The Spatial Scale and Spread of Child Victimization

Abstract

Previous research shows that large, densely populated urban areas have higher rates of child victimization that have persisted over time. However, few investigations have inquired about the processes that produce and sustain hot and cold spots of child victimization. As a result, the mechanisms that produce the observed spatial clustering of child victimization, and hence “why” harms against children tend to cluster in space, remains unknown. Does the likelihood of being a victim of violence in one location depend on a similar event happening in a nearby location within a specified timeframe? Rather, are child victims of violence more likely to reside in suboptimal neighborhood conditions? This paper aims to present an analytical and theoretical framework for distinguishing between these locational (point) processes to determine whether the empirical spatial patterns undergirding child victimization are more reflective of the “spread” via contagion (i.e., dependency) or whether they are produced by neighborhood structural inequality resulting from spatial heterogeneity. To detect spatial dependence, we applied the inhomogeneous K-function to Los Angeles Medical Examiner data on child homicide victim locations while controlling for regional differences in victimization events (i.e., heterogeneity). Our analysis found strong evidence of spatial clustering in child victimization at small spatial scales but inhibition at larger scales. We further found limited support for the spatiotemporal clustering of child victimization indicative of a contagion effect. Overall, our results support the role of neighborhood structural vulnerability in the underlying mechanisms producing patterns of child victimization across Los Angeles County. We conclude by discussing the policy implications for understanding this spatial patterning in geographical context and for developing effective and targeted preventive interventions.

Keywords

child victimization child homicide contagion point pattern spatial dependence

Introduction

According to a report issued by the World Health Organization (2016), the high rates at which children are victimized “paints an alarming picture of the extent to which children live with the impact of violence, in the absence of supports and services” (1, p. 13). The pervasiveness of child victimization in the United States and around the globe has become a public health crisis of epic proportions. In the United States, violence is the second leading cause of death among children and teens and the leading cause of death for Black children and teens (Children’s Defense Fund, 2020). The aftermath of violence alters the equitable distribution of a community’s resources and magnifies existing social, economic, psychological, and health disparities across sociodemographic groups (Slutkin et al., 2018).

A plethora of real-world phenomena, including but not limited to child victimization, demonstrate epidemic properties similar to a contagious disease, but the causal mechanisms remain unknown (Christakis & Fowler, 2013; Fagan et al., 2007; Funk et al., 2010; Loeffler & Flaxman, 2018; Papachristos et al., 2015). At a population level, both behavioral and disease states are influenced by similar social and spatial risk and protective factors. Research conducted in the early months of the COVID-19 pandemic, for example, demonstrated that rates of child victimization shifted, creating what some have called the “co-occurrence of two public health crises” (Shreffler et al., 2021). Increases in child victimizations have been attributed to caregiver disability (e.g., poor physical and health) (Milner, 2007; Olecká, 2022), public health policy (e.g., education policy, safety legislation; Draus et al., 2017; Gijzen et al., 2014), and structural neighborhood characteristics (e.g., widespread layoffs, poverty) (Barboza-Salerno, 2024). Identification of ecological correlates that contextualize the social disease layers is critical, including the immediate (i.e., individual), distal (e.g., cultural), and temporal socioecological contexts that accelerate the trajectory of the co-occurring development (Bronfenbrenner, 1979). Therefore, the individual-context interaction, an essential ingredient for understanding the potential spread of child victimization, must be considered when developing interventions.

Social contagion is defined as the spread of behaviors and attitudes through crowds and other types of social aggregates from one person to another (Martínez et al., 2023). Blumer (1939) defined social contagion as the transmission of ideas, feelings, or actions among individuals within a social context. He delineated two broad types of contagion: behavioral contagion, which involves the spread of specific behaviors or actions, and emotional contagion, which is the spread of emotions within a group. Previous research on child victimization contagion acknowledges that abusive behavior can spread via social contagion due to direct exposure to violence and aggression (Fagan et al., 2007; Grogan-Kaylor et al., 2020). According to social contagion theory, exposure to abusive behavior normalizes the occurrence of maladaptive behavior and creates an environment where future instances are more likely to happen. Over time, increased exposure heightens the likelihood of the behavior occurring and contributes to its spread to nearby geographical areas (Grogan-Kaylor et al., 2020).

Because social interactions are vulnerable to spatial and place-based effects, spatiotemporal modeling frameworks must be able to distinguish between clusters of behaviors produced by diffusion rather than the mere heterogeneity of underlying risk factors. However, although the concept of social contagion is well articulated, studies have yet to provide adequate empirical support for the untested proposition that social behaviors spread within confined geographic areas rather than being a product of neighborhood risk factors only (G. Barboza et al., 2022; Barboza-Salerno, 2020b). More specifically, we do not know whether the observed association between potentially violent and/or abusive behavior is more likely to result from a deterministic process that produces “hot spots” of both or rather from co-location and/or physical distance.

To respond holistically to the public health crisis of child victimization, it is critical to identify neighborhoods that lack the necessary resources to respond at multiple contextual levels and the corresponding failure to implement effective preventive interventions. In this framework, child victimization is viewed not as an individual or cultural phenomenon but rather as the product of social interactions that are situated within the broader contexts in which those interactions take place (Pérez-Figueroa et al., 2022). For example, the past two decades have seen an emergence of empirical studies confirming that certain forms of child victimization (e.g., child physical abuse) are clustered across densely populated, urban environments and associated with specific “neighborhood” characteristics such as economic inequality, health equity, environmental justice, and/or educational attainment (Coulton et al., 2007; Freisthler, Merritt, & LaScala, 2006). This work has identified neighborhood areas with higher rates of maltreatment that persist through time. Yet this work could be obscuring smaller geographic clusters that may change due to social processes rather than the structural conditions associated with where people live (Wolf, Freisthler, et al., 2017). A better understanding of the causal processes undergirding such patterns is important for interpreting social behavior and community norms around child protection across neighborhoods of varying spatial risk (Barboza-Salerno, 2020a).

Here, we argue that a clearer understanding of these processes will deepen our understanding of how child victimization is spread and transmitted at different spatiotemporal scales. Is the observed pattern more likely the product of exogenous or endogenous neighborhood characteristics or some combination of both? On the one hand, the spatial concentration of child victimization in each region may be produced by individuals living in proximity who share similar values/norms about violence, child-rearing strategies and/or who reside in an area for similar reasons. In this case, if norms change or a population with different norms moves into the area, these clusters may change accordingly. Also possible, however, is the higher risk of child victimization in areas characterized by fewer community-based resources, transportation, and housing insecurity, and an overburdened child welfare system. Without attention to building the necessary infrastructure to support families, these clusters may appear more “entrenched” over time. Regardless of whether child victimization is produced through the spread of norms or the lack of resources, the aggregation of all child victimization incidents into “hot spot” areas demonstrates a spatial pattern that looks similar regardless of the underlying cause. Different causes, however, could very well necessitate different types of preventive action (Eck et al., 2005).

Accordingly, a geographic cluster of child homicides is not sufficient to show a contagion process, especially if it is constrained by a particular event or results from an accumulation over time. Further, the underlying mechanisms may have space and time dimensions. As an example, an analysis that shows a spatial cluster that resulted from a murder-suicide of a family with seven children could emerge due to the psychopathology of the perpetrator (e.g., severe trauma experiences) or because of external pressures (e.g., job loss) of the perpetrator (i.e., the person who committed suicide). In other words, violence may be the product of an individual’s response to specific circumstances and/or experiences rather than a structural or neighborhood condition. Here, since the violence is due to a specific pathological response in the perpetrator, regular yearly clusters of homicides in this area would be unexpected. Rather, we would expect the data to reflect more cases in short space and time intervals than would be expected if the data were randomly generated. On the other hand, if we change the context to the Great Recession of the mid-2000s, individuals who have lost a house, job, or both and who lack access to other resources to mitigate the effects of those circumstances may see violence as a “solution” to an unsolvable problem. To better identify this mechanism, we start with a more basic framework by introducing spatial and temporal aspects into the study.

Literature Review

Spatial and Spatiotemporal Studies of Child Maltreatment

Decades of empirical research reveal that child victimization tends to cluster in densely populated urban areas with high social fragmentation. Factors like housing vulnerability, neighborhood poverty, concentrated affluence, unemployment, alcohol availability, vacant housing, and racial segregation are consistently associated with increased risks of child harm (Barboza et al., 2021; Barboza-Salerno, 2020a; Barboza, 2018; Deccio et al., 1994; Klein & Merritt, 2014; Freisthler, 2004; Freisthler et al., 2004). More recently, research has begun to address whether child victimization is spatially clustered or randomly dispersed, but this work focuses on child maltreatment. Analyzing physical child abuse point data using nearest-neighbor and single kernel density methods, Paulsen (2004) found a hot spot in the center of a large urban city (Paulson, 2004). Similarly, Shenoi et al. (2013) used the nearest-neighbor method on a dataset of child homicides in Harris County, Texas, finding 12 clusters, all primarily within the limits of Houston. Using case-control and Poisson spatial scan statistical methods on a dataset of child maltreatment fatalities and hospitalizations, Thurston et al. (2017a) found four clusters that moved across the county in time and space (Thurston et al., 2017a). Similarly, Barboza (2018, 2019, 2020b) identified space-time clusters of child maltreatment in Los Angeles County, California, and in the state of New Mexico. These studies focus on the place-based mechanisms producing aggregate observable patterns of child victimization rather than the role of both space and time to examine locational codependence between individual victimization events. The failure to examine dependency between events within short time intervals is an important limitation of past research because it provides evidence for contagion.

The social contagion of child victimization has been articulated but not studied directly as many datasets do not have required spatial resolution (see Freisthler et al., 2016, 2020; Grogan-Kaylor et al., 2020). As such, these small exploratory studies have yet to provide adequate empirical support for the untested proposition that child victimization spreads over a geographic area (Holinger et al., 1987) analogous to a disease capable of contagion (Loftin, 1986) rather than being produced by space-time heterogeneity (Loeffler & Flaxman, 2018) or spatial spillover (Grogan-Kaylor et al., 2020). Considering the case of child maltreatment, for example, Freisthler and colleagues (2020) found that clusters of parents who use physical abuse and/or corporal punishment may shop at the same stores but do not provide evidence that actual contagion has occurred. A different study used a spatial contagion framework to examine whether child physical abuse incidents in one neighborhood influence abusive incidents in nearby neighborhoods (Grogan-Kaylor et al., 2020). The study focused on geographic proximity to determine spatial spread, which states that social behaviors, defined in the study as child physical abuse, are vulnerable to diffusion processes due to people in proximal social structures. Operationalizing co-location of child physical abuse as a function of neighborhoods, the study found evidence of spatial spillover that was evidence of contagion. The present study seeks to add to existing research using point pattern locations of child homicides to determine if the underlying socio-spatial process is more reflective of spatial dependence (i.e., “true” contagion) or spatial heterogeneity (i.e., “apparent” contagion). In what follows, we center our discussion on contagion using network principles as a lens by which to focus on the spatial dynamics and structures that emerge from the underlying connections between individuals that produce the observed spatial patterns of child victimization in social context (Gonzalez Canche, 2019).

A Diffusion Framework for Understanding Child Victimization Contagion

A theoretical model of child victimization contagion must incorporate three key characteristics of infectious disease: clustering, spread, and transmission. Previous research confirms that many maladaptive social behaviors, including violent victimization, are highly clustered across space and over time (Barboza, 2018; Loeffler & Flaxman, 2018; Papachristos et al., 2015). However, the causes of this observed clustering remain unknown: is it caused by spatial heterogeneity of underlying indicators (indicating only an apparent contagion process), or can it be attributed to spatiotemporal dependence (which would indicate a true contagion process)? Apparent contagion arises from neighborhood structural vulnerability that produces clusters of maladaptive behavior that vary in intensity in person-to-person transmission in which physical distance or social connection is used to capture relationships between individuals. In contradistinction to apparent contagion, another source of spatial clustering due to proximity of neighboring incidents arises from spatial dependence or true contagion. True contagion is more consistent with person-to-person transmission in which physical distance and/or proximity are used to capture relationships between victimization events. Empirically, true contagion exists when a given phenomenon exhibits a distinct, non- random geographical pattern in which higher incidences of an event are observed closer to the location where the initial incident occurred. In other words, the presence of child victimization in one location increases the probability that another incident will be found nearby. For example, true contagion results when cultural norms around the appropriateness of violence give rise to local sub-populations that “spread” violence to surrounding neighbors. True contagion is produced by correlated point processes that make it more likely to observe co-located behaviors.

In contrast to spatial heterogeneity, which can be identified using regression-based models, spatial dependence is best captured by point pattern methods and/or spatial network analyses (Gonzalez Canche, 2019). These characterize the transmission process, for example, by detecting spatiotemporal proximity to other victims or potential victims in space and over time. As noted by others (see for e.g., [Slutkin, 2013]), the speed of transmission, whether violence spreads more quickly than slowly, is an important characteristic of transmission or contagion dynamics. Studying the spread of violence in Chicago, Slutkin (2013) found that violence contagion is comprised of “waves upon waves” of violent events due to their diffusion over time; thereafter, contact with new susceptible populations in new locations coupled with the emergence of new violence-precipitating factors results in new outbreaks. In contrast, there is some evidence that child victimization spread more slowly than other forms of violence. For example, using 12 years of data tracking serious injury and death, Thurston et al. (2017a) found only four spatiotemporal hot spots shifting over time and space (Thurston et al., 2017a). In contradistinction, in the case of violence in Chicago, Slutkin (2013) found that violence spreads rapidly because one initial “infectious event” can result in many subsequent cases (for example, in the case of gang violence). The same may not be true of the spread of harm perpetrated against children.

Moving Toward Contagion

A true social contagion process is naturally represented with spatial models in which connection probabilities are modeled as a function of the distance from spatial and temporal constraints. Due to data limitations, studies have relied on data aggregated to the county level, census tract, or, in rare cases, census block group levels. Reliance on areal data raises several methodological concerns. Results from small areas may be biased due to variance instability associated with the intrinsic heterogeneity of victimization rates computed for varying at-risk populations (Messner & Anselin, 2004). Recent work has attempted to address this by using Bayesian models that deal with small areas and unstable estimates by “borrowing strength” from a location’s neighbors (Waller & Gotway, 2004). In addition, the use of areal data with defined but arbitrary boundaries may lead to improper inferences about the distribution of certain phenomena due to the ecological fallacy (Gibson et al., 2000) and the modifiable areal unit problem (Martin & Bracken, 1991; Openshaw, 1984). While these have been assessed by examining child victims at differing spatial scales (see Lery, 2009), the concern is not fully mitigated.

Spatial Networks

Spatial heterogeneity is driven by external decisions imposed on systems (e.g., boundaries of zip codes, which change with postal regional demand), whereas true contagion involves decisions imposed on systems from within (e.g., individuals in an area refusing to take adequate precautions to prevent the spread of a fatal disease). The most difficult spatial phenomena may have characteristics of both. The conceptualization of dependency in shared spaces and/or places (Gonzalez Canche, 2019) may be useful to identify how being part of a network defined by close physical proximity can influence the behaviors and norms of nearby individuals. Importantly, a network lens allows researchers to posit questions that account for spatial dependence in ways that are not available using other statistical techniques. In the present case, for example, research has demonstrated an association between child victimization and substance use. Patterns of parents’ substance use, including where and with whom a person drinks, have been found to alter the risk of specific types of harm to children (Freisthler, 2011; Freisthler & Gruenewald, 2013; Freisthler, Holmes, & Price Wolf, 2014, Freisthler, Price Wolf, & Johnson-Motoyama, 2015). Using a geographical network analysis makes it possible to pinpoint the effect of local networks on perpetrators’ behaviors and norms before assessing whether their common exposure to drugs or alcohol increases the probability of perpetration (Gonzalez Canche, 2019): are individuals located near others who misuse alcohol more likely to use physical aggression with children? Understanding these microcontexts provides a richer and more dynamical assessment of how nearby structures and circumstances further influence outcome dependence. Our proposed empirical models will allow us to disentangle these factors.

Research Question and Hypothesis

Clustering can arise from two non-exclusive pathways. In a true contagion framework, child victimization is assumed to locate randomly in space, while those that “follow” these behaviors have a positive probability to locate close by. On the other hand, if exogenous conditions are determinative of the location of perpetration, apparent contagion is in place. These different processes lead us to posit the following research questions: (1) Are the locations of child homicide victimizations randomly distributed across Los Angeles County? (2) If child homicide victimizations are clustered across the county, was the clustering produced by apparent or true contagion? and (3) At what spatiotemporal scale can we expect the next child homicide to occur? We address these questions by using methods to detect whether child victimizations are co-located in both space and time (i.e., is there a space-time interaction) and by analyzing the spatiotemporal scale associated with the probability of observing the new child homicide closest in space and time to the one occurring before it. True contagion as a probable explanation (i.e., spread via social processes) is ruled out if space-time clustering is not observed because that means that events that are closer in space are not also closer in time.

Methodology

Study Design

In this exploratory, descriptive study, we examined whether homicides perpetrated against children under 6 years of age clustered geographically further if any observed clustering can be attributed to a process of true contagion.

Data

Publicly available data from the Los Angeles Homicide Reports was used for this study (The L.A. Homicide Report, http://homicide.latimes.com/). The website includes all homicides committed in Los Angeles County that were investigated by the Los Angeles Department of the Medical Examiner-Coroner (ME-C). The ME-C is mandated by law to “inquire into and determine the circumstances, manner, and cause of all violent, sudden, or unusual deaths; unattended deaths”; and deaths where “the deceased has not been attended by a physician in the 20 days before death” (California Government Code Section 27491).¹ The Python language was used to scrape the data from the website and save it to an Excel spreadsheet before being imported into the R programming environment. The data and code used for this analysis can be found at https://github.com/elisegia/coroner_data/blob/master/Final%20web%20scrap%20medium.ipynb.

Sample

Previous research has shown that the circumstances, perpetrators, and risk factors of homicides among very young children differ across many dimensions and should be analyzed separately (Finkelhor & Ormrod, 2001). For example, homicides of infants and toddlers tend to be committed by family members, including parents or caregivers, and precipitated by abuse or neglect (Wilson et al., 2023). Therefore, we chose to analyze n = 473 homicides involving very young children under the age of 6 years old that took place during the period spanning 2000 to 2021 (up through June). Table 1 shows the demographic characteristics of the sample. Fifty percent of the child homicide victims were identified as Latine, 29.7% were Black only, 11.7% were White only, and 4.9% were Asian, the remainder being some other race. Among homicide victims, 53.5% were male and 43.8% were female (with 2.6% unknown). The majority of victims were under the age of 1 year old (54.2%). The most common cause of death indicated by the ME-C’s officer was “other,” followed by blunt force trauma (19.2%) and gunshot wounds (12.6%).

Table 1.

Descriptive Characteristics of Child Homicide Victims in Los Angeles County.

Characteristic	N	Percent
Neighborhood
Long Beach	21	6.3%
Compton	12	3.6%
Inglewood	12	3.6%
Lancaster	11	3.3%
Westlake	9	2.7%
Boyle Heights	8	2.4%
Palmdale	8	2.4%
Downtown	7	2.1%
Age
0	246	52.1%
1	63	13.3%
2	61	12.9%
3	47	10.0%
4	34	7.2%
5	21	4.4%
Gender
Female	148	44.8%
Male	182	55.2%
Cause of death
Blunt force	71	21.6%
Gunshot	55	16.7%
Other	169	51.4%
Stabbing	5	1.5%
Strangled	2	0.6%
Unknown	27	8.2%

Figures 1 and 2 show the temporal and spatial distribution of the child homicides from January 1, 2000, through June 2021. Figure 1 shows that homicides increased between 2000 and 2005, reached a peak in 2005, and declined thereafter. Figure 2(A) shows the locations of child homicides across the county. The geographic concentration is apparent from Figure 2(B), which shows the density of child homicides is higher in the southcentral parts of the county (see Supplemental Figure 1 for a map of Los Angeles County by race/ethnicity and service area for reference).

Measures

Child Homicide

The final dataset included the geographic locations of all homicides for any manner of death perpetrated against children under 6 years old in Los Angeles County, California, and that received an investigation by the Los Angeles County Coroner’s Office. In addition to the latitude and longitude, the death date, age, race, and gender of the child were recorded.

The Human Development Index

The Human Development Index (HDI; Social Science Research Council, 2016) was used to provide context to the victimization events. The HDI is a composite measure of child well-being created by the Social Science Research Council for Los Angeles County. The HDI is comprised of three essential measures of well-being including health, access to knowledge, and standard of living across multiple domains. The health indicator includes life expectancy at birth; access to knowledge encompasses two indicators: school enrollment for the population aged 3 and over and educational degree attainment for the population 25 and over; standard of living is measured using median personal earnings of full- and part-time workers 16 and over (Measure of America, n.d.). The HDI was calculated using data from the California Department of Public Health, Health Information and Research Section, Death Statistical Master File from 2010 to 2014, and population data from the US Census Bureau and the CDC WONDER Bridged-Race Population Estimates from 2010 to 2014. The HDI was calculated by first creating an index for each of the three dimensions separately to transform the indicators into a common scale ranging from 0 to 10. The results from the three scales are average to obtain on value between 0 to 10, with 10 representing the highest level of human development. More information about the HDI, as well as the actual data, can be found at https://data.lacounty.gov/d/j7aj-mn8v

Statistical Analysis

Geographical network analysis of point patterns is a multifaceted method that reveals meaningful structures and patterns in location data and helps to elucidate contagion processes across a geographic region (Gonzalez Canche, 2019). Spatial analysis using point pattern data overcomes the limitations of aggregation to provide further insight into the processes that drive child victimization clustering at different spatial scales (i.e., distances) (Podur et al., 2002). As such, we utilized primary and secondary point pattern methodology to examine the geographic clustering of child homicide events. First, the coordinates associated with each child homicide location were retrieved using the urllib, selenium, beautiful soup, and requests libraries in Python. To overcome the problem of varying geographic administrative boundaries, a raster layer was created using the county polygon shapefile with a 5,000 km resolution to create a 24 × 24 grid with 576 cells. The number of child homicides in each quadrat was computed using the rasterize function in R. Quartic KDE was used to smooth the density of the points using a bandwidth selected by minimizing the mean squared error (MSE) (using the bw.diggle function in R).

To begin, first-order spatial statistics were used to quantify the relative intensity λ(x) of point patterns of child homicides at or around each location x without using explicit relational data regarding inter-point information. Next, second-order statistics (i.e., K- and g- function) were used to assess spatial clustering only, that is, whether the homicide events cluster in space without regard to time. Spatial dependence is expressed as a second-order intensity $λ_{2} = (x, y)$ , where x and y denote the coordinates of arbitrary points (Espa et al., 2010). A point pattern process is homogenous when the intensity does not vary across space, that is, λ(x) = x for all x. The null hypothesis of homogeneity (i.e., Complete Spatial Randomness [CSR]) was tested using Ripley’s K (Espa et al., 2010). Ripley’s K-function denoted K(d), reports the expected number of additional points located in a circle of radius d surrounding an arbitrary event. CSR assumes that the number of points (n) observed in a specific area follows a Poisson distribution with intensity λ = n/A, where A is the area of Los Angeles County; and (2) the actual locations are uniformly distributed over the region (i.e., each location is random and has the same probability of occurrence). The null hypothesis is that the point pattern is homogenous across the county; hence, rejecting the null hypothesis is evidence of spatial heterogeneity. In that case, the inhomogeneous K-function can be applied to the point pattern process using second-order, intensity-reweighted stationarity (see Baddeley et al., 2000) discounted for the effect of spatial heterogeneity (Espa et al., 2010). In cases where there are no spatial interactions between events, $K_{1} (d) = π d^{2}$ . On the other hand, when $K_{1} (d) > π d^{2}$ or $K_{1} (d) < π d^{2},$ the point pattern is more (or less) aggregated compared to one drawn from an inhomogeneous first-order intensity λ(x) with no spatial interactions between events (Diggle et al., 2007). Both Ripley’s K and the inhomogeneous K-function are available from the spatstat library in R.

Next, we addressed the question of whether the child homicide locations clustered in both space and time, that is, whether the homicide locations are space-time independent? For this analysis, the bivariate K-function from the splancs library (Bivand, Rowlingson & Diggle, 2017) in R was used to test the space-time interaction between events, K(s, t). More specifically, this analysis addresses the question of whether events that are closer in space are also closer in time (Tonini, Pereira, Parente, & Orozco, 2017). $K (s, t)$ is computed as the cumulative number of cases that are expected within a given distance, s, and a specified time interval, t, of a random case, divided by the expected number of cases per unit space and per unit time. In the absence of a space-time interaction, K(s, t) is equivalent to the product of the purely spatial and purely temporal K-function. However, if space and time interact to generate clusters, the K-function difference will be greater than 0 ( $D (s, t)$ > 0). $D (s, t)$ estimates the cumulative number of cases expected within distance, s, and time interval t, of an arbitrarily selected case attributable to the interaction between space and time, scaled by the intensity (lambda). For given space and time separations, the proportional increase in cases attributable to space-time interaction is computed as $D_{0} (s, t) = \frac{D (s, t)}{K_{s} (s) K_{T} (t)}$ .

To assess the significance of the K-functions used here (or its linearized transformation denoted L[d]), Monte-Carlo simulations of inhomogeneous Poisson processes were derived to obtain confidence envelopes. Monte-Carlo methods were used to simulate 999 CSR patterns for the construction of confidence envelopes used to test deviations from CSR. The edge correction was applied to account for edge effects near the boundary of the study area. A significant departure from the null hypothesis results when the observed L(d) lies outside of the envelopes. Spatiotemporal thresholds were created using the Knox test (Knox & Bartlett, 1964). The Knox statistic represents the number of “close” pairs of events that occur within specified distances and times to compare the interaction between child homicide locations across different time/distance thresholds (Ornstein & Hammond, 2017). The Knox statistic uses the observed data to simulate 999 Monte-Carlo simulations to derive the expected distribution under the assumption of independence. If the null hypothesis that the clustering is due to spatial or temporal clustering (but not both) is not rejected, then that is evidence against contagion. The null hypothesis is rejected when the estimated Knox statistic is greater than a statistically significant proportion of Monte-Carlo-generated Knox statistics. Finally, QGIS was used to map the point pattern locations of child homicides across key variables of the HDI and to compute the spatial correlation and descriptive statistics within child homicide quartiles.

Results

Are the Locations of Child Homicide Victimizations Randomly Distributed Across Space?

Child homicide counts were aggregated within each of the 272 neighborhoods in Los Angeles County. As shown by Table 1, more than one-quarter of the homicides came from only nine neighborhoods. To measure spatial influence, we first calculated the spatial weights matrix to represent the neighborhood structure and account for spatial dependence. Spatial connectedness was measured by a first-order queen’s contiguity. The spatial weights matrix is represented by a matrix w_ij such that the elements of the matrix = 1 if the geographical units are spatially connected and 0 otherwise. We then computed the minimum distance from each point to every other point and then the mean nearest-neighbor distance. The minimum and maximum distances between child homicide locations were 92.23 (~1/20 of a mile) and 17603.06 m (~10 miles), respectively. The nearest-neighbor analysis revealed a mean nearest-neighbor distance(nnd) of 1250.631 (standard deviation = 1359.249; minimum = 7.435; maximum = 11360.05) (see Figure 3).

Child homicide counts for n = 24 quadrants are shown in Figure 4, and the resultant counts and variances are shown in Table 2. The Chi-square test of CSR for the point pattern based on the quadrat count was statistically significant ( $χ^{2}$ = 2372.5, df = 435, p-value < .001). The mean, variance, and variance-mean ratio (VMR) were .543, 3.24, and 5.962, respectively. Since a VMR > 1 is strong indication of clustering, the calculated VMR suggests a highly clustered pattern. Further, the high variability in the VMR implies that there are many more quadrants containing fewer child homicides than would be expected by chance. Next, the cumulative frequency distribution of nearest-neighbor distances was computed from the child homicide locations (Figure 5). The cumulative distribution function, G(d), represents the probability that a location involving child homicide will have a nearest-neighbor within distance d. The value of G for any distance, d, tells us what fraction of all the nearest-neighbor distances in the pattern is <d. In this case, as shown by Figure 5, when G(d) = .5 (i.e., the median), d = 1,275. Therefore, half of the nearest-neighbor distances are less than 1,275 m. Again, the G function shows that the homicides are very closely clustered together because G increases rapidly at short distances. These results strongly indicate heterogeneity in child homicides across the county.

Table 2.

Quadrat Counts and Calculation of the Variance for the Child Homicide Point Pattern.

# of deaths, K	# of quadrats, X	$K - μ$	${(K - μ)}^{2}$	$X {(K - μ)}^{2}$
0	483	−0.543	0.295	142.623
1	31	0.457	0.208	6.463
2	20	1.457	2.121	42.434
3	17	2.457	6.0359	102.593
4	6	3.457	11.948	71.688
5	3	4.457	19.861	59.584

What is the Spatial Scale of Child Victimization?

The results from the inhomogeneous K-function are presented in Figure 6. The results confirm that child homicides cluster across the county but further indicate that the spatial dependence is very strong and statistically significant at very small spatial scales up to about 2,000 m, whereas inhibition is evident at larger distances (~7,500 m). This suggests a need to further investigate the spatial trends to assess how child homicides cluster at varying spatial distances.

Is the Observed Clustering Due to Apparent or True Contagion (i.e., What is the Spatiotemporal Scale of Child Victimization)?

Figure 7 demonstrates the varying spatial intensity of the point process (i.e., the homicide locations) for each year, indicating non-stationarity or inhomogeneity. Since a completely inhomogeneous point process for the homicide locations would indicate that all deaths took place at the same location, the results seem to suggest that the homicides were concentrated into hotspots with similar intensity over time. If child homicides are both spatially dependent and spread via contact, however, space-time clustering should characterize the data. This means that events that are closer in space are also closer in time. The Knox test results are shown in Figure 8. The Knox test was computed for between 0–5,000 days and 0–5,000 m. The Knox test revealed significant clustering in only one space-time category representing between [400–800) m and [60, 90) days (Knox Ratio > 2.2, p = .039). This result means that following an initial child homicide incident, another child homicide was more likely to occur within 400 to 800 m and 2 to 3 months of the initial event than would be expected if the times and distances were independent. To derive further insight, we calculated the probability of a child homicide happening within a 2-week time period at varying distances. The number of homicides was classified into 400-m intervals from 400 to 1,600 m for 2- to 4-week intervals. The joint and marginal probabilities were then calculated for the discrete times and distances. The results confirmed that most (51%) of the homicides happen within small distances (<800 m) but that the days that a child homicide occurred were more heterogeneous. The likelihood of a homicide occurring within 400, 800, 1,200, and 1,600 meters of the previous child homicide within the first two weeks is only 3%, 7%, 9%, and 10%, respectively. However, for all consecutive child homicides, the likelihood of occurrence within 400, 800, 1,200, and 1,600 m is 15%, 51%, 66%, and 75%. The chances of a second homicide happening within 800 m of another is greater than 50%, but the chances of a second homicide happening within 800 m of another within a 2-week time frame is only 7% (Table 3).

Table 3.

Probability of a Second Child Homicide Event at Varying Distances.

(m)	Study Period	≤14 days
400	0.15	0.03
800	0.51	0.07
1,200	0.66	0.09
1,600	0.75	0.10

Is There a Relationship Between Spatial Dependence (Contagion) and Spatial Heterogeneity?

The child homicide locations were overlaid onto a map of the HDI by census tracts to explore the possible exogenous factors associated with victimization events. The HDI indicators were summarized within quantiles of child homicide counts. The results, which are presented in Table 4, show significant differences across quantiles and a strong and significant spatial association between the HDI and number of homicides in each census tract (see Figure 9). For example, the HDI for the census tracts in the first quartile (Q1) of child deaths is 6.403, but 3.926 for census tracts in the fourth quartile (Q4). Overall, there is a graded relationship between the indicators and child homicides, where the lowest quartile tracts have much higher mean scores across all indicators.

Table 4.

Means and Spatial Correlations of the Human Development Index, Items, and Subindices.

Quartile	HDI	School Enrollment	Life Expectancy	Less than HS	Income Index	Health Index	Graduate Degree	Child Homicide Count
Q1	6.403	82.472	83.586	17.171	5.921	7.322	15.110	0
Q2	5.566	80.713	82.449	22.000	4.765	6.853	11.044	1.36
Q3	4.625	77.754	81.573	28.619	3.579	6.488	5.673	4.36
Q4	3.926	75.373	79.764	34.309	2.813	5.739	5.745	11.91
$ρ$	−0.289***	−0.391***	−0.308***	−0.373***	−0.390***	−0.291***	−0.403***

Notes. Quartiles of child homicide deaths across key indicators from the Human Development Index (HDI). HDI = overall human development index.

***

p < .05

Discussion

The central aim of this paper was to explore contagion effects in child victimization events to yield unique insights into the underlying mechanisms (Messner & Anselin, 2004) responsible for producing the spatial clustering documented by prior research. A strong tendency for child homicide events to cluster at small distances during narrow time intervals is an indication that the cluster was characteristic of true contagion and suggests that child victimization is susceptible to social contagion processes (Huesmann, 2012; Papachristos et al., 2015). We further found that when a child homicide event occurs at one location, another victimization event is likely to occur nearby (between 400 and 800 m) within a 2- to 3-month time frame. Therefore, the limited evidence we found for contagion suggests that it is a slow process and dissipates with distance. We further found a strong spatial association between neighborhood structural factors and child homicide locations, indicating that spatial heterogeneity is produced, at least in part, by structural disadvantage.

Regarding contagion effects, our results are consistent with other studies suggesting that behaviors associated with child victimization, including excessive physical punishment, may become normalized, which in turn contributes to its spread (Grogan-Kaylor et al., 2020). Whereas this research has focused on spatial spillover effects, our work examined spatial dependence defined as the likelihood of observing a future victimization event, and the spatiotemporal scale to which the next event is more probable. As there is compelling evidence that both mobility and communication are spatially dependent, with the frequency of both human behaviors degrading over distance (Deville et al., 2016), one possible explanation consistent with our results is that some of the violence perpetrated against children spreads through personal networks with beliefs, attitudes, and behaviors that support violence (Papachristos et al., 2015). We can think of these networks as the disease source, much like a contaminated water supply. In this paradigm, abusive behaviors are normative within a person’s social network. However, our results further demonstrated that not all child homicides could be explained by dependency or true contagion. This was shown by overlaying the point patterns of child homicides onto the human development index at the census tract level and examining descriptive spatial correlations between child homicide counts and indicators of structural disadvantage. Therefore, structural neighborhood characteristics are plausible mechanisms that impact one’s susceptibility to social contagion or child victimization. This is consistent with other studies attributing spatial patterns of child homicides to neighborhood structural vulnerability, which persists over time. For example, it is known that alcohol outlet exposure and housing insecurity make children more susceptible to violence (Barboza-Salerno, 2020b; Freisthler et al., 2007). However, in the present study we further viewed child victimization as events produced by spatiotemporal point processes that generate patterns containing geographic locations and timestamps resulting in emergent social behavior. In examining interactions between events, we showed that the next victimization event is more likely to occur about 2 to 3 months following and within 800 m surrounding the first event. Thus, social contagion of child victimization is slower at covering greater distances compared to other forms of violence contagion, including gun violence (Loeffler & Flaxman, 2018).

Whether or not personal networks are the original source of transmission, we can think of environmental factors operating as prevention efforts—analogous to masks and vaccines for influenza—in mitigating the transmission and spread of the phenomenon. Most child victims of homicide were under 1 year of age and non-White (88.3%) who were living in the more impoverished and hyper-segregated areas of Los Angeles County at the time of their death, such as South Central and Long Beach (Yee, Bosler, Velasquez, Patterson & Blackwell, 2020). These were also neighborhoods with the lowest scores on the human development index across multiple indicators of health, income, and education. It is worth highlighting that such areas of concentrated disadvantage are historically rooted in market practices of redlining, illegal real estate practices, gentrification, and race-restrictive neighborhood covenants, all of which segregated people of color into areas of inferior housing quality with limited potential for wealth accumulation (An et al., 2019) and resulted in violence (Rothstein, 2017). The subprime predatory practices which targeted residents in these areas only further cemented these areas as markets for investment (rental properties) excluding them from potential market forces that enhance largely owner-occupied neighborhoods (Dymski et al., 2013). Future work should continue to address the macro-contexts associated with child victimization in a socio-spatial framework to demonstrate the impact of these policies on harms perpetrated against children.

Overall, our findings are in accordance with previous research identifying highly vulnerable areas where combined influence of risk is concentrated. For example, Garbarino and colleagues (1978, 1980, 1992) surveyed residents from areas with similar socio-economic profiles but either high or low child maltreatment rates. The researchers found that in the low-rate areas, residents indicated much higher levels of social interaction and social support (Garbarino & Crouter, 1978; Garbarino & Sherman, 1980; Garbarino & Kostelny, 1992). Here, we present evidence of spatial heterogeneity in child homicide locations within neighborhoods, but we do not investigate the characteristics of those neighborhoods in much detail. Future research should continue to explore the mechanisms that produce spatial heterogeneity and dependence to provide more robust explanations for child victimization and abuse.

This study illustrates the tremendous contribution of advancing technology to the public health issue of child victimization. Our unique dataset is limited, however, by nuances and definition. First, child homicide as a contagion is imperfect, as this “disease” has many underlying co-morbidities. Some filicides arise from revenge (e.g., after a divorce) or altruism (e.g., in the case of delusions that led the parent to believe the child is better off dead). Especially with psychosis-related homicides, the parent may have never previously demonstrated aggressive parenting or any propensity to violence. Second, the included events were just a subset of certain other populations. For example, children who are murdered are a subset of the larger population of children who are victimized at the hands of their caregivers or by community-based gun violence. Our dataset is a subset of all child deaths caused by homicide. We were not able to subset the child homicides by either manner or cause of death due to data limitations; nevertheless, research suggests that the majority of child homicides are caused by either parent inaction (neglect) or physical harm (Douglas & Lee, 2020). It is very possible that disaggregating child homicides will yield different results, and we, therefore, cannot rule out the possibility of under-ascertainment bias. As well, we did not adjust for factors known to be associated with child victimization, such as regional poverty and/or racial/ethnic composition, as our goals were largely descriptive. Future work would benefit from expanding the present analysis to model child victimization using more advanced modeling frameworks, such as self-exciting spatiotemporal point process models (Reinhart, 2018). Finally, we have no information about the actual values and norms of perpetrators of harm against children but rather can only statistically test for the presence of dependence, which is an indication of contagion but not dispositive. However, in this paper, we have laid out a theory that can ground further discussions about the spread of child victimization and introduced geostatistical methods that are useful in describing the underlying patterns observed in existing datasets.

Limitations and Implications for Future Research

Future work should continue to examine the role of true contagion in child victimization as our results may not be generalizable across different contexts and time periods. Nevertheless, in addition to exploring contagion effects and visually represent incidents and clusters of offenses against children to approximate exposure to multiple cumulative risks (Bautista et al., 2008; Tanser et al., 2009), spatial point pattern analyses can be a critical component of program evaluation. This type of analysis can point to circumstances where reducing apparent contagion of child victimization would require broader intervention than child welfare agencies alone could provide. For example, interventions that only seek to provide additional and alternative social networks for parenting norms are unlikely to be effective on their own without considering the historical circumstances that produce spatial heterogeneity and vice versa. In the previously mentioned study of 12 years of serious child maltreatment in a large metropolitan area, risk of death or hospitalization decreased with family’s distance from family resource centers, suggesting that the centers were both well placed and insufficient as prevention efforts (Thurston et al., 2017b). Therefore, examining child victimization using socio-spatial models will give policymakers new insights into how complex processes interact under different socio-environmental constraints and in light of different activity spaces and mobility patterns. Child welfare authorities should routinely utilize information derived from spatial analyses to assess not only the location of prevention and intervention services but the sufficiency of these services alone to reduce negative outcome events in the neighborhoods they serve.

Supplemental Material

sj-docx-1-jiv-10.1177_08862605241245388 – Supplemental material for The Spatial Scale and Spread of Child Victimization

Supplemental material, sj-docx-1-jiv-10.1177_08862605241245388 for The Spatial Scale and Spread of Child Victimization by Gia Elise Barboza-Salerno, Holly Thurston and Bridget Freisthler in Journal of Interpersonal Violence

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interests with respect to the authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research and/or authorship of this article.

ORCID iDs

Gia Elise Barboza-Salerno

Bridget Freisthler

Supplemental Material

Supplemental material for this article is available online.

Notes

Author Biographies

Gia Elise Barboza-Salerno’s scholarship focuses on the manifestation of violence across the lifespan from childhood to old age. Their work explores the multiple contextual influences of risk, including trauma, externalizing behaviors, and substance abuse, on manifestations of interpersonal violence (e.g., domestic abuse, adolescent bullying), self-harm (e.g., suicide), and neglect in vulnerable populations (children, adolescents, LGBT individuals and the elderly). Barboza-Salerno’s research utilizes big data, nationally representative datasets, quasi-experimental and longitudinal research designs, and methodologies, such as Growth Mixture Modeling, Parallel Process Modeling, and Bayesian Space-Time techniques. Their work has recently appeared in Applied Spatial Analysis and Policy, Child Maltreatment, The Journal of Interpersonal Violence, and The Journal of Urban Health. Barboza-Salerno’s work has been funded by the National Science Foundation, State Street, and the United Way. Barboza-Salerno currently serves as the Statistical Associate Editor for the journal Child Maltreatment. Barboza-Salerno is also an attorney who has worked in the courts as an advocate assisting domestic violence victims navigate the legal and criminal justice system.

Holly Thurston is currently a Research Analyst with the Ohio State University College of Social Work. She has over 15 years of experience as a researcher with the Sacramento County Department of Health and Human Services, coordinating and conducting research projects and program evaluations with all the divisions, specializing in the use of geographic information systems (GIS) techniques to better understand child maltreatment, the role of services in child maltreatment prevention, and how to better structure services to address the needs of families spatially. She has 7 years of experience as a child welfare worker and supervisor and lived welfare experience as a foster parent.

Bridget Freisthler’s research focuses on how situation, social, and location characteristics affect the use of child abuse and neglect. Specifically, she is interested in how microcontexts (e.g., where a person is during a particular event) shape behavior, such as parenting or substance use. These microcontexts might include where and with whom parents drink alcohol, use marijuana, or experience higher levels of stress; all of these may affect parenting behaviors. The goal of this research is to design, implement, and evaluate intervention strategies that reduce substance misuse, child abuse, and neglect. This work falls under three broad categories: (1) basic science to better understand how context affects both parenting and substance misuse; (2) how specific features of environments or microcontexts can be modified to reduce or prevent child maltreatment and substance misuse; and (3) studying the effects of interventions designed to reduce child abuse and neglect and/or substance misuse. Freisthler employs community engaged strategies to partner with agencies in order to ensure this work is useful and meaningful for the populations she studies. Her work often focuses on studies of parents in the general population to identify avenues for prevention and intervention before involvement with the child welfare system is necessary. She also collaborates with child welfare and community agencies on these efforts. She is leader in the use of geospatial statistics in studies of child abuse and neglect and is one of the first to use Ecological Momentary Assessments with parents to study problematic parenting behaviors.

References

Orlando

A. W.

Rodnyansky

(2019). The physical legacy of racism: How redlining cemented the modern built environment [Conference session]. American Real Estate and Urban Economics Association, Washington, DC, USA.

Baddeley

A. J.

Møller

Waagepetersen

(2000). Non-and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54(3), 329–350.

Barboza

(2018). A secondary spatial analysis of gun violence near Boston schools: A public health approach. Journal of Urban Health, 95(3), 344–360.

Barboza

Angulski

Hines

Brown

(2022). Variability in opioid-related drug overdoses, social distancing, and area-level deprivation during the COVID-19 pandemic: A Bayesian spatiotemporal analysis. Journal of Urban Health, 99(5), 873–886.

Barboza

G. E.

Schiamberg

L. B.

Pachl

(2021). A spatiotemporal analysis of the impact of COVID-19 on child abuse and neglect in the city of Los Angeles, California. Child Abuse & Neglect, 116, 104740. https://doi.org/10.1016/j.chiabu.2020.104740

Barboza-Salerno

G. E.

(2020a). Examining spatial regimes of child maltreatment allegations in a social vulnerability framework. Child Maltreatment, 25(1), 70–84. https://doi.org/10.1177/1077559519850340

Barboza-Salerno

G. E.

(2020b). Variability and stability in child maltreatment risk across time and space and its association with neighborhood social and housing vulnerability in New Mexico: A Bayesian space-time model. Child Abuse & Neglect, 104, 104472. https://doi.org/10.1016/j.chiabu.2020.104472

Barboza-Salerno

G. E.

(2024). Material hardship, labor market characteristics and substantiated child maltreatment: A Bayesian spatiotemporal analysis. Children and Youth Services Review, 157, 107371.

Barboza

G. E.

(2019). The geography of child maltreatment: A spatiotemporal analysis using Bayesian hierarchical analysis with integrated nested Laplace approximation. Journal of Interpersonal Violence, 34(1), 50–80.

10.

Bautista

C. T.

Sateren

W. B.

Sanchez

J. L.

Singer

D. E.

Scott

(2008). Geographic mapping of HIV infection among civilian applicants for United States military service. Health & Place, 14(3), 608–615.

11.

Bivand

Rowlingson

Diggle

Petris

Eglen

Bivand

M. R.

(2017). Package ‘splancs’. R package version, 2-01.

12.

Blumer

(1939). Social contagion. New York: Barnes & Noble Publishers.

13.

Bronfenbrenner

(1979). The ecology of human development: Experiments by nature and design. Harvard University Press.

14.

Christakis

N. A.

Fowler

J. H.

(2013). Social contagion theory: Examining dynamic social networks and human behavior. Statistics in Medicine, 32(4), 10.1002/sim.5408. https://doi.org/10.1002/sim.5408

15.

Children’s Defense Fund (U.S.). (2020). The state of America’s children. Washington, D.C.: Children’s Defense Fund. https://www.childrensdefense.org/wp-content/uploads/2020/02/The-State-Of-Americas-Children-2020.pdf. (accessed Sept. 2022).

16.

Coulton

C. J.

Crampton

D. S.

Irwin

Spilsbury

J. C.

Korbin

J. E.

(2007). How neighborhoods influence child maltreatment: A review of the literature and alternative pathways. Child Abuse & Neglect, 31(11), 1117–1142.

17.

Deccio

Horner

W. C.

Wilson

(1994). High-risk neighborhoods and high-risk families: Replication research related to the human ecology of child maltreatment. Journal of Social Service Research, 18(3–4), 123–137.

18.

Deville

Song

Eagle

Blondel

V. D.

Barabási

A.-L.

Wang

(2016). Scaling identity connects human mobility and social interactions. Proceedings of the National Academy of Sciences, 113(26), 7047–7052.

19.

Diggle

P. J.

Gómez-Rubio

Brown

P. E.

Chetwynd

A. G.

Gooding

(2007). Second-order analysis of inhomogeneous spatial point processes using case–control data. Biometrics, 63(2), 550–557.

20.

Douglas

E. M.

Lee

K. A.

(2020). Challenges in determining child maltreatment fatalities: What do we really know? Child Abuse Review, 29(6), 505–517.

21.

Draus

J. M.

Costich

Pollack

S. H.

Currie

M. L.

Fallat

M. E.

(2017). Injury prevention and state law as strategies for the reduction of child maltreatment fatalities. Current Trauma Reports, 3(2), 89–96. https://doi.org/10.1007/s40719-017-0080-4

22.

Dymski

Hernandez

Mohanty

(2013). Race, gender, power, and the US subprime mortgage and foreclosure crisis: A meso analysis. Feminist Economics, 19(3), 124–151.

23.

Eck

Chainey

Cameron

Wilson

(2005). Mapping crime: Understanding hotspots. U.S. Department of Justice Office of Justice Programs.

24.

Espa

Arbia

Giuliani

(2010). Measuring industrial agglomeration with inhomogeneous K-function: The case of ICT firms in Milan (Italy). Artículo de Trabajo, 14, 1–11.

25.

Fagan

Wilkinson

D. L.

Davies

(2007). Social contagion of violence. In Flannery

D. J.

Vazsonyi

A. T.

Waldman

I. D.

(Eds.), The Cambridge handbook of violent behavior and aggression (pp. 688–724). Cambridge University Press. https://doi.org/10.1017/CBO9780511816840.037

26.

Finkelhor

Ormrod

(2001). Homicides of children and youth. Juvenile Justice Bulletin. https://scholars.unh.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1009&context=ccrc

27.

Freisthler

(2011). Alcohol use, drinking venue utilization, and child physical abuse: Results from a pilot study. Journal of Family Violence, 26, 185–193.

28.

Freisthler

Thurston

Price Wolf

(2020). An exploratory study of parenting in public places: What can we learn from parents’ activity locations and physical punishment? International Journal on Child Maltreatment, 3(2), 249–269.

29.

Freisthler

Midanik

L. T.

Gruenewald

P. J.

(2004). Alcohol outlets and child physical abuse and neglect: Applying routine activities theory to the study of child maltreatment. Journal of Studies on Alcohol, 65(5), 586–592.

30.

Freisthler

(2004). A spatial analysis of social disorganization, alcohol access, and rates of child maltreatment in neighborhoods. Children and Youth Services Review, 26(9), 803–819.

31.

Freisthler

Merritt

D. H.

LaScala

E. A.

(2006). Understanding the ecology of child maltreatment: A review of the literature and directions for future research. Child Maltreatment, 11(3), 263–280.

32.

Freisthler

Gruenewald

P. J.

Remer

L. G.

Lery

Needell

(2007). Exploring the spatial dynamics of alcohol outlets and child protective services referrals, substantiations, and foster care entries. Child Maltreatment, 12(2), 114–124.

33.

Freisthler

Gruenewald

P. J.

(2013). Where the individual meets the ecological: A study of parent drinking patterns, alcohol outlets, and child physical abuse. Alcoholism: Clinical and Experimental Research, 37(6), 993–1000.

34.

Freisthler

Holmes

M. R.

Wolf

J. P.

(2014). The dark side of social support: Understanding the role of social support, drinking behaviors and alcohol outlets for child physical abuse. Child Abuse & Neglect, 38(6), 1106–1119.

35.

Freisthler

Wolf

J. P.

Johnson-Motoyama

(2015). Understanding the role of context-specific drinking in neglectful parenting behaviors. Alcohol and Alcoholism, 50(5), 542–550.

36.

Freisthler

Thomas

C. A.

Curry

S. R.

Wolf

J. P.

(2016, April). An alternative to residential neighborhoods: An exploratory study of how activity spaces and perception of neighborhood social processes relate to maladaptive parenting. In Weems

C. F.

(Ed.), Child and youth care forum (Vol. 45, No. 2, pp. 259–277). Springer US.

37.

Funk

Salathé

Jansen

V. A. A.

(2010). Modelling the influence of human behavior on the spread of infectious diseases: A review. Journal of The Royal Society Interface, 7(50), 1247–1256. https://doi.org/10.1098/rsif.2010.0142

38.

Garbarino

Crouter

(1978). Defining the community context for parent-child relations: The correlates of child maltreatment. Child Development, 49(3), 604–616.

39.

Garbarino

Kostelny

(1992). Child maltreatment as a community problem. Child Abuse & Neglect, 16(4), 455–464.

40.

Garbarino

Sherman

(1980). High-risk neighborhoods and high-risk families: The human ecology of child maltreatment. Child Development, 51(1), 188–198.

41.

Gibson

C. C.

Ostrom

Ahn

T.-K.

(2000). The concept of scale and the human dimensions of global change: A survey. Ecological Economics, 32(2), 217–239.

42.

Gijzen

Boere-Boonekamp

M. M.

L’Hoir

M. P.

Need

(2014). Child mortality in the Netherlands in the past decades: An overview of external causes and the role of public health policy. Journal of Public Health Policy, 35(1), 43–59. https://doi.org/10.1057/jphp.2013.41

43.

Gonzalez Canche

(2019). Geographical, statistical, and qualitative network analysis: A multifaceted method-bridging tool to reveal and model meaningful structures in education research. In Paulsen

M. B.

Perna

L. W.

(Eds.), Higher education: Handbook of theory and research (Vol. 34, pp. 535–634). Springer. https://doi.org/10.1007/978-3-030-03457-3_12

44.

Grogan-Kaylor

Lee

S. J.

Klein

(2020). A longitudinal analysis of the spatial spread of police-investigated physical child abuse. Child Abuse & Neglect, 99, 104264.

45.

Holinger

P. C.

Offer

Ostrov

(1987). Suicide and homicide in the United States: An epidemiologic study of violent death, population changes, and the potential for prediction. American Journal of Psychiatry, 144(2), 215–219.

46.

Huesmann

L. R.

(2012, February). The contagion of violence: The extent, the processes, and the outcomes. In Social and economic costs of violence: Workshop summary (pp. 26–34). Washington, DC: National Academies Press.

47.

Klein

Merritt

D. H.

(2014). Neighborhood racial and ethnic diversity as a predictor of child welfare system involvement. Children and Youth Services Review, 41, 95–105.

48.

Knox

E. G.

Bartlett

M. S.

(1964). The detection of space-time interactions. Journal of the Royal Statistical Society. Series C (Applied Statistics), 13(1), 25–30.

49.

Lery

(2009). Neighborhood structure and foster care entry risk: The role of spatial scale in defining neighborhoods. Children and Youth Services Review, 31(3), 331–337.

50.

Loeffler

Flaxman

(2018). Is gun violence contagious? A spatiotemporal test. Journal of Quantitative Criminology, 34(4), 999–1017.

51.

Loftin

(1986). Assaultive violence as a contagious social process. Bulletin of the New York Academy of Medicine, 62(5), 550.

52.

Martin

Bracken

(1991). Techniques for modelling population-related raster databases. Environment and Planning A, 23(7), 1069–1075.

53.

Martínez

Jiménez-Molina

Á.

Gerber

M. M.

(2023). Social contagion, violence, and suicide among adolescents. Current Opinion in Psychiatry, 36(3), 237–242. https://doi.org/10.1097/YCO.0000000000000858

54.

Messner

S. F.

Anselin

(2004). Spatial analyses of homicide. Spatially Integrated Social Science, 12, 127–144.

55.

Milner

J. S.

(2007). Child physical abuse assessment: Perpetrator evaluation. Assessing Dangerousness, 2, 45–70.

56.

Olecká

(2022). Early identification of risk of child abuse fatalities: Possibilities and limits of prevention. Children, 9(5), 594.

57.

Openshaw

(1984). Ecological fallacies and the analysis of areal census data. Environment and Planning A, 16(1), 17–31.

58.

Ornstein

J. T.

Hammond

R. A.

(2017). The burglary boost: A note on detecting contagion using the Knox Test. Journal of Quantitative Criminology, 33(1), 65–75. https://doi.org/10.1007/s10940-016-9281-1

59.

Papachristos

A. V.

Wildeman

Roberto

(2014). Tragic, but not random: The social contagion of nonfatal gunshot injuries. Social Science & Medicine, 125, 139–150.

60.

Paulsen

D. J.

(2004). No safe place: Assessing spatial patterns of child maltreatment victimization. Journal of Aggression, Maltreatment & Trauma, 8(1–2), 63–85.

61.

Pérez-Figueroa

R. E.

Obonyo

D. J.

Santoscoy

Surratt

H. L.

Lekas

H. M.

Lewis

C. F.

Lyons

J. S.

Amesty

S. C.

(2022). Housing instability, structural vulnerability, and non-fatal opioid overdoses among people who use heroin in Washington Heights, New York City. Behavioral Medicine, 48(4), 320–330. https://doi.org/10.1080/08964289.2021.1922347

62.

Podur

Martell

D. L.

Knight

(2002). Statistical quality control analysis of forest fire activity in Canada. Canadian Journal of Forest Research, 32(2), 195–205.

63.

Reinhart

(2018). A review of self-exciting spatio-temporal point processes and their applications. Statistical Science, 33(3), 299–318.

64.

Rothstein

(2017). The color of law: A forgotten history of how our government segregated. Liveright Publishing.

65.

Shenoi

Levine

Donaruma-Kwoh

M. M.

Lyn

M. A.

Hunter

J. V.

Giardino

A. P.

(2013). The spatial relationship of child homicides to community resources in a large metropolitan area. Sage Open, 3(2), 2158244013483132.

66.

Shreffler

Shoff

Thomas

J. J.

Huecker

(2021). Brief report: The impact of COVID-19 on emergency department overdose diagnoses and county overdose deaths. The American Journal on Addictions, 30(4), 330–333. https://doi.org/10.1111/ajad.13148

67.

Slutkin

(2013). Let’s treat violence like a contagious disease. TED Conferences LLC.

68.

Slutkin

Ransford

Zvetina

(2018). Response to “metaphorically or not, violence is not a contagious disease.” AMA Journal of Ethics, 20(5), 516–519.

69.

Social Science Research Council (2016). Measure of America: About Human Development. Retrieved from http://www.measureofamerica.org/human-development/

70.

Tanser

Bärnighausen

Cooke

G. S.

Newell

M. L.

(2009). Localized spatial clustering of HIV infections in a widely disseminated rural South African epidemic. International Journal of Epidemiology, 38(4), 1008–1016.

71.

Thurston

Freisthler

Bell

Tancredi

Romano

Miyamoto

Joseph

J. G.

(2017a). The temporal-spatial distribution of seriously maltreated children. Spatial and Spatio-Temporal Epidemiology, 20, 1–8.

72.

Thurston

Freisthler

Bell

Tancredi

Romano

P. S.

Miyamoto

Joseph

J. G.

(2017b). Environmental and individual attributes associated with child maltreatment resulting in hospitalization or death. Child Abuse & Neglect, 67, 119–136.

73.

Tonini

Pereira

M. G.

Parente

Vega Orozco

(2017). Evolution of forest fires in Portugal: from spatio-temporal point events to smoothed density maps. Natural Hazards, 85, 1489–1510.

74.

Waller

Gotway

(2004) Applied spatial statistics for public health data. Wiley.

75.

Wilson

R. F.

Fortson

B. L.

Zhou

Lyons

B. H.

Sheats

K. J.

Betz

C. J.

Blair

J. M.

Self-Brown

(2023). Trends in homicide rates for US children aged 0 to 17 years, 1999 to 2020. JAMA Pediatrics, 177(2), 187–197. https://doi.org/10.1001/jamapediatrics.2022.4940

76.

Wolf

J. P.

Freisthler

Kepple

N. J.

Chavez

(2017). The places parents go: Understanding the breadth, scope, and experiences of activity spaces for parents. GeoJournal, 82(2), 355–368. https://doi.org/10.1007/s10708-015-9690-y

77.

World Health Organization. (WHO). 2016. Violence against children fact sheet. Retrieved September 26, 2022, from https://www.who.int/news-room/fact-sheets/detail/violence-against-children

78.

Yee

Bosler

K. M.

Velasquez

Patterson

T. B.

Blackwell

(2020). California Tax Credit Allocation Committee.

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