Predicting Public Violent Crime Using Register and OpenStreetMap Data: A Risk Terrain Modeling Approach Across Three Cities of Varying Size

<jats:title>Abstract</jats:title><jats:p>The aim of the current study is to estimate whether spatial data on place features from OpenStreetMap (OSM) produce results similar to those when employing register data to predict future violent crime in public across three Swedish cities of varying sizes. Using violent crime in public as an outcome, four models for each city are produced using a Risk Terrain Modeling approach. One using spatial data on place features from register data and one from OSM, one model with prior violent crime excluded and one with prior crime included. The results show that several place features are significantly associated with violent crime in public independent of using register or OSM data as input. While models using register data seem to produce more accurate and efficient predictions than OSM data for the two smaller cities, the difference for the largest city is negligible indicating that the models provide similar results. As such, OSM place feature data may be of value when predicting the spatial distribution of future violent crime in public and provide results similar to those when using register data, at least when employed in larger compared to smaller cities. Possibilities, limitations, and avenues for future research when using OSM data in place-based criminological research are discussed.</jats:p>

section_content: Crime mapping has for decades been an important tool among law enforcement authorities to guide the allocation of resources in crime preventive purposes (see e. g., Ratcliffe, 2004), and there is a continuously growing body of literature focusing on methods to forecast the spatial distribution of crime (see Kounadi et al., 2020). While different methods for these purposes are available, Risk Terrain Modeling (RTM) has become a popular forecasting approach. Unlike conventional hot spot mapping techniques, which use previous years' crime data to forecast future distribution of crime, the premises for RTM is that crime varies across space as a result of varying opportunities for crime (Caplan & Kennedy, 2016; Caplan et al., 2011). The number of opportunities at different places are, in turn, a result of the built and social fabric of the urban landscape (see Newton & Felson, 2015). However, a potential downside with the RTM approach is that it requires additional spatial data aside from crime, that is data on place features or hypothesized risk factors, which from a theoretical point of view often are referred to as crime generators and crime attractors (Brantingham & Brantingham, 1993, 1995). These could, for instance, include bars and nightclubs, restaurants, schools, and bus stops (for an overview see Table 7 in Appendix). 

The typical approach for gathering this type of spatial data is by requesting it from various local authorities (e. g., the local police department or city office), synthesize all gathered information, clean, and geocode it. Another common approach is to purchase the data from actors, such as marketing companies, holding such information (e. g., Caplan et al., 2017; Garnier et al., 2018; Piza et al., 2017). However, in cases when such data are not available, or when the time and/or economic resources are limited, there are other options to gather spatial data on place features. One such source of information is OpenStreetMap which is an open-source digital map application based on volunteered geographic information, meaning that its content is generated by its users (Coetzee et al., 2020; Goodchild, 2007). However, given this user-generated nature of these data, their reliability has been up for debate. While there are previous studies evaluating the reliability of OpenStreetMap place feature data -suggesting that it may be incomplete, have varying coverage across different contexts, and suffer from some degree of outdatedness (Bright et al., 2018; Vonthron et al., 2023) -there is to our knowledge no study evaluating the feasibility of using these data when employing a RTM approach to forecast the spatial distribution of violent crime in public. Thus, the current study aims to fill this gap in knowledge by employing three years of crime data, across three cities of varying sizes in the most southern part of Sweden and examine whether the results from RTM-models differ when employing data on place features from OpenStreetMap and register data respectively.
section_name: Introduction

section_name: Background

section_content: While environmental criminology traditionally has focused on neighbourhoods as unit of analysis, some scholars have argued that using aggregated neighbourhoods as unit of analysis may omit to account for important within-unit variance because of the heterogeneity of smaller places within larger neighbourhoods (Weisburd et al., 2012). A major claim supporting this perspective is that a large majority of all crime in a city tend to cluster to a very small share of micro-places (Weisburd, 2015). However, the fact that crime tends to cluster in certain locations does not answer the main question, namely why it concentrates at certain micro-places. To answer this question, focus is often turned to opportunity theories of crime (see Wilcox & Cullen, 2018). The common denominator of these perspectives is their focus on the crime event, occurring in a given slice of space and time (Felson & Boba, 2010). By focusing on crime as an event, less attention is paid to individual inclination or propensity to commit crime, which is taken for granted (e. g., Cohen & Felson, 1979). The focus is instead on how contextual settings create opportunities that may facilitate individual propensity into criminal action (Wilcox & Cullen, 2018). According to the crime pattern theory, the built and social fabric of the urban landscape is key to understand this variation in opportunities for crime. Brantingham and Brantingham (1993) notes that crime tends to cluster at certain nodes (e. g., home or workplace) and along pathways connecting these nodes. Although nodes and paths are individually exclusive, opportunities for crime increase where these overlap between motivated offenders and suitable targets, especially in the absence of capable guardianship (see Cohen & Felson, 1979; Felson & Boba, 2010). Such "nodal high activity spots", where the convergence of suitable targets and motivated offenders are higher, have been defined as crime generators (Brantingham & Brantingham, 1993:16 ). These places usually attract large number of people and are generally fostering activities unrelated to crime (e. g., shopping areas and public transportation nodes), but due to the increased convergence of potential offenders and victims in space and time, these locations provide more opportunities for crime (Brantingham & Brantingham, 1995). On the other hand, crime attractors are places which are known to provide opportunities for crime by the ongoing activity (e. g., bar districts and illegal drug markets), which may make these locations well-suited for crime, and consequently attract motivated offenders (Brantingham & Brantingham, 1995; Caplan et al., 2011). Crime attractors thus tend to have more crime than would be expected based on the number of people there, whereas crime generators tend to have crime that is proportional to the number of people at the location.
section_name: Micro-Places and Spatial Distribution of Crime

section_content: Awareness of the spatial distribution of crime across micro-places has made crime mapping a well-researched topic during recent decades (for a review see Kounadi et al., 2020). While hot spot mapping using, for instance, Kernel Density Estimations (KDE) of previous years crime occurrences has been employed to forecast future spatial distribution of crime (Chainey et al., 2008), using previous crime as a sole explanatory variable is problematic because it may (at best) serve as a rather crude proxy for future risks. But perhaps more importantly, such an approach may also be subject to criticism relating to tautology, i. e., explaining crime by crime. So, although such crime mapping methods are useful for predicting the future spatial distribution of crime, other approaches are needed to explain the spatial distribution of crime from a theoretical point of view. 

Based on ideas from environmental and opportunity theories, Caplan et al., (2011:361) introduced the RTM approach to estimate spatial risks for future crime events and compared this to "(…) a geographical adaptation of offender-based risk assessment". As such, the fundamental idea of RTM is that the uneven distribution of (opportunities for) crime across urban space is dependent on the "environmental backcloth" of the built and social urban landscape, where the risk for crime at a given location can be assessed based on the presence or absence of a specific combination of spatial risk factors (Caplan et al., 2011 ; see also Brantingham & Brantingham, 1993, 1995). More specifically, Caplan and Kennedy (2016) suggest that all places are at some risk for crime, but some places are at substantially elevated risk compared to others because they comprise multiple criminogenic features which facilitates or encourage criminal behaviours. RTM is thus an analytical approach to estimate, in a probabilistic manner, which places that are more vulnerable to crime given their unique set of criminogenic features. In its simplest form, RTM can be described as a multi-layer map where different hypothesized risk factors have been superimposed and together form a composite map of crime risk across any given spatial area (Caplan et al., 2011). 

Several studies have used RTM to forecast a range of different crime outcomes -such as residential burglary (Andresen & Hodgkinson, 2018), motor vehicle theft (Piza et al., 2017), and drug related crime (Barnum et al., 2017) -and their association with a wide range of place features. However, the perhaps most studied outcome in RTM research is different forms of violent crime, such as assault (e. g., Drawve & Barnum, 2018; Gerell, 2018; Kennedy et al., 2016), robbery (e. g., Caplan et al., 2017; Connealy & Piza, 2019; Garnier et al., 2018; Wheeler & Steenbeek, 2021), homicide (e. g., Barton et al., 2021; Kennedy et al., 2021), or a combination of the three (Burgason et al., 2017; Caplan et al., 2013; Connealy, 2020; Drawve et al., 2016; Fox et al., 2021; Piza & Gilchrist, 2018). 

While the aim of many of the above studies has been to examine the association between different place features and future crime, several studies have also estimated the reliability of different spatial forecasting methods by assessing both hit rates and predictive accuracy. Hit rates can be described as the amount of crime captured by the method in question. For instance, how large share of all crime within a forecasted time period (e. g., a year) being within the identified hot spot (Chainey et al., 2008). A main drawback of only looking at hit rates, however, is that it does not consider the size of the predicted hot spot. As stated by Chainey et al., (2008:12), "(…) a hit rate could be 100 per cent, but the area where crimes are predicted to occur could cover the entire study area". Therefore, predictive accuracy of spatial forecasting methods is often assessed by employing the Predictive Accuracy Index (PAI; Chainey et al., 2008). Although the PAI includes the hit rate (as the numerator), it also considers the predicted hot spot area size (as the denominator). In other words, the PAI considers how many crimes that are predicted relative the size of the forecasted hot spots. While there are more techniques to assess the predictive validity of spatial crime mapping methods (e. g., Levine, 2008 ; see also White et al., 2024), several studies have concluded that RTM may in fact outperform traditional hot spot mapping (Caplan et al., 2020; Daley et al., 2016; Ohyama & Amemiya, 2018). On the other hand, some studies have concluded that the accuracy of RTM may be contended compared to both simpler count methods (Doyle & Gerell, 2024), and more advanced machine learning forecasting methods (e. g., Wheeler & Steenbeek, 2021 ; see also Drawve, 2016).
section_name: Crime Mapping and Risk Terrain Modeling

section_content: Unlike more conventional hot spot mapping techniques, which only demand historical spatial information on crime, the RTM approach requires additional data on place features that may serve as potential spatial risk factors and can be acquired in several ways. While much data is often available from local authorities (e. g., various departments at city offices, the local police agency, etc. ) this includes consulting several databases held by different local agencies, but also time-consuming efforts to gather, synthesize, clean, and geocode the data. Another alternative is to turn to private actors (e. g., marketing cooperates) who hold such data and buy it (e. g., Caplan et al., 2017; Garnier et al., 2018; Piza et al., 2017). However, in cases where there is a lack of reliable spatial data from local authorities, and/or limited financial resources, there are other potential sources with applicable spatial data. 

While there is a growth in spatial data infrastructures and openly available spatial data, this progress is at different stages in different countries (see Coetzee et al., 2020). In the US, for instance, several city offices provide spatial data relevant for RTM studies within an open-source framework. For instance, Connealy (2020) employed RTM to assess the significance of different spatial risk factors for violent crime in three American cities, with one main reason for study area selection being publicly available data for these cities. However, in instances when researchers have not been able to get hold of relevant spatial data, some have turned to OpenStreetMap (OSM). This is an online mapping platform building on volunteered geographic information meaning that the underlying data are generated by its users (Goodchild, 2007 ; see also Präger et al., 2019). As such, OSM serves as a single source of open spatial data, thereby eliminating potential sources of error associated with manually collecting, synthesizing, cleaning, and geocoding data from multiple traditional databases. For RTM purposes, Briz-Redón et al. (2022) complemented administrative data with OSM data relating to public transportation stops and parks when examining spatial risk factors associated with various crime types, while Giménez-Santana et al. ( 2018 ) used environmental variables from OSM to predict road traffic incidents. 

However, given the user-generated nature of OSM data, its reliability can be questioned, and by extension, its suitability for research purposes in general and RTM purposes in particular. Previous research examining the reliability of OSM data has found that place features relating to alcohol and food outlets respectively are far from complete, although the representativeness differs relating to various types of outlets (Bright et al., 2018; Vonthron et al., 2023; Pinho et al., 2023). In addition, it has been noted that OSM data suffers from some degree of outdatedness by including decommissioned establishments (Bright et al., 2018), and there is also a spatial heterogeneity in its coverage, which in turn is associated with area characteristics (Vonthron et al., 2023). This latter finding may also raise questions relating to what extent OSM data is up-to-date and reliable outside of larger urban areas where the crowdsourcing resources are theoretically smaller. Despite these limitations, however, Bright et al., (2018) concludes that using OSM data in health research may produce results similar to those using other sources of spatial information. Similarly, Präger et al. (2019) points out that OSM data may suffer from some limitations but is still reasonable in its validity. While some RTM studies have employed OSM data in their analysis (e. g., Briz-Redón et al., 2022; Giménez-Santana et al., 2018), it has not been formally evaluated how well these data perform. This includes studying the extent to which OSM data may produce results similar to those when other, more conventional spatial data sources, are employed.
section_name: Spatial Data in Crime Forecasting

section_content: The aim of the current study is to estimate with what accuracy violent crime in public can be predicted when using information on place features from two different sources of information, that is (1) register data, and (2) OSM data. In addition, the study aims to compare results from these models when they are employed in three cities of varying size. This aim can be concretized in the following research questions:

1. Which spatial place features are associated with violent crime in public and do the results differ when employing different sources of information? 2. With what accuracy and efficiency is crime predicted using information on spatial place features from different sources? 3. To what extent do the results from models using different sources of information identify the same high-risk places?

By answering the research questions above, the current study may provide important insights to researchers interested in the geography of crime, and the potential use of opensource databases for spatial crime analysis.
section_name: Current Study

section_name: Data and Methods

section_content: Three cities of different sizes located in the most southern region of Sweden are included in the current study. 1 Malmö is one of three Swedish metropolitans and has a population of above 325,000 making it the third largest city in Sweden. Helsingborg is the ninth largest city in Sweden with a population of about 114,000. Kristianstad is a smaller city with a population of roughly 41,000 which makes it the thirtieth largest city in Sweden. All three municipalities, where the included cities are located, experienced violent crime rates per 100,000 inhabitants above the national average in 2022 (Malmö: 1,154; Helsingborg: 1,139; Kristianstad: 918; Sweden: 862). 2 For the current study, each city is defined by the geographical administrative boundaries of the urban area representing the city (i. e., not the municipality as a whole). However, as parts of the urban area of Malmö cross the municipality border, this rather small area has been excluded from the Malmö study area.
section_name: Study Areas

section_content: The outcome data consists of police reported crimes occurring in public (outdoors), comprising assaults (including aggravated) and robberies against a person. These two crime categories are combined as a joint measure of violent crime in public. Crime data have been provided by the regional police office and include information on crime classification code, date and time, and geographical coordinates for each crime incident across the three municipalities. A total of about 8,800 violent crimes (7,200 assaults and 1,600 robberies) are included in the dataset within the study period, that is October 2020 and October 2023, out of which the vast majority had a geographical coordinate attached (95,9%). For the purposes of the current study, only crimes occurring within each of the study areas -that is the administrative city boundaries -have been included, which corresponds to roughly 7,700 crimes. Crimes reported between the first of October 2021 and the last of September 2022 are used as the outcome variable in the RTM analyses to identify high-risk grid-cells as described below, while crimes reported between the first of October 2022 and the last of September 2023 are used to evaluate the predictive accuracy and efficiency of different RTM-models (see Table 1 ).
section_name: Crime Data

section_content: The current study employs a total of ten place features hypothesized to serve as risk factors for future crime, in addition to prior violent crime in public (see Table 1 ). These variables are similar to several of those used in previous research using RTM to forecast violent crime outcomes (see Table 7 in Appendix for a review). Although there may be additional variables of relevance when forecasting violent crime, these are considered sufficient to include for the purposes of the current study because the main aim is to compare two sources of information rather than producing an optimized RTM. 

All place features have been operationalized using data from two different sources of information. The first dataset consists of register data from i) each municipality's licensing unit, ii) the National Agency for Education, iii) the Swedish Transport Administration, and iv) Statistics Sweden. From each municipality, information about premises with licenses to serve alcohol have been used to operationalize bars/nightclubs as premises with a permit to serve alcohol beyond 01:00, while premises with a permit until 01:00 or earlier have been operationalized as restaurants with license to serve alcohol. From the municipality, data on premises that have registered food handling were used to operationalize fast-food restaurants (e. g., street-food stands, pizzerias, hamburger joints) and cafés. In addition, data on premises with a license to sell tobacco and/or low-alcohol beer was retrieved from each municipality's licensing unit and used to operationalize convenience stores and grocery stores. From the National Agency for Education data on both public and private educational units was retrieved to operationalize preschools and schools. Data on bus stops was retrieved from the Swedish Transport Administration's national road database. Finally, data from Statistics Sweden on parks and green areas was retrieved to operationalize green areas/parks. All included risk factors refer to the calendar years of 2022/2023. Aside from the data regarding bus stops and green areas/parks, which was in a geographically projected data format, all register data included the name of the premise and street address. After all data were cleaned and any duplicates removed, the data was geocoded with Google Maps as reference using the 'ggmap' package (Kahle & Wickham, 2013) in R version 4. 1. 2 (R Core Team, 2021). 

The second dataset consists of OSM data collected during the spring (Malmö) and fall (Helsingborg and Kristianstad) of 2023 (OpenStreetMap contributors, 2023). The data was collected using the OSM API through the Python package OSMNx (Boeing, 2017). Given a geographical area (e. g., Malmö), this package allows for collecting place features of different types using a single request. By using the key-value combination of, for instance, "amenity:pub" together with the place indicator "Malmö, Sweden" returns a dataset of all pubs within the specific city. A total of 17 key-value combinations are used to match the ten place features outlined above. It is important to note that the operationalization of place features may be different between the two sets of data. For instance, a place feature operationalized as a bar/nightclub in the register data (a permit to serve alcohol beyond 01:00) may in fact be operationalized as a restaurant by OSM users. A detailed description of the operationalizations for both register data and the key-value combinations used for this study is available in the Appendix (Table 8 ). 

As seen in Table 1, there are clear discrepancies between the two data sources, where register data generally includes higher counts of place features than the OSM data, and this is especially pronounced in the smaller cities. For instance, the ratio of fast-food restaurants between register and OSM data for Malmö is close to one (0. 98), while it is less so for Helsingborg (0. 67) and Kristianstad (0. 16). Although it is unreasonable to assume a perfect correspondence between the data sets due to the various operationalizations of place features, this discrepancy may also indicate that the completeness of the OSM data decreases with city size -at least for some place features. 3
section_name: Data on Spatial Risk Factors

section_content: The relationship between place features and violent crime in public have been examined by employing an RTM approach. For this analysis, equally sized gridcells across each of the three study areas are used as the unit of analysis. The size of these cells has been determined by taking the average street length as measured within a GIS for each city respectively (see e. g., Kennedy et al., 2011), resulting in a grid-cell size of 123 × 123 m for Malmö (N = 5,310), 120 × 120 m for Helsingborg (N = 3,281), and 106 × 106 m for Kristianstad (N = 2,387). Next, each place feature must be considered in terms of its spatial operationalization. In other words, whether a given set of risk factors influence opportunities for a given crime by proximity or density. For instance, violent crime may be influenced by proximity to a bar -that is, the mere presence of a bar may lead to an increased risk of violence in public. On the other hand, it may be that a single bar does not increase the risk of violent crime, the risk is only increased where bars tend to cluster (e. g., a bar district). Following the procedure outlined by Caplan and Kennedy (2016), a Nearest Neighbor (NN) analysis of the included place features was conducted to determine whether each of the variables were to be tested using a proximity or density operationalization, or both. Next, place features not showing a significant spatial clustering, or with an observed mean distance above a given NN threshold, were set to proximity only. Place features showing a significantly clustered pattern and an observed mean distance below the NN threshold were tested as both proximity and density (see Table 9, 10, 11 in Appendix for a full account of these analyses). 4 Given that green areas/parks are in a polygon format this variable was only set to proximity and given the "floating" nature of prior violent crime this was only tested as density (see Caplan & Kennedy, 2016). In the next step, the spatial influence of each risk factor operationalization must be considered -that is at what distance it may exert an increased risk for crime. In the current study, each operationalization is tested by three whole increments using the specific grid-cell size (e. g., 123, 246, and 369 m for Malmö). Given the polygon nature of parks/green areas, which already covers large spatial areas of each city, the spatial influence was only tested with one whole increment (e. g., 123 m for Malmö). 5
section_name: RTM Specification

section_content: RTM-models have been produced using the RTMDx software which is specifically developed to examine the spatial relationship between place features and an outcome variable using count-based regressions (see Caplan & Kennedy, 2016). Since a single place feature, due to operationalization and spatial influence, can range between three and six variables the analysis is set to use bidirectional stepwise regression where variations of each variable are included in a full model. By repeatedly evaluating the Bayesian Information Criteria (BIC) value of each regression, when variations of variables are included or dropped, the most favorable model is selected as the final output where a Relative Risk Value (RRV) for each statistically significant variable (p < 0. 05) is reported (Caplan & Kennedy, 2016). The RRV can be compared to the Incident Rate Ratio (IRR) from a generalized linear regression (an exponentiated coefficient) and here interpreted as the relative or percentual change when the independent variable is present (Piza, 2012). Each grid-cell then receives a summarized RRV value relative to its intersection with the spatial influence of significant place features serving as risk factors (for an elaboration on the RTM statistical approach, see Caplan & Kennedy, 2016). 

For the purposes of this study, four separate models are produced for each city where the outcome variable is violent crime in public between the first of October 2021 and the last of September 2022. First, two models are produced using place features based on either register or OSM data respectively. In these models, data on prior violence (i. e., October 2020 to September 2021) is not included to examine differences when only data on spatial place features from different sources are employed. However, two consecutive models are produced where prior violence is included to examine whether there are any differences when this variable is included. To examine the accuracy and efficiency of each model, two different metrics are employed. Both metrics use violent crime in public between October 2022 and September 2023 as the outcome variable. First, the predictive accuracy is estimated by calculating the PAI following the suggested approach by Chainey et al. (2008) :

In Eq. 1, n is the number of crimes within the predicted area a, which here represents the total area of grid-cells with a RRV of two standard deviations above the specific model mean. The number of crimes in the predicted area (n) is divided by the total number of crimes (N) within the study area and multiplied by a hundred, making the numerator representing the percentual share of all crimes being within the predicted area (i. e., the hit rate). The area of the predicted grid-cells (a) is divided by the total study area A and multiplied by one hundred, making the denominator an area percentage. 6 The interpretation of the PAI index is quite straightforward. Finding 50 percent of crime in 50 percent of the full study area would return a PAI of one (1), while finding 50 percent of all crime in 25 percent of the study area would result in a PAI of two (2). As such, when comparing models or techniques, a higher PAI suggests a more favorable result (see Chainey et al., 2008). Four indexes are calculated for each city using both register data and OSM data, with and without prior violence. 

Second, the predictive efficiency is estimated by calculating the PEI * as outlined by White et al., (2024; see also Lee et al., 2020) :

In Eq. 2, n' is the number of predicted crimes within a given area using a specific forecasting method, while n * is the maximum number of crimes that, in practice, can be predicted within an area of corresponding size (Lee et al., 2020; White et al., 2024). For example, suppose an RTM-model identifies 50 grid-cells as high-risk, where these grid-cells predicts 100 future crimes, n' equals 100. However, by ranking the grid-cells by counts of crime, the top 50 grid-cells sum to 150 crimes, making n * equal to 150. Thus, this example would generate a PEI* of 0. 667, which could

be interpreted as the percentual degree of the efficiency of the model compared to the best (or maximal) possible outcome. Finally, to visualize the extent to which RTM-models identify the same grid-cells as high-risk when using different sources of information (i. e., grid-cells with a RRV of two standard deviations above the specific model mean), UpSet plots (see Lex et al., 2014) and choropleth maps have been produced. This allows an overview of the number of grid-cells that are only found for one model output, and the number of grid-cells that overlap between model outputs. To assist in the interpretation of these plots, an overlap or Szymkiewicz-Simpson (SS) coefficient has been calculated using the following equation (see Vijaymeena & Kavitha, 2016) :

According to Eq. 3, X and Y are the sets containing the high-risk cells for two different feature sets (register and OSM data). The SS coefficient is calculated as the absolute value of the intersection of X and Y, divided by the absolute size of the smallest of two data sets. The main reason for choosing the SS coefficient rather than other measures of similarity is that it considers that different data sets may be of different sizes, which is the case in the current study. Other similarity measures, such as the Jaccard index, would result in more strict comparisons because the highest theoretical value (which for the Jaccard index is 1. 0) would be restricted given the unequally sized data sets. The SS coefficient is consequently a more lenient coefficient which also allows for equally maximum theoretical values (i. e., 1. 0). 7 However, since this analysis only focuses on grid-cells with the highest RRV from each model, this have been complemented with a bivariate Spearman's rank order-correlation to examine the relationship between the RRV for the full set of grid-cells.
section_name: Analytical Approach

section_name: Results

section_content: Tables 2, 3 to 4 report the operationalization and spatial influence used for each included variable, in addition to the results from the four models for each city using register or OSM data, with prior violent crime excluded and included. The results from the models without prior violence shows that bars/nightclubs and schools are significantly associated with future violent crime across all models and cities. Similarly, fast-food restaurants, convenience stores, grocery stores, preschools, and bus

The Jaccard index is calculated by taking the intersection of two data sets (A, B) and divide this by the union of the two (see e. g., Vijaymeena & Kavitha, 2016). Imagine a case where data set A has a size of 100, and B a size of 120, with an intersection of 80. The Jaccard Index would thus be 0. 571. However, the maximum theoretical Jaccard index for this example would be restricted to 0. 833. In comparison with a situation where data set A has a size of 100 and data set B a size of 105, independent of the intersection, the maximum theoretical Jaccard index would be 0. 952. Thus, comparing Jaccard Index values between these two examples would be unjust, or at least very strict. stops are also significant across all but one of the models. An additional takeaway is that green areas/parks are not associated with violent crime in any of the models. Turning to the models where prior violence is included, the most consistent result is that prior violence is the top ranked variable associated with future violent crime across all cities, with the exception of one model where it is ranked second. Bars/ nightclubs and grocery stores are also significantly associated with violent crime in all but one of the models. 

When comparing results within the same city, but using different data sources, there are some discrepancies where one place feature is significant when using one dataset but not when using the other. For instance, bars/nightclubs, restaurants, and cafés are significantly associated with an increased risk for future violent crime in Malmö when using one dataset, but not the other. The same is true for, for instance, convenience stores, preschools, and bus stops for Helsingborg and Kristianstad. However, these differences are more prominent for Kristianstad and less for Helsingborg and Malmö.
section_name: Spatial Risk Factors Associated with Violent Crime in Public

section_content: Turning to the predictive accuracy and efficiency of the models, Table 5 shows that for Malmö there is only small differences in PAI values when using register or OSM data as input, excluding prior violence. In fact, using OSM data provides a marginally higher PAI value and provides a slightly more efficient model in terms of PEI*. However, when turning to the somewhat smaller cities there are some discrepancies in results. For Helsingborg, the model using register data shows 28 percent higher PAI (Reg: 20. 963; OSM: 16. 369) and 16 percent higher PEI* (Reg: 0. 658; OSM: 0. 568). For Kristianstad, however, the pattern is the opposite where the model using OSM data provides 15 percent higher PAI (Reg: 18. 983; OSM: 21. 883) and 12 percent higher PEI* (Reg: 0. 518; OSM: 0. 580). 

When adding prior violence to the models the result for Malmö is similar to when prior crime is excluded, namely that there are only small differences in PAI and PEI* values between models. Introducing prior violence also shows that both the accuracy and efficiency of the models are somewhat increased, but only for models using register data. For Helsingborg, the difference in PAI values between register and OSM models when prior crime is included decrease but is still in favor of register data (Reg: 17. 572; OSM: 15. 456), while the difference in PEI* values remain about the same (Reg: 0. 692; OSM: 0. 614). Compared to the models where prior crime is excluded, PAI values are in fact somewhat decreased when using both register and OSM data. On the other hand, PEI* values are slightly increased. This indicates that introducing prior violence to the models provides somewhat less accurate, but slightly more efficient models for Helsingborg. For the smallest city, Kristianstad, there are quite large discrepancies in results when prior crime is included with the PAI value being 36 percent higher for the model using register data compared to the OSM model (Reg: 26. 202; OSM: 19. 283). The register data model also has a somewhat higher PEI* than the OSM model, but this difference is not as pronounced (Reg: 0. 619; OSM: 0. 574). In comparison to the models where prior crime is excluded, there are some noteworthy discrepancies. While the model employing OSM data provided higher PAI and PEI* values when prior crime is excluded compared to the register data model, the model where prior crime is included gives a lower PAI value, and a more or less equivalent PEI*. This resembles the pattern observed for Helsingborg, namely that including prior violence provides less accurate, but similarly efficient, models when using OSM data as input. However, turning to the models using register data shows that including prior violence in the model provides 38 percent higher PAI compared to when prior crime is excluded (excluded: 18. 983; included: 26. 202 ). The efficiency of the model is also considerably higher (excluded: 0. 518; included: 0. 619). One explanation for this difference, which can be observed in the data, is that the model using register data when prior crime is excluded identifies 28 high-risk grid-cells and 71 counts of violent crime. However, when prior crime is included, the number of grid-cells is reduced to 20, but still captures only one fewer violent crime incident.
section_name: Predictive Accuracy and Efficiency

section_content: Turning to the question relating to whether the different models identify the same places as high-risk, Fig. 1 illustrates the agreement of grid-cells with a RRV above two standard deviations of the mean between the different models using UpSet plots. 

For each city, two plots are shown; one when prior crime is excluded, and one with prior crime included. To assist in the interpretation of these plots, SS coefficients are produced by simply dividing the count of grid-cells that intersect between the data sets with absolute size of the smallest of the two data sets, where the result can be interpreted as a percentual similarity (see Eq. 3). 

In the models where prior crime is excluded, the SS coefficients suggest that there is roughly 60 percent similarity in grid-cells identified as high-risk between data sets and across cities (Malmö: 0. 569; Helsingborg: 0. 578; Kristianstad: 0. 615). However, when prior crime is included in the models the SS coefficient for Malmö and Kristianstad is notably increased, showing a similarity of about 80 percent between models using register and OSM data (Malmö: 0. 833; Kristianstad: 0. 800). However, for Helsingborg, the SS coefficient (0. 582) is almost identical to the model where prior crime is excluded. It should be noted, however, that when the relative difference between the two data sets is large (i. e., Helsingborg without prior violence and Kristianstad with prior violence), the SS coefficient will not highlight the unique set difference between the larger and the smaller set. As such, a large difference might result in a high SS coefficient although the actual overlap is rather small. To complement the UpSet plots, Fig. 2 provides a visualization of the spatial overlap of high-risk grid-cells (RRV above two standard deviations of the mean) between models and cities. The general pattern across all maps is that the overlapping cells seem to be concentrated to the immediate center of each city. Another noticeable pattern is that unique high-risk grid-cells from either register or OSM models, when not overlapping, tend to be adjacent or at least in close proximity to either overlapping or high-risk grid-cells from the other data source model. This indicates that the different models tend to identify about the same geographical area as high-risk, but with some offset. One likely explanation to these patterns is that both data sets contain much place features located in the inner-city area. 

However, there are exceptions to this general pattern. For instance, in the Malmö model, when prior crime is excluded (exhibit a in Fig. 2 ), the register data identifies one cluster of high-risk grid-cells located just west of the large cluster of overlapping cells, and another smaller one to the south, not considered high-risk by the OSM model. Both these clusters are, in fact, adjacent to two shopping malls. One possible interpretation of this discrepancy is that the register data is more comprehensive by including all relevant place features at these locations (e. g., bars, fast-food restaurants, cafés, and convenience stores), which is not the case for the OSM data. A similar pattern can also be observed for the Helsingborg comparison (exhibit c and d in Fig. 2 ), where the register data tend to identify several grid-cells scattered outside of the city center as high-risk, which are not considered high-risk in the OSM model. Taken together, these results may indicate that there is a spatial heterogeneity in the OSM data, where place features are more extensively mapped and better reflects the actual distribution of these features in some parts of the city than in others. 

Since the above analysis only considers the top high-risk places, Table 6 shows the results from a bivariate Spearman ranked-order correlation between grid-cell RRV across models using register and OSM data in all cities. While not being a measure of absolute agreement, this analysis provides some guidance in understanding whether grid-cells being ranked as high (or low) risk in one dataset has a similar rank in the other. Since there is a considerable share of grid-cells having no risk (i. e., a RRV equal to one), which consequently may impact the correlation coefficients, the upper diagonal of Table 6 show correlation coefficients when all cells are included, and the lower when no-risk cells are excluded. The results show that for Malmö there is a quite strong correlation in the ranking of grid-cells between models when prior crime is both excluded and included, and when considering all grid-cells or excluding those with no risk. For Helsingborg, the analysis when all grid-cells are included shows a somewhat weaker association. This is further pronounced when no-risk cells are excluded where the association, at least when prior crime is excluded, must be considered rather weak. This indicates that the correlation coefficient by all accounts is influenced by the two different models identifying a considerable share of grid-cells as no-risk but are less consistent in the ranking of high-risk grid-cells. A similar pattern in results can also be seen for Kristianstad when prior crime is excluded, but not when included.
section_name: High-Risk Places Agreement

section_content: The result from the current study shows that there are several place features serving as risk factors for future violent crime in public across three Swedish cities of varying sizes. This is independent of using register or OSM data as input, and whether or not prior Fig. 2 Choropleth maps visualizing the spatial overlap of high-risk grid-cells between models when prior crime is excluded a, c, e and included b, d, f for Malmö a, b, Helsingborg c, d, and Kristianstad e, f OSM: OpenStreetMap ▸ violence is included in the models. The most consistent result, however, is that bars/ nightclubs are significantly associated with increased rates of future violent crime at micro-places in all but one of the twelve models. This corroborates results from previous studies in other contexts (e. g., Caplan et al., 2013 Caplan et al.,, 2017;; Connealy, 2020; Connealy & Piza, 2019; Drawve et al., 2016), and suggests that violent crime in public is associated to nightlife economy areas and alcohol intoxication in all three of the studied cities. This also rhymes well with the view of the Swedish National Council for Crime Prevention, which describes the typical case of violent crime in public as occurring at night, between two unfamiliar individuals, where both parties -but especially the offender -are intoxicated (Olseryd, 2015). Another consistent result in the current study is that parks/green areas are not associated with public violent crime in any of the models. Although they may be of importance for some types of crime, and often locations that may be perceived as unsafe (see Kronkvist, 2024), several studies employing RTM do not find any support for an association between parks and violent crime outcomes (e. g., Barton et al., 2021; Connealy, 2020; Connealy & Piza, 2019; Fox et al., 2021). 

Another finding from the present study is the observed differences and similarities in predictive accuracy and efficiency of RTM-models when using register and OSM data, and between cities. In sum, the results shows both consistencies and inconsistencies. When prior crime is excluded from the models, using register or OSM data provides similar accuracy and efficiency for the largest of the three cities, Malmö. For Helsingborg, the mid-sized city, the model using register data outperforms the model using OSM data in terms of both accuracy and efficiency. However, Table 6 Bivariate Spearman's rank-order correlations in grid-cell RRV between models using register and OpenStreetMap data for Malmö, Helsingborg, and Kristianstad Hbg: Helsingborg; Kstd: Kristianstad; OSM: OpenStreetMap; Reg. : Register; w/o: without. Upper diagonal coefficients when all cells are included, lower coefficients when no-risk cells are excluded. All correlations are significant at p < 0. for the smallest city, Kristianstad, the model using OSM data is more accurate and efficient in forecasting future incidents of public violent crime. Thus, these results do not signify any evident pattern in favor of using either register or OSM data to forecast future violent crime in public between cities of varying sizes. However, when including prior violence in the models, there is a somewhat more concise pattern. For Malmö, there is still no notable difference in either PAI or PEI* values between models, while for Helsingborg the register data model provides both higher PAI and PEI* values than the OSM model. For Kristianstad, the register data model gives a considerably higher PAI and slightly higher PEI* value than the OSM model. As such, this indicates that the smaller the the larger the discrepancy is in predictive accuracy and efficiency (although to a lesser degree) in favor of using register data, but only when prior crime is included. One explanation for these differences is that place features in the OSM data are considerably fewer compared to the register data in the smaller cities (see Table 1 ) suggesting that the OSM data may not be complete (see Bright et al., 2018; Vonthron et al., 2023; Pinho et al., 2023), which in turn provides less accurate predictions of future risk. More specifically, the results show that although there is an overlap in which grid-cells that are considered highrisk between models, there are still substantial differences. This is also shown by the gridcell RRV correlation coefficients between models using register and OSM data, which in most cases can be considered rather low. Considering the PAI and PEI* it seems like the non-shared grid-cells identified using register data generally capture cells with (more) future crime than models using OSM data, especially for Helsingborg and Kristianstad. Summing up, it should be noted that using OSM data seems to provide results that are similar to those when employing register data for Malmö, which according to Swedish measures is considered a large city. However, with a population of roughly 325,000 it is a city that, by international standards, most likely is considered relatively small. 

While it is beyond the aim of the current study to evaluate the accuracy and efficiency of the RTM-models compared to other methods (see e. g., Wheeler & Steenbeek, 2021; Doyle & Gerell, 2024), this is an important topic for future research. The models used in the current study are limited to a number of theoretically and empirically relevant factors available from both register and OSM repositories. As such, the RTM-models produced here should not be viewed as optimized but rather models produced to compare results when using two different sources of information as input, and therefore unsuitable for comparative purposes with other spatial forecasting techniques. Given that OSM includes a vast amount of place features or key-value combinations that have not been included here, but that still may be of relevance for the outcome (e. g., parking lots, ATMs, cinemas, etc. ), there is potential value in adding additional features and produce optimized RTM-models using OSM data. To continue evaluating the feasibility of employing OSM data to forecast the spatial distribution of crime, future research should therefore scale by producing such optimized RTM-models with complete sets of relevant place features, with and without prior crime included, and evaluate the accuracy of these models in relation to other spatial forecasting techniques. Preferably, such studies should also be produced and evaluated across different contexts and cities of varying sizes. Here, it would also be reasonable to consider OSM data as a complement to register data, when such data on specific place features is unavailable, or even try to optimize models using both register and OSM data. Furthermore, future research should also consider forecasting other crime outcomes and using other forecasting methods when incorporating OSM data. The current study has had an exclusive focus on violent crime in public by using an RTM-approach, but results may differ in regard to other crime types and when using other analytical methods. In addition, it would also be interesting to examine the extent to which RTM could aid crime mapping methods in producing future crime locations that are more consistent over time. I. e., to compare if traditional crime mapping methods that include place features could predict future crime locations that are more consistent over several years of data compared to the same models without such place features. 

However, when employing OSM data in research one must consider some potential drawbacks. OSM data may, due to its crowdsourced nature, suffer from some degree of outdatedness since updates and corrections to the data depend on user revisions, which are not necessarily timely. However, it is reasonable to assume that popular places, in larger cities, are more likely to have timely updates than less popular places. In contrast, the register data is often updated according to national laws and regulations. For instance, bars/nightclubs, restaurants, and convenience stores must have permits to conduct business and licenses to serve alcohol, handle food, or even sell tobacco. As such, the register data is more likely to be more up-to-date in a timely manner. Logically, register data thus seems more accurate for smaller cities, especially for places not located in the city center or similarly popular areas. Moreover, and related to the crowdsourced nature of OSM data, its coverage may vary both across and within cities. While the current study does not evaluate the reliability of OSM data by comparing it to register data as such, the spatial patterns of identified high-risk grid-cells across models (see Fig. 2 ) suggest that there may be issues with spatial heterogeneity in the OSM data (see Vonthron et al., 2023). That is, some areas of a city (e. g., the immediate inner-city) may be more complete in terms of place features compared to others, which evidently is problematic and may produce spatially biased models. However, it should still be stressed that OSM data produce results that are highly similar to those using register data, but only in the largest of the three studied cities (see Bright et al., 2018). 

Furthermore, using OSM data may also present issues with construct validity. While there are systematic guidelines for reporting to OSM, and the definition of specific key-value combinations (see OpenStreetMap, 2023), there are no guarantees that contributors follow these to the letter (Pinho et al., 2023). However, these guidelines also restrict the flexibility in the operationalization of place features, which is possible when using register data. In relation to the current study, for instance, register data from the National Agency for Education offers the possibility to separate between elementary and high schools, being privately or publicly governed. However, the key-value combination representing schools (i. e., amenity:school) in OSM includes both primary, middle and high schools (OpenStreetMap, 2023). 

Aside from these general limitations of the OSM data, there are a few things that are unique to Swedish cities that might affect the generalizability of the results. Most noticeable is the Swedish alcohol monopoly, which regulates the off-permit sales of alcohol above 3. 5 percent alcohol by volume. As such, liquor stores are always state-run, limited in number, and have restrictive opening hours. While it would be reasonable to include liquor stores as a potential risk factor for violent crime in public, the limited number of liquor stores in the study areas made the inclusion of these features unfeasible (e. g., Kristianstad has one). Additionally, to be able to serve alcohol in venues, a serving permit issued by the municipality is necessary, with limitations on who can be served and when. These regulations mean that a person must either plan their alcohol purchase in advance or consume alcohol in bars at a higher cost. Another aspect that might affect generalization is the size of the cities in Sweden. Malmö is the third largest city in Sweden, but compared to international cities, it is rather small. Similarly, Kristianstad, with a population of about 41,000 inhabitants, is by international standards most likely to be considered a town. 

Despite these limitations and potential drawbacks of OSM and the generalizability of results, the current study still suggests that these data may be of beneficial value to place-based criminological research in general, and RTM studies in particular. However, there are indications that OSM data are more reliable for these purposes in larger urban areas than in smaller ones. Yet, it is evident that more research on this topic, from a broad range of contexts, is highly warranted.
section_name: Discussion and Conclusion

section_content: Tables 7, 8, 9, 10 and 11
section_name: Appendix

section_content: Acknowledgements We would like to express our gratitude to Mona Tykesson ( Malmö University ) and Kenneth Lewenhagen ( Blekinge Institute of Technology ) for providing valuable comments and input on the current manuscript.

section_content: Data Availability Map data copyrighted OpenStreetMap contributors is available from https:// www. opens treet map. org. The raw crime data in the present study are not publicly available due to confidentiality reasons. The aggregated datasets analyzed in the current study are however available from the corresponding author on reasonable request.

section_name: Declarations

section_content: Author Contribution Karl Kronkvist: Conceptualization, data curation, investigation, methodology, resources, visualization, writing -original draft, writing -review & editing. Anton Borg: Conceptualization, data curation, methodology, resources, visualization, writing -original

section_content: Ethics Approval This study has been reviewed and approved by the Swedish Ethical Review Authority (Dnr. 2023-07467-01). 

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
section_name: Declarations