars, trucks, buses, etc.) without the involvement of pedestrians or cyclists accounted for 34%, and road incidents without the involvement of motor vehicles accounted for 10% of all accidents. The time of year and the time of day also seem to be significant factors in the frequency of accidents. First, it can be seen that a large proportion of accidents occurred in the summer months (40%), while the lowest number was observed in the winter months (26%). In the context of the meteorological situation in Poland in different seasons, this may seem incomprehensible. Most likely, however, the heavy road conditions in winter made road users more vigilant and careful, while the good driving conditions in summer made drivers “relaxed”, which may have resulted in a higher number of accidents. The time of day also determined the frequency, with the least number of incidents naturally occurring at night (6%), and the remaining accidents evenly distributed over the other parts of the day. On a city-wide scale, it should be emphasized that a small number of accident participants were identified as driving under the influence of alcohol (5%), and speeding or not adapting to the prevailing road conditions were more important (15%). Both of these factors occurred together in only 7 incidents (

Table 2. Quantitative characteristics of traffic incidents.

Indicator	Classification Criterion	Number
Participants	Only vehicles (cars, trucks, bus)	183
	Vehicles, pedestrians, cyclists	301
	Other (without cars)	53
Part of the year	January–April	139
	May–August	214
	September–December	184
Time of day	6:00–14:00	250
	14:00–22:00	253
	22:00–6:00	34
Type of accident	Alcohol	27
	Speed	82
	Other	428

).

A positive phenomenon seems to be the regularity according to which the vast majority of participants in the analyzed accidents suffered only minor injuries (370 records). Incidents in which at least one person suffered serious injuries, defined in the database below primarily by health problems lasting more than 7 days, amounted to 158 records (29%). Although every fatal accident is a serious problem, it should be emphasized that such accidents were marginal in the analyzed database with only 9 events (1.7%), which is objectively a positive phenomenon. The spatial distribution of fatal accidents across the city is relatively even, with the exception of the eastern districts, where there are significantly fewer accidents than in other parts of the city. This may be related to differences in land use (differences in the size of urbanized areas) (Figure 3).

2.3. Methodology

The initial statistical analysis of the collected data included, first of all, the calculation of basic descriptive statistics for both the dependent and independent variables. This allowed for the identification of initial differences, minimum and maximum values, and the determination of distribution (for the analyzed variables) in individual parts of the city. The selected features were then subjected to a correlation analysis, which had a two-fold purpose. First, it aimed to determine the initial identification of the sources of accident rate. Second, based on its results, it aimed to exclude variables characterized by a very strong linear dependence on other independent variables (over 90%) from further analysis. This assessment was made on the basis of Pearson’s linear correlation coefficient calculated from the formula:

$$r(x,y)={\displaystyle \frac{cov(x,y)}{\sigma x\times \sigma y}},$$

(1)

where

• cov(x,y) = E(x × y) − [E(x) × E(y)],
• $r\left(x,y\right)$—r-Pearson correlation coefficient between applied variables x and y,
• cov(x,y)—covariance between the applied variables x and y,
• σ—standard deviation,
• E—expected value.

The primary objective of the study was to identify the variables that determine the rate of traffic accidents in individual districts of Poznań in 2023. This task was carried out in the first stage using ordinary least squares (OLS) regression analysis. This method is one of the basic methods of linear modeling of the relationship between the dependent variable (number of road accidents—in the study) and a series of independent variables. According to the theoretical concept of this technique, these relationships can be defined by a straight line for which the y values are estimated by the x values (characteristics). Considering the modeling accuracy, it is important that the sum of the squares of the estimated parameter errors is as small as possible [30]. The dependent variable in the model can be presented in logarithmic form if the condition of normal distribution is not met. In summary, the OLS regression model can be presented according to the following formula:

$$Y={\beta }_0+{\Sigma }_{i=1}^K{\beta }_i{X}_i+\epsilon$$

(2)

where

• Y—number of road accidents in a cadastral district,
• ${\beta }_{0 }$…… ${\beta }_i$—regression coefficients,
• $X_{1 }$…… $X_i$—values of the analyzed parameters,
• $\epsilon$—standard error.

The OLS technique is often referred to as a global method due to the fact that it can be used to formulate universal dependencies for the analyzed phenomenon in non-uniform locations [31]. As a consequence, obtaining representative analyses specific to a given location is problematic and very often impossible. This leads to the impossibility of identifying variables that are crucial in a specific location. It should also be noted that the results obtained using the OLS technique may be biased due to the heterogeneity of the spatial relationship of a given attribute across the entire study area. Furthermore, the number of accidents at a certain location can often depend on the frequency of events in the immediate vicinity. This phenomenon is called spatial autocorrelation and can affect not only the dependent variable but also the independent variables. In such a situation, it may not be sufficient to determine the common dependencies within the analyzed set, and it may be necessary to apply other techniques. In the case of the analyzed data set, whether the number of events in specific recording areas is subject to spatial autocorrelation was assessed using Moran’s I test, which is used to verify H₀: the spatial distribution of the analyzed feature is completely random. The global Moran’s I statistic was calculated according to the following formula:

$$I={\displaystyle \frac{N}{{\Sigma }_i{\Sigma }_j{w}_{ij}}}{\displaystyle \frac{{\Sigma }_i{\Sigma }_j{w}_{ij}{(X}_i-\overline{X}){(X}_j-\overline{X})}{{{\Sigma }_i(X}_i-\overline{X}{)}^2}}$$

(3)

where

• I—Moran’s I global statistics index,
• $X_{i }$—value of an attribute of an object i,
• $X_{j }$—value of an attribute of an object j,
• $N$—number of objects,
• $w_{ij}-$ connection weights of objects i and j.

The null hypothesis is verified based on the evaluation of the Z-score and p-value obtained by the structural analysis tools. The Z-score is a standardized value of the Moran’s I statistic and indicates how much the result deviates from the expected average value (it is a multiple of the standard deviation). The p-value is the probability of making a mistake when rejecting the null hypothesis. If the p-value is very small, it means that it is very unlikely that the observed spatial structure is the result of random processes. The Z-score is calculated according to the following formula:

$$Z={\displaystyle \frac{I-\mu }{\sigma }}$$

(4)

where

• Z—Z-score value,
• I—Moran’s I Global Statistics Index,
• $\mu$—E(I)—expected value I,
• $\sigma$—standard deviation of a random variable I.

Considering the results of Moran’s I test, I applied geographically weighted regression (GWR) analysis later in the paper, which is a kind of solution to the problem of spatial autocorrelation. The method, which can be considered as an extension of traditional OLS regression, was proposed in 1996 [32]. The main difference is that GWR allows for the estimation of local coefficients based on samples within a certain location band. Taking this into account, the GWR model can be represented by the following formula:

$$Y={\beta }_0(x_i,y_i)+{\Sigma }_{i=1}^K{\beta }_i(x_i,y_i)X_i+\epsilon$$

(5)

where

• $x_i,y_i$—geographical coordinates of the i-th object,
• ${\beta }_0(x_i,y_i)$—location-specific intersection object,
• ${\beta }_i(x_i,y_i)$—regression coefficient relevant to the location of the given object,
• $X_i$—variable related to the coefficients ${\beta }_i(x_i,y_i)$,
• K—number of estimated parameters,
• $\epsilon$—standard error.

The coefficients in the GWR model are estimated in a way that is comparable to classical techniques, and the difference that weights that depend on the location of the individual observations are taken into account in this process:

$${\beta }^{^}\left(x_i,y_i\right)={\left(X^{T}W\left(x_i,y_i\right)X\right)}^{-1}{X}^{T}W\left(x_i,y_i\right)y$$

(6)

where $W\left(x_i,y_i\right)$ is a diagonal matrix of weights, which are a function of the distance between the location given by the coordinates $\left(x_i,y_i\right)$ and the location of each object where the observation occurred.

The weights are usually determined by a function similar to the Gaussian curve, taking into account the bandwidth of the parameters that define the spatial range from which the observations are taken into account in the calculation. The results of the GWR approximate the global model as a result of the wider bandwidth. The GWR model produces a series of objects or points defined by the estimated parameters. This makes it possible to observe the variation of these parameters within the analyzed area.

In summary, the local model (GWR) can be interpreted as a special case of the global model (OLS). The most significant difference between the compared models is the assumption that the parameters in the global model are interpreted as constants, while the coefficients in the local model vary spatially. A key element in the implementation of GWR is the calibration of the equation, during which it is assumed that the observations occurring in the immediate vicinity of a given object have a significantly greater impact on the estimation of parameters compared to data located at a greater distance because closer observations have a greater weight than observations located further away [33,34,35,36].

3. Results

3.1. Characteristics of the Variables Included in the Analysis

The variables included in the analysis can be organized into two main groups. The first group includes variables that characterize the land use structure of the analyzed cadastral districts (AR (area—km²), BA (developed area—% [scale 0–1]), GA (green area—% [scale 0–1])). The second group includes variables that characterize the transportation infrastructure of a given district, both in terms of its quality and the presence of accompanying infrastructure (RD (road network density—km/km²), PBD (walking and cycling infrastructure density—km/km²), RQ (roads with the best quality (bituminous mass)—% [scale 0–1]), CS (number of public transport stops), PN (number of car parks), LN (number of traffic lights), SN (number of ‘STOP’ road signs), LAN (number of road lighting installations), RON (number of important intersections—roundabout, junction), and CN (number of road crossing)). These variables were selected based on a review of the literature [37,38,39,40], the availability of city-wide data, and the conclusions of the report of the Traffic Office of the Police Head Office: “Road Accidents in Poland in 2023” [41].

First, a synthetic characterization was made for the adopted variables, taking into account the dependent variable (DV), within which basic descriptive statistics were calculated, including the mean ($\overline{x}$), standard deviation (σ), median (Me), and maximum (Max) and minimum (Min) values. The average number of accidents in a single registration area was 13.38, while the median was 8.50. The highest number of accidents was recorded in the Łazarz registration area, and the lowest was noted in six areas (Daszewice, Wielkie, Psarskie, Piotrowo, Głuszyna II, and Radojewo), with 64 accidents and 0 observations, respectively. The collected data clearly indicate a significant difference in the development and quality of road infrastructure in different parts of the city (

Table 3. Descriptive statistics of dependent and independent variables.

Variable	$\overline{\mathit{x}}$	Max	Min	Me	σ
AN	13.38	64.00	0.00	8.50	14.97
AR	6.55	13.78	0.06	5.92	3.48
BA	0.26	0.67	0.00	0.24	0.16
GA	0.19	0.50	0.00	0.20	0.14
RD	10.07	17.41	3.16	9.46	3.71
PBD	5.56	18.94	0.00	2.90	5.35
RQ	0.47	0.77	0.00	0.51	0.18
CS	29.25	82.00	0.00	23.50	20.87
PN	49.75	343.00	0.00	18.00	74.98
LN	34.38	203.00	0.00	15.00	47.76
SN	4.03	19.00	0.00	2.00	5.12
LAN	210.10	688.00	0.00	210.00	193.02
RON	1.40	6.00	0.00	1.00	1.56
CN	260.45	1106.00	0.00	172.50	264.24
Number of observations	537

).

The correlation analysis for the independent variables showed the strongest positive relationships between the features LN and CN (0.872) and RD and BA (0.823). This seems logical and is related to the fact that in the first case, a greater number of intersecting roads must result in a greater number of traffic lights. In the case of the RD and BA features, on the other hand, it is rational that the larger the built-up area is, the greater the density of the road network must be to guarantee convenient access to these areas. The strongest negative correlations were observed for the features GA and RD (−0.376) and GA and BA (−0.391). This is completely understandable and results from the fact that the more green areas there are in a given area, the fewer built-up areas transformed by humans, including roads. The results of the analysis of the correlation between AN and the non-independent variables indicate that most of the features included in the analysis had a positive impact on the number of accidents, with the highest correlation observed for the variable CN (0.876). The exception is the GA feature, based on which it can be preliminarily concluded that a greater share in the land use structure of a given cadastral districts resulted in fewer road accidents (

Table 4. Results of the correlation analysis (red—negative correlation, blue—positive correlation).

	AN	AR	BA	GA	RD	PBD	RQ	CS	PN	LN	SN	LAN	RON	CN
AN
AR	0.140
BA	0.666	−0.176
GA	−0.228	0.278	−0.391
RD	0.666	−0.127	0.823	−0.376
PBD	0.586	−0.173	0.454	−0.182	0.709
RQ	0.599	0.048	0.306	−0.280	0.679	0.696
CS	0.724	0.416	0.489	−0.093	0.629	0.590	0.603
PN	0.742	−0.081	0.466	−0.077	0.531	0.679	0.539	0.573
LN	0.785	0.021	0.621	−0.172	0.723	0.706	0.598	0.722	0.682
SN	0.519	0.140	0.337	0.023	0.402	0.225	0.407	0.499	0.370	0.412
LAN	0.768	0.210	0.387	−0.119	0.557	0.599	0.641	0.681	0.596	0.566	0.651
RON	0.273	0.183	0.141	−0.171	0.405	0.533	0.532	0.495	0.273	0.252	0.290	0.415
CN	0.876	0.193	0.617	−0.105	0.696	0.686	0.597	0.801	0.776	0.872	0.582	0.770	0.319

).

3.2. OLS Regression

Two additional factors were taken into account before applying the OLS technique. The first was the question of skewness, which defines the measure of asymmetry of the analyzed observations. In the case of the analyzed data set, it should be emphasized that this parameter had the highest value for the LN feature, but did not exceed 3 and was equal to 2.04. This indicates that it is slightly asymmetrical and close to normal distribution (a limit value of 3 was assumed) [42]. Therefore, for the purposes of statistical analysis, none of the variables was logarithmically transformed, and they were accepted in their standard form.

Secondly, the extended aspect took into account the phenomenon of collinearity between the adopted attributes. It was recognized that correlation coefficients are insufficient to determine the real relationships between the adopted characteristics. Therefore, an OLS regression was performed to calculate the VIF (variance inflation factor), which indicates to what extent the variance of the regression coefficient of a given variable is increased by other predictors. This coefficient characterizes the referred phenomenon in a more complex and accurate way. Thus, its knowledge allows for a proper interpretation of the obtained results. It was assumed that variables with a VIF coefficient value greater than 7.5 will be removed from the final part of the analysis. For the analyzed data set, these were the variables RD and CN, and these values were equal to 10.3801 and 14.9729, respectively (

Table 5. Summary of ordinary least squares (OLS) regression results (1).

	Coefficient	Standard Error	T-Value	p-Value	VIF
Intercept	−4.1912	5.6237	−0.7453	0.4628	-
AR	0.2307	0.5179	0.4455	0.6596	3.3964
BA	48.8856	15.9005	3.0745	0.0049 *	6.9797
GA	−2.4309	8.8254	−0.2754	0.7851	1.6814
RD	−1.6214	0.8488	−1.9102	0.0672	10.3801
PBD	−0.5473	0.4756	−1.1508	0.2603	6.7886
RQ	22.5509	11.8570	1.9019	0.0683	4.5927
CS	−0.0135	0.1054	−0.1282	0.8990	5.0734
PN	0.0375	0.0250	1.4989	0.1459	3.6799
LN	0.0788	0.0534	1.4752	0.1522	6.8255
SN	−0.3092	0.3282	−0.9418	0.3549	2.9553
LAN	0.0296	0.0106	2.8038	0.0094 *	4.3523
RON	0.0904	0.9635	0.0938	0.9260	2.3739
CN	0.0118	0.0143	0.8218	0.4187	14.9729
Number of Observations (cadastral districts)			40
Multiple R-Squared			0.8893
Adjusted R-Squared			0.8340
AICc			291.9662

* An asterisk next to a number indicates a statistically significant p-value (p < 0.01).

).

After eliminating the variables from the analysis, regression was again applied using the OLS technique. Based on the results obtained, it can be concluded that four variables (BA, PN, LN, and LAN) are statistically significant when the p-value is 1%. The obtained model explains about 82% of the variability of the observed phenomenon (the value of the adjusted R-Squared parameter was 0.8206). It should be noted that positive coefficient values indicate that this feature increases the number of accidents. Accordingly, negative values decrease the number of analyzed events. Most variables obtained expected coefficient values. An exception, which may also be debatable, is the attribute related to the share of roads with the best quality (the greater the share is, the greater the number of accidents), but it was not statistically significant (

Table 6. Summary of ordinary least squares (OLS) regression results (2).

	Coefficient	Standard Error	T-Value	p-Value	VIF
Intercept	−7.4859	5.6003	−1.3367	0.1921	-
AR	0.4778	0.4850	0.9851	0.3330	2.7567
BA	26.6077	9.5622	2.7826	0.0095 *	2.3364
GA	−4.3855	9.1194	−0.4809	0.6343	1.6617
PBD	−0.6754	0.4660	−1.4493	0.1583	6.0327
RQ	7.7123	9.7643	0.7898	0.4363	2.8829
CS	−0.0203	0.1094	−0.1857	0.8541	5.0537
PN	0.0608	0.0214	2.8450	0.0082 *	2.4880
LN	0.1003	0.0442	2.2676	0.0313 *	4.3278
SN	−0.2372	0.3221	−0.7365	0.4676	2.6337
LAN	0.0335	0.0102	3.2716	0.0028 *	3.7922
RON	−0.2047	0.9808	−0.2087	0.8362	2.2765
Number of Observations (cadastral districts)			40
Multiple R-Squared			0.8712
Adjusted R-Squared			0.8206
AICc			288.0237

* An asterisk next to a number indicates a statistically significant p-value (p < 0.01).

).

It should be noted that in the case of spatial data, the phenomenon of spatial autocorrelation must be verified, which is why the Moran’s I test was carried out in the next stage. The analysis of the parameters Z-score and p (values: 0.655790 and 0.000004, respectively) shows that there is very little likelihood that the observed spatial structure is the result of random processes. This allows H₀ to be rejected (the spatial distribution of the analyzed feature is completely random). Thus, traffic accidents are most likely spatially correlated and form clusters, which may ultimately result in their location not being random and being conditioned by selected local features (Figure 4).

3.3. GWR Regression

Considering the identified phenomenon of spatial autocorrelation of the analyzed observations, GWR analysis was applied, which is an extension of the OLS technique and at the same time a solution to the recognized phenomenon. The MGWR 2.2 software was used to perform the geographically weighted regression [43]. The results obtained after applying GWR indicate comparable modeling accuracy in relation to the OLS technique. The R-squared value was 0.872 (OLS: 0.871), and the adjusted parameter was 0.814 (OLS: 0.821). Taking into account the regression specification with the GWR technique, the number of observations (determined by the percentage) was determined, which was statistically significant based on the T parameter value. The adjusted critical T-value (at p = 95%) is equal to 2.029. The obtained results are similar to the results of the OLS regression. Specifically, the variables BA, PN, LN, and LAN proved to be significant, and these variables were statistically significant in each of the analyzed cadastral districts. At the same time, it should be noted that no observation was recorded for which the phenomenon of collinearity of at least one independent variable occurred (Table 6).

It should be emphasized that the analysis of the average values of the GWR model parameters indicates that the mode of interaction of all statistically significant attributes is very similar to the results of the model estimated using the OLS technique. However, it should be noted that the spatial variation in the size of the impact of these variables seems to be significant, which is defined, among other things, by the minimum and maximum values of these coefficients (

Table 7. Summary of squares (GWR) regression results.

	Coefficient					Percent of Significant Cases at 95%	Percent of Cases with Local VIF > 7.5
	$\overline{\mathit{x}}$	σ	Min	Me	Max
Intercept	−0.0003	0.0004	−0.0010	−0.0003	0.0004	0%	0%
AR	0.1115	0.0008	0.1098	0.1115	0.1128	0%	0%
BA	0.2909	0.0007	0.2894	0.2910	0.2923	100%	0%
GA	−0.0417	0.0010	−0.0435	−0.0417	−0.0397	0%	0%
PBD	−0.2428	0.0016	−0.2456	−0.2429	−0.2399	0%	0%
RQ	0.0919	0.0006	0.0908	0.0920	0.0930	0%	0%
CS	−0.0295	0.0004	−0.0303	−0.0295	−0.0287	0%	0%
PN	0.3042	0.0004	0.3034	0.3042	0.3051	100%	0%
LN	0.3195	0.0016	0.3167	0.3197	0.3224	100%	0%
SN	−0.0818	0.0010	−0.0835	−0.0818	−0.0799	0%	0%
LAN	0.4336	0.0011	0.4312	0.4334	0.4354	100%	0%
RON	−0.0206	0.0014	−0.0230	−0.0207	−0.0174	0%	0%
Number of Observations (cadastral districts)						40
Multiple R-Squared						0.872
Adjusted R-Squared						0.814
AIC						57.637
AICc						72.083
Bandwidth used						47396.740

). Therefore, although the results obtained using the GWR technique are comparable, they indicate the heterogeneity and complexity of the studied phenomenon in the analyzed area.

The model obtained by means of GWR showed that the share of built-up area in the land use structure (BA) is a statistically significant variable that increases the frequency of road accidents. This seems to be understandable because more intensive development inevitably leads to a higher frequency of road traffic, which in turn can result in a higher rate of road accidents. The significance of this variable was confirmed for all cadastral districts of the city. However, it should be noted that although the coefficients had a similar value for the whole city, a clear spatial variation in the magnitude of the impact of this determinant can be observed. In general, the strongest impact of the variable (BA) can be observed in cadastral districts located in the eastern part of the city. However, in several western districts, the impact was marginally lower (Figure 5a). In practice, this may mean that, assuming that there are two districts with identical areas but located in two opposite zones, they could differ in the number of accidents.

The smallest spatial variation, as evidenced by the similar Min and Max values of the coefficients and their standard deviation among the significant features, concerns the number of car parks (PN) feature. As with the variable BA, a higher number of parking lots resulted in a higher number of accidents. This regularity can be interpreted from different angles. First of all, a higher number of existing parking lots is usually associated with a higher density of the road network, which was also confirmed by the correlation analysis (Table 3). A higher road density can, in turn, be associated with a higher frequency of road traffic, which, in the end, similarly to the BA feature, leads to a higher probability of accidents. On the other hand, however, parking lots themselves, as an element of road infrastructure, can create hotspots of events due to their often complicated organization, which can lead to conflict situations among drivers. It should also be taken into account that the “vigilance” of drivers may be reduced in such places, exacerbating this problem. In contrast to the first characteristic, the greatest impact of the PA determinant was in the western part of the city (Figure 5b).

The other two statistically significant variables are directly related to the equipment of the accompanying infrastructure, namely the variables number of traffic lights (LN) and number of road lighting installations (LAN). For these variables, the spatial variation is greater, especially for the LN feature, and the mode of impact is comparable, i.e., a higher number results in a higher number of accidents. Although the infrastructure is supposed to improve traffic flow, the failure of road users to follow traffic lights can have the opposite effect. It is worth noting, however, that the solution may lie not in reducing this type of infrastructure but in applying innovative solutions such as intelligent traffic lights [44]. This fact also confirms that a roundabout seems to be a better solution than a complicated intersection with a lot of traffic lights, as confirmed by this analysis (Table 5 and Table 6), with the proviso that the variable was not statistically significant. In the case of the number of lamps, which are usually found along roads, it should be emphasized that, on the one hand, they can facilitate traffic for participants (especially pedestrians). However, on the other hand, in certain situations, their excessive intensity and incorrect design can negatively affect drivers, for example by dazzling them. It should be noted that in the case of six identical areas located in the south-western part of the city, the impact of both characteristics was the strongest (Figure 5c,d).

4. Discussion

4.1. Findings

The frequency of road accidents in specific locations depends on two groups of factors. The first group is related to human factors, including the observance of basic rules and behavior by road users (speeding, drunk driving, or falling asleep at the wheel). The second group, on the other hand, is related to external independent factors (among others locational conditions) to road users that multiply the intensity of road accidents. The aim of this study was to identify the determinants that are significant for the number of accidents at specific locations on a city scale. Identifying these variables can enable traffic organizers to gain a proper understanding of local determinants. This knowledge will enable the introduction of effective preventive measures in the right locations and in the right areas, which may result in fewer accidents.

The process of identifying significant variables is complex and may depend, among other things, on the location of the research object, the characteristics of the research material adopted, the way a particular transport system functions, and the statistical tools used. For this reason, among others, the results obtained cannot be generalized and considered valid for other research areas. The indisputable advantage of this study is its credibility because the obtained and recorded source data come directly from the database prepared and recorded by the police. Therefore, it can be assumed that this collection is a complete database of information about all accidents that occurred in a specific time and location and that the circumstances and the location itself were reliably described. This fact is extremely important and largely determines the reliability of the obtained results. Regarding the research material, it should also be emphasized that, in accordance with the basic assumption of the work, accidents from a specific (relatively short) period of time were included in the analysis compared to other studies [19,28]. These characteristics may be ambiguous over a longer period of time and may be subject to modification. Therefore, a possible extension of the time frame in subsequent analyses may be appropriate and may provide a lot of valuable information in this field. Similarly, in terms of spatial coverage, the results, although statistically significant, are relevant to the location. It seems both purposeful and very interesting to compare the results obtained on other objects (using a comparable methodology).

4.2. Advantages of the Research—Implications

The above-mentioned issue of the significance of the adopted spatial scope of the analysis is confirmed by the fact that significant determinants can be ambiguous, even on the scale of one city, which has been confirmed by the obtained results and other studies in this field [45,46]. Therefore, it is important to emphasize that the analysis of this kind should always take into account the characteristics of the location. In other words, it is crucial to consider the area not only as a whole, but also to conduct a detailed analysis. This work takes this issue into account, which is confirmed by the methods used. Consequently, this is one of the greatest advantages of the study. Confirmation of this thesis can be found in the results obtained using the GWR technique, despite the fact that, in principle, the characteristics and mode of impact were identical to those of the OLS technique, the magnitude of the impact of the determinants in different locations in the city of Poznań was different. Therefore, it should be indicated that making uniform conclusions, e.g., based on the results of OLS regression for the entire studied area, could result in significant cognitive errors and some researchers overlook this issue [47,48]. In conclusion, it should also be emphasized that the GWR analysis made it possible to identify zones within the city that are characterized by comparable conditions in terms of the size of the impact on the number of accidents. This makes it possible to introduce precise preventive measures appropriate for a given location. For example, in the case of the variable related to car parks, the number of this type of place in the eastern part of the city might be higher as it does not clearly cause more accidents compared to the rest of the city.

4.3. Disadvantages of the Study—Directions for Future Research

Despite the advantages of the proposed methodology, it also has certain limitations related not only to the previously mentioned issue of spatial and temporal scope. It should be noted that the inclusion of additional attributes in the analysis, which would characterize specific parts of the city (cadastral districts) in a more precise manner, would allow for more comprehensive results. It could be very interesting to include characteristics that could characterize the population living in a given district in terms of broadly understood socio-economic development. Determinants such as the age pyramid structure, car ownership rate, unemployment rate, crime rate, or even the average amount of alcohol consumed per person in a given location could improve and enrich the obtained results which is confirmed by other studies [49,50,51]. Unfortunately, it was not possible to obtain such detailed information in the national (Polish) context. Taking these characteristics into account in future research would undoubtedly improve its quality, and it is therefore recommended that they be employed whenever possible. Additionally some limitations are related to applied methodology. It should be underlined that crash characteristics and outcomes vary significantly by vehicle type and number of participants. The inclusion of more detailed accident characteristics would increase the cognitive quality of the model and future studies are advised to take this into account. Finally it should be noted that analyzed period of time is also relevant. Road accidents frequencies and patterns may vary year to year due to many factors like weather, infrastructure changes, enforcement measures, and others. Taking this into account, these findings cannot be generalized for long-term safety planning. Extending the time period would increase the quality of the research and make it more representative.