Examining Crime Trajectories at Micro Geographic Locations Across Varied Urban Contexts in the U.S.

Abstract

Objectives

There is a lack of research for the spatial distribution of crime at micro geographic units across a variety of places. To address the research gap, this study examines crime trajectories over the most recent decade across a wide range of cities in the U.S.

Methods

Using cities of different sizes, developmental stages, and employment levels as the three criteria, official crime data from 12 U.S. cities between 2010 and 2018 are analyzed to examine crime trajectories at the street segment level. Group-based trajectory models are used to determine the distinct longitudinal trajectory profiles of violent crime and property crime.

Results

The results provide evidence that the overall crime trend varies across cities, but crime incidents, both violent and property, are clustered in a small proportion of street segments over the time period for all the 12 cities. Moreover, street segments in large cities or stagnant cities are more likely to experience higher crime trajectories over time than those in small or growing cities.

Conclusions

Crime is predominantly concentrated within a very small percentage of street segments across cities, regardless of the city context. However, city context plays a significant role in shaping overall crime trajectories. This underscores the importance of taking city-specific factors into account when designing crime prevention and intervention strategies.

Introduction

Crime concentration is a well-established concept. As Eck and Weisburd (1995) noted, “Crime events are not uniformly distributed, a fact known for over a century. At every level of aggregation, some geographic areas have less crime than others” (p. 12). Historically, research has highlighted crime variation across different geographic scales, from nations or states (Baumer et al. 2012), across counties (Baller et al. 2001; Phillips 2006) or cities (Baumer et al. 1998; Beaulieu and Messner 2010; Hipp 2011; McDowall and Loftin 2009), to neighborhoods (Sampson 2012; Shaw and McKay 1942). By the late 1980 s, criminologists shifted their focus to micro-geographic crime patterns, along with the term criminology of place introduced by Sherman et al. (1989), emphasizing the study of crime at small geographic units, such as street segments or specific addresses (Sherman et al. 1989; Weisburd et al. 2004). Since then, numerous studies have confirmed that crime is significantly concentrated in micro places (Groff et al. 2010; Schnell 2017; Weisburd et al. 2004), and this crime concentration is relatively stable over time (Weisburd et al. 2024). In addition, researchers also posit that crime shows relatively similar levels of concentration across cities.

Yet, there are still challenges in the “Crime and Place” literature. First, one commonly noted limitation in individual studies is the lack of diversity in the cities being analyzed. The majority of studies on crime trends of micro geographic places focus on one single, large city, such as Seattle, Vancouver, Chicago, etc. (Andresen et al. 2017a, b; Curman et al. 2015; Griffiths and Chavez 2004; Groff et al. 2010), or on specific counties, such as one study about Bronx County, New York (Herrmann 2013). However, at the broader literature level, recent work demonstrates growing heterogeneity in study locations. For example, a recent systematic review of crime concentration by Weisburd et al. (2024) examined data from over 50 cities across 47 studies. In addition, several studies have expanded their scope beyond individual cities by analyzing the level of crime concentration in micro-locations across multiple urban areas simultaneously (e.g., Hipp and Kim 2017; Walter et al. 2023; Weisburd 2015). Some studies have also explored crime in less traditional settings, such as Brooklyn Park, Minnesota, a suburban area (Gill et al. 2017) or across a variety of neighborhoods within different cities in the 2000 s (Krivo et al. 2018). While progress has been made, it remains important to further expand the range of urban contexts studied to enhance the generalizability of findings in this field.

Second, while there is growing research examining developmental patterns of crime at micro-places within cities, many existing studies are still limited in geographic scope or focus on older time periods, often from the 1990s to early 2010s. Although several studies have explored crime trends over time (e.g., Andresen et al. 2017a, b; Schnell and McManus 2022), there remains a need for updated analyses that examine more recent trends across a broader range of cities and micro-geographic units, such as street segments. In particular, few studies combine both recent data and spatial diversity to assess crime trajectories. To fill in this gap, this study examines crime trends for the most recent decade (2010–2018) across a wide range of cities in the United States by selecting cities based on different demographic information to understand the crime trajectories more deeply. Specifically, this study addresses the following research questions:

• R1: What are the spatial–temporal crime trajectories in street segment across cities and how representative are the trends in different areas of a city?

• R2: How do crime trajectories differ across different city contexts?

This study offers a unique contribution by building on and extending recent advancement in the crime concentration literature. Prior research has introduced sophisticated methods for measuring crime concentration, including the use of Lorenz curves and Gini coefficients (Bernasco and Steenbeek 2017; Mohler et al. 2019; O’Brien, 2019), along with comparative analyses of concentration metrics to evaluate their interpretive value (Lee and Eck 2019). Chalfin et al. (2021) further proposed a simulation-based method to assess “marginal crime concentration” across cities. While these approaches offer valuable insights into static crime patterns, this study adopts a trajectory-based method to examine how crime changes over time at micro places. Moreover, this study builds on recent longitudinal micro-spatial research (e.g., O'Brien et al. 2023) by expanding the analytical scope to include a diverse set of U.S. cities selected for demographic variation. In doing so, it aims to offer a more comprehensive understanding of spatial–temporal crime trajectories and how they may differ across urban contexts.

Spatial Crime Patterns and Concentration

With the advent of powerful computer systems and software packages in the late 1980s, researchers began to further explore crime patterns at smaller geographic units, such as street segments or intersections (Groff et al. 2010; Weisburd et al. 2004). Street segments, or street block faces, are defined as “the two block faces on both sides of a street between two intersections” (Weisburd et al. 2004: 290). Intersections, often called street corners, were defined as locations where two or more streets crossed. A number of studies investigated crime changes at microspatial units, and it was consistently demonstrated that crime concentrated at a range of spatial scales within a city (Ratcliffe 2004; Weisburd et al. 2004), which was termed the “law of crime concentration at places” in the literature (Weisburd 2015; Weisburd et al. 2012). These highly localized places with crime were referred to as “hot spots” (Ratcliffe 2004). Crime in hot spots tended to cluster at street addresses, groupings of street blocks, or particular street intersections and street segments (Braga and Clarke 2014), and this spatial concentration was similar across different cities such as Seattle (Weisburd et al. 2012), Vancouver (Andresen et al. 2017a, b; Curman et al. 2015), and Albany (Wheeler et al. 2016), to name a few examples.¹

Crime did not occur in as wide a range of spaces as people may think; instead, crime concentration was generalized at the area/street level and spatial clustering at the point level (Johnson 2010). Additionally, research found that general crime patterns were somewhat similar at all spatial scales, with more variation within larger units, which highlighted the importance of analyzing crime patterns at small scales (Andresen and Malleson 2010). With increasing research examining crime in smaller units, from tracts, to blocks, then street segments or even points, the crime pattern consistently showed that crime tended to cluster chronically in a small number of places, such as street segments near public facilities and along segments that were arterial roads or bus routes (Andresen et al. 2017a, b; Andresen and Malleson 2010; Groff et al. 2010; Weisburd et al. 2004; Weisburd et al. 2009). Specifically, research indicated that more crime events were commonly found in criminogenic facilities and places such as bars, subway stations, schools, halfway houses, or drug treatment centers (Groff and Lockwood 2013; Haberman and Ratcliffe 2015). Further, most micro-places had stable trajectories, and a small group of street segments and intersections accounted for changes in trends for the city as a whole (Braga et al. 2011, 2010).

This crime concentration at the street segment level also shows some consistency across cities. For example, a body of work by Weisburd and colleagues (2004, 2009, 2012) analyzed crime on street segments in Seattle over a decade and a half and found that crime was highly concentrated among a small percentage of street segments, and it was the same for juvenile crime (Weisburd et al. 2009). Braga and colleagues (2010, 2011) analyzed both robbery and gun assault incidents in Boston over a 28-year period and found that only 1 percent of all Boston street segments accounted for almost half of commercial robberies, and 8 percent accounted for one-third of all street robberies (Braga et al. 2011). Likewise, a study using the same data revealed that 3 percent of volatile places in Boston accounted for almost half of the gun incidents, which drove Boston’s overall trend in gun violence (Braga et al. 2010). The findings from individual studies are supported by recent systematic reviews on crime concentration (Lee, et al. 2017; Weisburd et al. 2024). Weisburd et al. (2024) analyzed data from over 50 cities and found that 50% of crime occurs on approximately 4.5% of street segments, and 25% on just 1.25%. Even when excluding extreme cases, 50% of crime is concentrated on 2.5% of streets, and 25% on just 1.4%. These results align with Lee et al.’s (2017) earlier meta-analysis of studies from 1970 to 2015, which similarly concluded that crime is highly concentrated at micro places, with a small percentage of locations consistently accounting for a large share of total crime.

Although much research examines the concentration of crime at hot spots, less attention has been given to longitudinal changes at smaller geographic units. The literature predominantly focuses on the spatial distribution of crime, attributing concentration to increased crime opportunities in certain areas. However, there is less much research on temporal crime changes at micro units. A key question remains: does crime concentration in micro-units persist over time, or do patterns shift? For studies of this kind, Weisburd et al. (2004) took a first step and analyzed crime trajectories on street blocks in Seattle from 1989 to 2002, finding that a very small fraction of blocks accounted for most of the city’s 24% crime reduction. Curman et al. (2015) extended this research in Vancouver (1991–2006) and found that while some locations exhibited significant increases or decreases in crime, most micro-locations remained stable. Wheeler et al. (2016) replicated this approach in Albany, New York (2000–2013), identifying 8 trajectory groups and each followed the overall citywide decline (Wheeler et al. 2016). While Albany’s overall trends mirrored Vancouver’s, they diverged from Seattle’s pattern. Moreover, Groff et al. (2010) addressed this concern by explicitly examining both spatial and temporal crime variations in Seattle over 16 years, finding significant street-to-street heterogeneity, particularly in high-crime areas. When testing a suburban setting, Gill et al. (2017) observed higher crime concentration but lower street-by-street variability in Brooklyn Park, Minnesota compared to urban areas. All in all, these studies highlight the importance of examining crime trends at very local geographic levels, but more research is needed beyond a single city context.

Why City Contexts Matter?

This research expands its scope beyond uniform big cities by considering the varied city contexts to which micro geographic units belong. One might naturally wonder why city contexts matter. According to strain theory, crime arises when individuals cannot achieve societal goals through legitimate means, leading to strain and frustration (Agnew and Brezina 2010). General strain theory (GST) extends this perspective to explain variations in crime at the community and societal levels (Agnew 1999). He argued that contextual differences in strain contribute to disparities in crime rates and identified key contributors to higher crime rates, including specific community characteristics, intervening mechanisms, aggregated negative affect, and conditioning variables (Agnew 1999; Sexton 2011). Communities characterized by economic deprivation and inequality expose residents to greater stressors and fewer legitimate coping mechanisms, increasing the likelihood of criminal responses. GST thus provides a theoretical foundation for understanding how broader structural conditions shape the shifts in crime rates over time and the differences in crime between communities/cities.

As one example, connecting GST with different city contexts: in high employment cities where job opportunities are abundant and economic resources are more evenly distributed, communities in these cities may experience less strain and have more resources and legal avenues for residents to achieve success, which could result in lower community crime rates. Conversely, in low employment cities with limited job prospects and economic hardship, communities are more likely to select and retain strained individuals (Agnew 1999), who may resort to criminal behavior as a means of coping with financial difficulties, leading to higher crime rates.

Complementing this perspective, social disorganization theory emphasizes the importance of community structure and collective efficacy in regulating behavior. It posits that structural disadvantages—such as poverty, residential instability, and ethnic heterogeneity—erode social cohesion and weaken informal social controls (Shaw and McKay 1942; Sampson et al. 1997). These conditions foster environments where crime is more likely to occur and persist. From this view, city-level factors influence how neighborhoods are organized, shaping residents’ capacity to uphold social order and prevent deviant behavior.

Further, according to a recent report by the Manhattan Institute, stagnant cities face numerous challenges and strains, including weak growth or even decline in population and employment, economies with lower value, below-average levels of college-degree attainment compared to the national average, and higher costs of municipal services (Renn 2019). These factors collectively contribute to conditions that are typically associated with higher crime rates. But there is also research suggesting that crime rates rise with population growth due to an increase in residential mobility (Braithwaite 1975) or community disruption (Barton et al. 2024). Nonetheless, the city context that has been more extensively researched regarding its correlation with crime rates is typically the size of the city (Chang et al. 2019). A large number of empirical studies showed that crime rates in larger cities are still significantly higher than those in smaller cities, spanning from the 1970s to the 1980s (Ackerman 1998; Glaeser and Sacerdote 1999), or from the 2000s to the 2010s (Chang et al. 2019), one reason being that large cities have greater crime opportunities (Braithwaite 1975). One limitation is that the unit of analysis typically focuses on the city level. The present research advances the literature by integrating these different city contexts into a single study and examining changes in crime at smaller geographic units over the most recent time period.²

In summary, city context matters for understanding crime patterns because it shapes the socio-economic conditions, opportunities, and structural factors that influence individuals’ likelihood of engaging in criminal behavior. By examining different city contexts, researchers can gain insights into the complex interplay between macro-level factors and crime patterns, ultimately informing strategies for crime prevention and intervention.

Research Context

To access the crime trajectories across cities, there are three important dimensions in choosing the cities. First is the size of the city, as small cities are qualitatively and quantitatively different than larger cities in the U.S. (Norman 2013). The cutoff for city size that is utilized is based on population, where a city with over 500,000 population is referred to as large size city, a city with population of 150,000 to 499,999 is medium size, and a city with a population of less than 150,000 is small size.³ Second, whether a city is growing or stagnant over the past decade as a reflection of city development is another dimension, in which growth or stagnation is defined based on county population change from 2000 to 2010. Here I choose the change in county population instead of city population is because the county better captures broader housing and labor market conditions that influence regional development. City boundaries can obscure true population growth—especially in well-developed urban cores—whereas counties often include adjacent suburban and peri-urban growth areas. Counties thus offer a more comprehensive representation of how a region evolves demographically and economically. For instance, Reia et al. (2022) demonstrated that population growth at the county level smooths local shocks by capturing migration flows beyond dense city centers, providing a more stable reflection of regional change. In addition, prior research and national data systems have utilized county-level metrics as proxies for regional context in urban and crime studies (Maltz 2000). Cities with a county population growth of at least 10 percent over the decade are categorized as growing cities, and those with a county population change of between −4 and 4 percent over the decade are categorized as stagnant cities.⁴

The last dimension is the employment presence, which is measured as the ratio of total employment to population in 2010 in the city. There are several theoretical motivations for choosing this measure. From the perspective of opportunity theory, more businesses in an area provide a greater number of potential targets for criminals. This abundance of targets, such as stores, offices, or restaurants, increases the opportunities for criminal activities. Also, crime often occurs near commercial districts, and these large commercial areas attract high volumes of pedestrian and vehicular traffic, therefore, a city with more businesses would be more likely to have more crime. In terms of social disorganization theory, it focuses on how structural factors like poverty and residential instability weaken informal social controls, contributing to crime (Shaw and McKay 1942). While the theory does not directly link employment to informal control, later research suggests that stable employment may promote neighborhood stability and social cohesion by providing individuals with a sense of purpose and belonging in their communities (Sampson et al. 1997). When individuals have access to stable employment, they are less likely to engage in criminal behavior driven by economic necessity. In any case, employment presence can serve as a useful indicator to stratify cities when examining crime trends. Specifically, cities with a ratio of over 50 percent are considered as high ratio employment city and below 50 percent as low ratio employment city.

In summary, size of cities, city growth, and employment presence are important criteria to distinguish cities. Because of the limited scale of land use and job opportunities, small cities may not experience the absolute number of criminal events as large cities have. However, it is possible that when adjusting for population size, crime rates in small cities could be significantly lower or, in some cases, higher than those in larger cities. When there is a mass influx of people into cities, it brings more opportunity for jobs, but also more crime. In short, it is expected that crime patterns vary across different cities, such as differences between small and large cities or differences between growing and stagnant cities.

Obtaining access to a wide range of cities with crime data in the U.S. is not an easy task; fortunately, I have access to a large dataset with crime information across multiple years, multiple cities, and across different geographic units through the National Incident Crime Study (NICS) (Kubrin et al. 2024).⁵ Using the NICS as the data pool, 12 cities have been selected through a stratified random sampling process based on three city contexts dimensions—city size, city growth, and employment presence, and all 12 cities have crime data available from 2010 to recent years (e.g., 2018).⁶ The list of cities is Seattle, San Antonio, Memphis, Los Angeles, Scottsdale, Riverside, Minneapolis, Akron, Asheville, Reading, Santa Monica, and Diamond Bar, and these cities are broken down to a 3 (large, medium, small) by 2 (growing, stagnant) by 2 (high employment, low employment) table based on the criteria of city selection (See Luo 2025 for additional contextual details of each city). The key criteria information of the 12 cities are presented in Table 1.

Table 1 Summary statistics of selected cities

Data and Methods

Data

The main data is official crime data from 2010–2018 from the 12 cities mentioned above. All crime data were collected either from police department data requests or police department websites from specific cities and placed in street segments. I focus on six Part I Uniform Crime Report (UCR) offenses from the Federal Bureau of Investigation (FBI) reporting system, which include measures of violent crime (criminal homicide, robbery, and aggravated assault) and property crime (burglary, larceny-theft, and motor vehicle theft). These are the most serious crimes that are reported to the police, and the hierarchy rule is applied to UCR offenses.⁷

Crime incidents were geocoded to latitude–longitude point locations using a geographic information system (ArcGIS 10.7).⁸ Overall, the geocoding match rate was over 90% for all the 12 cities, and most cities have a match rate as high as 98% or above.⁹ Then all crime incidents were aggregated and placed in appropriate street segments.¹⁰ When crime incidents were aggregated at the street segment level, some data have been lost, although not significantly. Across most cities, the percentage of missing data (crime incidents unable to be placed on street segment) over the years was negligible, around 2%.¹¹ Crime statistics in street segments in 2010 for all the 12 cities are presented in Table 2 (For full violent and property crime counts information for the 12 cities from 2010 to 2018, see Appendix Table 7). Overall, crime incidents in 2010 vary across cities, and large cities have substantially more crime incidents than medium-sized and small cities. But there are also variations among cities in the same category.

Table 2 Crime statistics of selected cities

Methods

Step 1: Overall Crime Trends and Crime Concentration

First is the raw crime counts for both violent and property crime from 2010 to 2018 for the 12 cities.¹² To compare the violent and property crime trends across different cities over the study period, I have standardized them as crime rate per 1,000 population, which is computed by dividing the raw crime counts by the city population in 2010, then multiplying by 1,000 in a specific year. To assess how crime is clustered for each city, I computed the annual number of violent and property crime incidents that occurred on each segment. For each year and city, I then ranked segments in descending order based on their crime counts and then identified the smallest proportion of segments that collectively accounted for at least 50% of total crime incidents.

Step 2: Group-Based Trajectory Models

To determine whether distinct longitudinal trajectory profiles of violent crime and property crime could be identified, a group-based approach was employed (Nagin 2005). This approach provides an empirical basis for identifying both the number and shape of trajectory classes (the TRAJ procedure in STATA) while clustering street segments that exhibit similar crime patterns over time. Briefly, the analyses were developed by first modeling the number of trajectory groups/classes, then modeling the distinctive trajectory shapes (e.g., linear or quadratic growth) of each trajectory group. Selecting the number of trajectory groups that best fits the data is the initial step in model estimation, and model selection is based on the Bayesian Information Criterion (BIC) and Entropy. Entropy measure assesses the quality of the classification by evaluating how well individuals (here street segments) are assigned to trajectory groups. It ranges from 0 to 1, with higher values indicating more precise classification. The logit model option in TRAJ for violent crime (recoded as 0 or 1) was used as on average 90% of the street segments had a value of 0 violent crime, ranging from 88.7% in 2010 to 91.3% in 2018. About 7% of the total street segments have a value of 1 violent crime, so just 3% had values greater than 1. The censored normal model option in TRAJ for logged property crime was used because the property crime data were skewed towards the scale minimum.

For each observation, the group-based approach provides the probability of belonging to each trajectory group, and the assigned trajectory group is based on the highest probability. According to Nagin (2005), observations in a given trajectory should have high probability of assignment in their group and low probability of assignment to the other identified groups, and if the mean probabilities equal to or greater than 0.7, it implies a satisfactory fit. When multiple alternate models had similar BIC scores, the selection of the best model was based on a combination of four things: the lowest BIC score, significant growth coefficients, posterior probabilities of > 70%, and the most parsimonious model (Cleverley et al. 2012). Based on these criteria, there are 7 distinct violent crime groups and 9 distinct property crime groups identified in the data, and I regrouped the property crime to 7 groups due to the similarities of 3 consistent crime-free to low level crime groups (See Appendix Table 8 for the optimal trajectory models).

Here, street segments are used as the unit of analysis. All the segments were stacked up across the 12 cities. Overall, there was a total of 297,199 street segments across these cities. Since it is common for crime over time to exhibit a non-linear trend, I included a quadratic trajectory in my analyses. The group-based trajectory models are estimated using the following form:

$$\text{P}\left({Y}_{i} \right|{ Time}_{i})=\sum_{j=1}^{j}{\uppi }_{j}\text{P}\left({Y}_{i} \right|{ Time}_{i},\text{ j};{\theta }_{j})$$

(1)

$$\text{logit}(\text{P}\left({Y}_{ij}=1|{Time}_{i,j}\right)={a}_{j}+{\beta }_{1j}\left({Time}_{i}\right)+{\beta }_{2j}{\left({Time}_{i}\right)}^{2}$$

(2)

where Eq. 1 denotes the probability distribution of each street segment’s trajectory of outcome (either violent crime or property crime) over time. ${\uppi }_{j}$ is the probability of membership in group j. $\text{P}\left({Y}_{i} \right|{ Time}_{i},\text{ j};{\theta }_{j})$ is the conditional distribution of ${Y}_{i}$ given membership in group j, indexed by the unknown parameter vector ${\theta }_{j}$. In Eq. 2, the link function is the logistic function for violent crime as it is a binary outcome. Time is coded to capture the change in time by showing the number of years since 2010, so there will be a total of 9 years. For property crime, the data are highly zero-inflated—50% of segments had zero property crimes, and over 75% had zero or one incident. Additionally, the distribution exhibits a long right tail, with maximum values exceeding 1,000 in some years, leading to extreme skewness and kurtosis. To address these issues, the property crime variable was log-transformed (using log(x + 1)), and trajectories were estimated using the censored normal distribution (cnorm) function in the traj plugin in Stata. A quadratic time term was also included in the model, consistent with the approach used for violent crime.

Results

Step 1: Overall Crime Trends and Crime Concentration Across Cities

Descriptive Accounts of Crime Trends Over Time

Figure 1 shows the violent and property crime rate changes over the decade for the 12 cities. Overall, there is a large variation of crime trends across cities. Regarding the violent crime rate, some cities show a decreasing trend, such as Akron and Reading; some show an increasing trend, such as Santa Monica and Seattle; some are flat, such as Scottsdale and Diamond Bar; and some are non-linear, such as Memphis, Asheville, and Los Angeles. Although Los Angeles has the largest population among these 12 cities, its violent crime rate is not the highest, rather, Memphis has a much higher violent crime rate than the other 11 cities over time. In terms of property crime, there are also a great variety of crime rate changes over time across cities, and most show a non-linear trend. Similarly, larger cities do not necessarily have higher property crime rates across these 12 cities. For example, Memphis and Seattle have a much higher property crime rates over time than other large cities. Santa Monica, as a small city with around 90,000 population, has a much higher property crime rate than other small cities like Diamond Bar and Reading and even other medium-sized cities such as Scottsdale and Riverside.

Fig. 1

Violent and property crime rate per 1,000 population over 12 cities from 2010–2018

Crime Concentration

Since crime incidents were geocoded and placed in the appropriate street segment for each city, the percent of segments accounting for 50% of violent and property crime in each year for each city is computed, as shown in Table 3. Table 3 Panel A provides strong evidence of violent crime concentration with a small percentage of street segments across all 12 cities, regardless of their size or growth status. For example, in Los Angeles, 3.4% out of 88,629 street segments (about 3,013 streets) account for 50% of violent crime incidents in 2010, and this crime concentration is consistent from 2010 to 2018, fluctuating between 3.4% in 2010 and 2% in 2017–2018. In Scottsdale, 0.4% out of 18,756 street segments (about 75 streets) consistently account for 50% of violent crime incidents annually. Panel B further demonstrates significant property crime concentration across the 12 cities. Compared to violent crime, a slightly larger proportion of street segments accounts for 50% of property crime incidents, ranging from 3.3% to 6.1% in Los Angeles and 0.9% to 1.5% in Scottsdale. Overall, the findings indicate a persistent clustering of both violent and property crime within a small fraction of street segments over time. I also computed the crime concentration at 60%, 70%, and 80% for violent and property crime across 12 cities (see Appendix Tables 9-11). This is a conventional way of computing crime concentration, but there are some statistical challenges for this method, such as in cities with relatively low crime levels, crime will always be observed in a small percentage of segments in the city (see (Hipp and Kim 2017) for detailed explanation). Despite the limitation, this technique is mainly used to broadly describe these patterns.

Table 3 Crime concentration

Step 2: Group-Based Trajectories of Crime on Street Segments Over Time

I have examined the distinct longitudinal trajectory profiles of violent and property crime on street segments across all 12 cities in one analysis. Figure 2 shows the crime trajectories for each group for violent and property crime. There are 7 distinct group trajectories over time for violent crime, and from the bottom to the top, it is: crime free group (68.9%), low crime increasing to decreasing group (4.2%), low to medium crime stable group (17.4%), low to medium crime increasing group (2.1%), medium crime decreasing group (5.6%), high crime stable group (1.6%), and high crime decreasing group (0.3%). This trajectory analysis reflects what we have seen regarding violent crime concentration, as most of the street segments fall into the crime free group. Notably, however, there are more segments that remain persistently high crime over time than those where high crime levels decline. There are 9 distinct group trajectories for property crime based on the best fit of group-based trajectory analysis, and I have regrouped them to 7 distinct groups by combining the bottom three groups as a low crime stable group. These groups are crime free group (27.1%), low crime stable group (39.6%), low crime increasing group (11%), low to medium crime stable group (14.2%), medium crime decreasing group (2.7%), medium crime stable group (4.6%), and high crime stable group (0.9%).

Fig. 2

Group-based trajectories of violent crime and property crime

Tables 4 and 5 further show the percentage of street segments falling into each violent and property trajectory group by each city. Here, the percentage for each trajectory group adds up to 100% in each city. In Table 4, overall, the percentage of street segments falling into the violent crime free group is the highest for any city, which is consistent with the literature that most streets have no violent crime. But it is more over-represented in cities of Scottsdale (96.2%), and two small cities—Asheville and Diamond Bar, which are over 90%. The second group with a large percentage of street segments in these 12 cities is low to medium violent crime stable group, from 22.4% in Akron to 2.8% in Scottsdale. The high crime groups are mainly observed in large cities of Memphis and Los Angeles, and medium city of Minneapolis.

Table 4 Group-based trajectories for violent crime by each city

Table 5 Group-based trajectories for property crime by each city

In Table 5, the distribution of street segments across various property crime trajectory groups shows higher dispersion compared to violent crime trajectory groups. The property crime free group is still over-represented in Scottsdale, about 61.7% of street segments experiencing no property crime over time. Besides crime free group, a large percentage of street segments falls into low property crime stable group for all the 12 cities, from 44.1% in Riverside to 25.7% in Scottsdale. Similar to violent crime, the medium to high property crime groups are also observed in Memphis, Los Angeles, and Minneapolis, about 8% to 12% of street segments in these cities experiencing medium to high property crime trajectory, but the percentages in other cities range from 1.8% in Scottsdale to just 0.6% in Diamond Bar. In addition, Seattle, San Antonio, Riverside, and Akron also tend to experience the high property crime stable trajectory, about 1.6% in Seattle, 1% in San Antonio and Riverside, to 0.5% in Akron.

Furthermore, hierarchical clustering analyses are employed to test the urban crime concentration processes based on results from Table 4 and 5 (The K-means clustering analyses yield the same results). The results reveal two distinct clusters of cities based on their crime trajectory patterns. Cluster 1 includes cities such as Seattle, Memphis, Los Angeles, Riverside, Minneapolis, Akron, Reading, and Santa Monica. These cities tend to exhibit greater variation in crime trajectories, with higher proportions of street segments experiencing moderate to high levels of crime. In contrast, Cluster 2 comprises cities like San Antonio, Scottsdale, Asheville, and Diamond Bar, which are characterized by a higher percentage of crime-free segments and fewer segments with persistent or escalating crime patterns. Notably, the alignment of cities across both violent and property crime clustering outcomes reinforces the robustness of these groupings (see Appendix Table 12 for clustering analysis results).

Table 6 shows how these crime trajectory groups differ across different city contexts. To be specific, each column is the percentage of street segment in each trajectory group in each city type. And the number in the parentheses is the relative proportion of segments within a particular city type that falls into each crime trajectory group. In Table 6 Panel A, for example, for violent crime-free group, 83% of segments in small cities fall into this category, 77% of segments in medium cities fall into it, and 72% of segments in large cities fall into this category. When summing these up, there is a total of 232%, dividing each of these by 232%, we get the proportion of 0.357 for small cities, 0.333 for medium cities, and 0.309 for large cities. The total number of street segments in each city type is 221,928 in large cities (about 75%), 56,564 in medium cities (about 19%), and 18,707 in small cities (about 6%). Since there is a much smaller number of street segments in small cities, the 35.7% of crime-free segments are more prevalent in small cities than in large cities. To put it another way, a crime-free segment is more likely to be present in small cities than in large cities. But moving to high violent crime trajectories, streets in large cities are much more likely to fall into higher crime trajectory group, such as high crime decreasing group and high crime stable group, than small cities. The story is very much the same for property crime, streets in small cities are more likely to fall into property crime free group than streets in big cities, but streets falling into higher property crime trajectories are more likely to be present in large cities than in small cities.

Table 6 Percentage (Proportion) of street segments in each crime trajectory group by city contexts

In terms of city growth, for violent crime-free group, 84% of segments in growing cities fall into this category, and 65% of segments in stagnant cities fall into this category. If summing these up, there is a total of 149%. The proportion in violent crime-free group for growing cities is 0.564 (84%/149%), and 0.436 (65%/149%) for stagnant cities. The total number of street segments in growing cities is 133,313 (about 45%) and 163,886 in stagnant cities (about 55%). Thus, violent crime-free segments are slightly more likely to be present in growing cities than in stagnant cities. However, when we look at the high crime groups, high violent crime decreasing segments or high violent crime stable segments are much more likely to be present in stagnant cities than in growing cities. There are also more streets falling into medium property crime trajectories in stagnant cities than in growing cities, but it is not as prominent as violent crime trajectories. For high property crime stable trajectory, unlike violent crime, it is more prominent in growing cities.

For cities with different employment level, the total number of street segments in high employment cities is 116,536 (about 39%) and 180,663 in low employment cities (about 61%). Around 74% of street segments in both high and low employment cities fall into violent crime free group. However, since there are more street segments in low employment cities, the violent crime-free segments are more prevalent in high employment cities than in low employment cities. There are more streets falling into high violent crime decreasing group in low employment cities, but less so for high crime stable group. For property crime, slightly more streets fall into higher crime trajectories in high employment cities than in low employment cities.

Discussion and Conclusion

The current study enabled me to probe important but understudied empirical questions: what are the spatial–temporal crime trajectories in street segments across different urban contexts in the U.S., and to what extent do these patterns reflect meaningful variation rather than modeling artifacts? By examining the crime trends over the most recent decade and across a diverse range of cities in the U.S., this study extends prior research on crime trajectories at micro geospatial units and offers important insights into the dynamics of street-level crime trends across urban environments. Several key findings from this study are highlighted.

From a broad point of view, the crime rate changes over the recent decade vary considerably across different cities, both for violent and property crime. We see that there are different patterns of crime rate changes over time, such as flat, increasing, decreasing, fluctuating, etc. Notably, the variety of crime rate changes across different cities reveals that larger cities do not necessarily have higher crime rates than smaller cities (Chang et al. 2019), as shown in the results that Memphis and Seattle have a much higher property crime rates over time than Los Angeles, although their population size is much smaller than Los Angeles.

When examining where crime occurs on street segments, the findings are consistent with previous research showing that crime is disproportionately concentrated in specific micro-geographic areas within cities (Braga et al. 2011; Weisburd et al. 2004). Overall, this study provides strong evidence that crime is consistently concentrated in a small percentage of street segments across cities, supporting the broader principle of the law of crime concentration (Weisburd 2015). However, while the pattern of concentration—where a small subset of streets accounts for a large share of crime—is evident across all cities studied, no matter the city is small or large, growing or stagnant, or no matter there are high employment rates or low employment rates in a city, the level or degree of that concentration varies notably by city type and context. For example, the percentage of street segments that accounts for 50% of total violent crime ranges from as low as 0.3% in Scottsdale (2014 and 2018) to as high as 4.3% in Akron (2011). Similarly, for property crime, this figure ranges from 0.9% in Scottsdale (2015) to 6.9% in Akron (2011). These findings suggest that although most urban streets do not experience regular crime, the intensity of concentration differs by city characteristics—such as size, economic growth, and employment—highlighting the importance of considering local context in understanding and addressing urban crime patterns.

Furthermore, the trajectory analysis reveals key patterns in the spatial distribution of violent and property crimes across diverse urban contexts. The findings indicate that violent crime is predominantly concentrated in a small number of street segments, but this pattern is particularly pronounced in cities like Scottsdale, or small cities like Asheville and Diamond Bar, where over 90% of street segments reported no violent crime. In contrast, cities such as Memphis, Los Angeles, and Minneapolis exhibit a higher proportion of street segments falling into high crime trajectory groups. These cities, characterized by larger urban populations and potentially more complex socio-economic dynamics, appear more susceptible to persistent and high levels of violent crime. The clustering analysis further reinforces the existence of multiple types of micro-spatial crime concentration processes. It distinguishes cities with lower overall crime intensity—often smaller or more affluent—from those with more persistent and complex crime patterns, typically larger or more economically diverse. However, this divide is not purely population-driven, suggesting that a mix of underlying factors—such as city management, economic diversity, local policing—also shapes these patterns (Glaeser and Sacerdote 1999).

When examining property crime trajectories, the dispersion is more varied compared to violent crime. While Scottsdale still maintains a high percentage of property crime-free street segments, other cities display a wider range of trajectories. This variation suggests that property crime, unlike violent crime, may be influenced by a broader set of factors including economic conditions, urban infrastructure, and local law enforcement practices (Hannon 2002; Newman 1972). Notably, cities like Memphis, Los Angeles, and Minneapolis also show significant percentages of street segments in medium to high property crime trajectories, reflecting similar challenges observed in violent crime patterns.

When considering the city contexts, the analysis reveals that larger cities are more prone to higher crime trajectories, both for violent and property crime. It is possible that larger cities inherently report more crime due to greater population density or simply by volume (Glaeser and Sacerdote 1999). Prior research also suggests that urban complexity—including greater population heterogeneity, increased social disorganization, and more economic activity—can contribute to environments more conducive to crime (Sampson et al. 2002). Furthermore, the comparison between growing and stagnant cities highlights that stagnant cities tend to have a higher proportion of street segments in high crime trajectories. This pattern is more evident for violent crime, where high violent crime decreasing and high violent crime stable segments are more prevalent in stagnant cities. Linked to what have discussed about the GST, stagnant cities, characterized by economic challenges and limited resources for crime prevention and socio-economic revitalization (Ludwig et al. 2001), may foster environments where residents face greater financial hardships, social instability, and reduced access to opportunities—all of which contribute to criminogenic strains. And people in large or stagnant cities are more likely to experience these strains. This alignment with GST highlights how economic stagnation and lack of urban development not only hinder crime prevention efforts but also sustain the social and structural conditions that perpetuate the persistence and concentration of crime in urban areas.

On the other hand, the stable trajectory of high property crime, in contrast to violent crime, is more frequently observed in cities experiencing population growth and high employment. This finding is largely aligned with crime opportunities theory (Cohen and Felson 1979), in which economically thriving areas, characterized by growing populations and employment opportunities, often attract an influx of individuals, businesses, and resources, increasing the density of potential targets such as residences, businesses, and vehicles. As these areas develop, the increase in goods and resources creates an environment rich with opportunities for property crime, which in turn sustains the persistently high levels of property crime (Clarke and Felson 1993; Brantingham and Brantingham 1995). In addition, crime is not merely a product of individual motivation but also heavily influenced by environmental and situational factors that facilitate criminal acts (Eck and Weisburd 1995). Thus, the persistence of high property crime in such cities can be also understood as a function of the ample opportunities that accompany economic growth and urban expansion.

Although the findings offer a comprehensive overview of crime trajectories in various urban settings, the underlying causes of these patterns remain unexplored, which is outside the scope of this study, but it underscores the necessity for further research focusing on crime trends at the street segment level across diverse cities and extended timeframes. By delving deeper into these trends, we can uncover the factors driving crime concentration and formulate more effective crime prevention and reduction strategies. Continued study in this area will enhance our understanding and ability to foster safer communities.

While I believe this study is a great contribution to literatures in crime and place, there are some limitations that deserve mention. The primary limitation is the inability to select cities fully randomly. The ideal research design is to have a large sample of representative cities across states in the U.S., but it is hard to expand my sampling pool as not all the cities in the U.S. have the capacity or the willingness to post their crime data online for public use. But the NICS is largely representative of tracts and cities in the U.S. (Kubrin et al. 2024), which, to some extent, mitigates the limitation. In addition, by narrowing down my city context to three dimensions as city size, city growth, and city employment, it potentially limits the ability to capture the full spectrum of urban contexts and crime dynamics across the nation. This restricted geographic focus may impact the applicability of the findings to other cities or regions. But on the other hand, this research presents some findings that are very informative to certain cities. Further, the study used aggregated types of crime measures (e.g., violent and property crime). Yet, it is possible that the crime trajectories might vary depending on the type of individual offenses. Further research is needed for examining the patterns of disaggregated crime types across various city contexts. In terms of methodological limitations, the trajectory-based approach, while effective for identifying broad temporal patterns over multiple years and providing insights into longitudinal stability or change in crime concentration, may overlook important short-term fluctuations—such as seasonal crime spikes or rapid responses to policy changes—that could influence localized crime dynamics.

Limitations aside, this study provides valuable insights into the crime trends at the street segment level across a diverse range of U.S. cities. The findings confirm the persistence of crime hotspots over time (Ratcliffe 2004). This underscores the continued need for targeted crime prevention strategies. However, the results of this study also indicate that current efforts—such as hotspot policing—may have limited effectiveness in reducing crime on persistently high-crime segments, pointing to the need for more sustained or comprehensive intervention strategies. Second, this study provides valuable insights into the spatial and temporal dynamics of crime across different urban contexts. It highlights the importance of considering city-specific factors such as size, growth, and employment levels when developing crime prevention and intervention strategies. By understanding the unique crime patterns in various cities, policymakers and law enforcement agencies can tailor their approaches to effectively address the root causes and mitigate the impact of crime in diverse urban environments.

Appendix 1

Table 7 Violent and property crime counts for 12 cities from 2010 to 2018

Table 8 Model results for trajectory models

Table 9 Crime concentration

Table 10 Crime concentration

Table 11 Crime concentration

Table 12 Clustering analysis results