Spatiotemporal Association Between Temperature and Assaults: A Generalized Linear Mixed-Model Approach

Abstract

We aim to analyze the association between temperature and assault at highly disaggregated spatial units with great temporal resolution to investigate their spatiotemporal dynamics. We applied generalized linear mixed models (GLMMs) to assault and weather data from 2015, aggregated weekly at 424 subdistricts in Seoul, South Korea, controlling for various socioeconomic and environmental variables. Analyses revealed a positive and significant linear association between temperature and assaults and a few small but significant interaction effects that relate to an increase in assaults. A more enhanced understanding of the spatiotemporal relationship between temperature and crime would provide useful implications for targeted crime prevention and resource allocations.

Keywords

weather crime spatiotemporal context South Korea

Introduction

Weather is one of the principal environmental conditions which has been assumed to influence human behaviors, including crime. While researchers have explored the relationship between various weather conditions and crime, the most widely studied and commonly acknowledged relationship between weather and crime would be that between temperature and violent crime (Cohn, 1990). Many researchers have reported that occurrences of violent crime increase during the (hot) summer season throughout a year (Anderson, 1989), and southern regions with higher annual temperature tend to have more crimes than their northern counterparts (Gastil, 1971; Lombroso, 1911; Nisbett, 1993). Temperature may have an impact on the biological and psychological status of offenders (Anderson & DeNeve, 1992), or the varying weather conditions may change the routine activities of offenders and victims, which eventually lead to opportunistic encounters for crime (Cohn & Rotton, 2000; Rotton & Cohn, 2003).

It is also the case that prior studies on weather and crime have given insufficient consideration to the spatiotemporal context. If temperature is assumed to make a difference in the level of crime by changing the structure of crime risks, it may also be that the differences are influenced by the unique characteristics of the areas over time which constitute the crime risks. In this aspect, the argument that temperature will affect the level of violent crime in the same way over time over the entire study area—usually a nation, a city, or even across different countries—may be somewhat naïve. Thus, spatiotemporal considerations can provide dynamic and enhanced predictions for the relationship between temperature and violent crime in the context of criminological theories. In addition, those dynamic predictions can provide important implications for crime prevention. If we know which places will get riskier for crime with increasing temperature, efforts may be made to attempt to deter predicted crime occurrences by deploying police patrol or other resources in a targeted manner (Braga & Weisburd, 2010; Weisburd, 2008).

This study analyzes the relationship between weather conditions and assault in the Seoul Metropolitan area of South Korea in 2015 with 424 subareal units. One of the unique contributions of this study is that it can provide practical implications for crime prevention because it analyzes the relatively small area with high temporal resolution compared with prior research. It uses generalized linear mixed models (GLMMs) that incorporate temporal change within the areal units. It investigates the extent to which a wide range of environmental factors moderate the intercept and the slope of the regression equation between temperature and assault.

In the next section, we present the theoretical background and prior studies explaining how crime is differentiated by areal characteristics and weather conditions focusing on temperature and violent crime. Then, we describe the data and methods for analysis and turn toward the presentation of study findings. We conclude with implications for subsequent research and policy proscriptions.

Theoretical Background

Linkage Between Crime and Place

Demographic, socioeconomic, or physical conditions of places where crimes occur may provide insight into explaining different levels of crime across different areas. Researchers have investigated the differences between places vulnerable to crime and their counterparts using several different theoretical frameworks.

Social disorganization is one of the most widely used theoretical frameworks in explaining the heterogeneity in crime patterns within cities. Traditionally, the social disorganization approach emphasizes that economic deprivation, among other factors, is related to high levels of crime (Shaw & McKay, 1942). The general hypothesis in this framework is that low socioeconomic status, family disruption, residential mobility, and ethnic heterogeneity may lead to social disorganization which produces a breakdown in informal social control and, in turn, increases the likelihood of crime and delinquency (Kubrin & Wo, 2016; Sampson & Groves, 1989).

While social disorganization theory places interest and priority on the ecological arrangement of the area and connects it to social control and/or self-regulation, the attention of crime opportunity theory lies more on the dynamic aspects of crime and delinquency. Routine activity theory, which makes specific use of opportunity, assumes that the illegal activities root from the legal activities of everyday life (Cohen & Felson, 1979). In other words, most crime happens where offenders spend their time for “routine activities,” while there are still some offenders who aggressively look for their targets (Eck & Weisburd, 1995). On the extension of this logic, scholars have paid attention to particular facilities such as alcohol outlets including bars and taverns (Block & Block, 1995; Peterson, Krivo, & Harris, 2000; Roncek & Maier, 1991), mass transit (Anselin, Syabri, & Kho, 2005; Hart & Miethe, 2014; Stucky & Smith, 2017), and apartment buildings (Clarke & Bichler-Robertson, 1998; Eck & Wartell, 1998; Newman, 1972) attracting people and eventually leading to an increased risk of an encounter between offenders and victims.

Another facet of crime opportunity theories is situational crime prevention theory which pays more attention to crime prevention by increasing risks and reducing the rewards (Clarke, 1980). In this sense, the focus here is on how the presence or levels of guardianship such as surveillance cameras (Blixt, 2003; Ratcliffe, Taniguchi, & Taylor, 2009; Welsh & Farrington, 2004), street lights (Farrington, 2008), or increased size of police forces (Kovandzic, Schaffer, Vieraitis, Orrick, & Piquero, 2016; Lee, Eck, & Corsaro, 2016) are related to lower crime. However, care should be taken because the effects of guardianship are often vague or misleading. The positive relationship between guardianship factors and crime reported in cross-sectional studies may imply that the increased level of guardianship can be a result of a high level of crime, and not vice versa. In addition, some researchers have argued that deterrence strategies do not usually work well for impulsive behavior such as violent crimes (Petee, Milner, & Welch, 1994) and that there is variability within persons regarding their deterrability (see Piquero, Paternoster, Pogarsky, & Loughran, 2011).

Temperature and Violent Crime

Prior research has commonly linked high temperature with increased levels of violent crime. In biological and psychological perspectives, a broad range of unpleasant conditions and aversive stimulation may generate instigation of aggression in both animals and humans (Berkowitz, 1983). In the framework of the temperature–aggression model, heat and high temperature have been considered as acute situational variables which can produce hostile affect, hostile cognition, and arousal which increase the likelihood of aggression (Anderson, 2001; Anderson & DeNeve, 1992; Bushman, Wang, & Anderson, 2005). According to this point of view, aggressive behaviors or violent crimes are expected to increase with increasing temperature.¹

Another explanation on the temperature–violence relationship focuses on the varying opportunistic conditions of crime. In this context, temperature is one of the indirect facilitators of increased violence which can change the risk structure of crime by modifying the routine activities of offenders and victims. That is, as offenders and victims stay longer outside their home or other private places in summer seasons, they are more likely to interact with one another in time and space. In the British Crime Survey, Hough and Mayhew (1983) revealed that people spending several evenings a week out tend to be more victimized of assault. In an international victimization survey in 14 countries, Van Dijk, Mayhew, and Killias (1990) also reported that the frequency of evening going-outs was one of the crucial determinants of victimization risk for all types of crime.

Although many studies have examined the relationship between crime and other elements of weather such as precipitation (Cohn, 1990; DeFronzo, 1984; Feldman & Jarmon, 1979), sunlight (Field, 1992; Heller & Markland, 1970; Rotton & Frey, 1985), wind (Rotton & Frey, 1985), barometric pressure (Feldman & Jarmon, 1979), and humidity (Rotton & Frey, 1985), their influences on violent crime are somewhat mixed and have not been as clear as those from the research with temperature.

Temperature and Crime in Spatiotemporal Context

It may be difficult to place the relationship between temperature and crime in the context of local environment. One of the reasons is that it is hard to observe the change of areal characteristics especially for short period of time, while temperature can show distinct difference throughout a year. Earlier literature integrating temperature and local environment to explain crime has ignored the temporal change by adopting annual mean temperature (Robbins, Dewalt, & Pelto, 1972; Van de Vliert, Schwartz, Huismans, Hofstede, & Daan, 1999) or counting the number of hot/cold days within a year (DeFronzo, 1984; Ranson, 2014) to bring the temperature to the yearly level. By aggregating temporal change of the temperature into one yearly value, data including weather, crime, and areal characteristics become cross-sectional, which can be analyzed by analysis of variance (ANOVA) or general multivariate regression. This approach, however, may lose the detailed information of changing temperatures throughout the year. In addition, the cross-sectional approach may have a large spatial unit of analysis such as cities or counties because sampling within small areal ranges cannot bring substantial differences in annual mean temperature between the cross-sectional observations. Consequentially, the approach also loses the detailed spatial information within subdistrict areas because it treats the large area such as a city or a nation as one unit of analysis.

However, recent research comparing seasonal dissimilarity of crime distribution in a city suggests that there is spatial disparity in seasonal change. Studies focusing on the spatial point pattern of crime location (Andresen & Malleson, 2013; Linning, Andresen, Ghaseminejad, & Brantingham, 2017; Pereira, Andresen, & Mota, 2016; Schutte & Breetzke, 2018) or areal cluster of crime (Butke & Sheridan, 2010; Ceccato, 2005) confirm that there are statistically significant dynamic changes in crime distribution with temporal changes, such as seasons. In other words, the distribution of crime may not be constant over time, and risky places in the summer do not necessarily match to risky places in the winter. These approaches can help us understand how seasonal changes or varying weather conditions can affect the spatial distribution of crime in relatively small areas. However, those studies focus more on analyzing the spatial distribution of crime instead of associating the distribution with regional characteristics. Furthermore, because those studies generally provide methods for one-on-one comparisons of distributions from different time points (e.g., summer distribution of crime vs. winter), analyzing change in multiple time points will require numerous comparisons whose implication is basically that the distribution at one time is different from another.

To place the seasonal change of crime in sequence or to understand the dynamic change of crime in relation to temperature, one may need to build a model that includes various other factors, rather than seasonal identification alone. A few studies have incorporated areal characteristics in the model to explain the varying levels of crime in space and time. They have linked changes of crime levels in relatively small areas to the characteristics of areal units such as predefined geographical neighborhood (Harries, Stadler, & Zdorkowski, 1984) census tract (Sorg & Taylor, 2011), or census block (Haberman, Sorg, & Ratcliffe, 2018; Quick, Law, & Li, 2017). Harries and colleagues (1984) tracked the level of assault by the economic status of the neighborhood in the city and found that low-status neighborhoods show a more distinct peak of assault in the summer. Quick et al. (2017) studied how specific land use or the presence of certain facilities is related to the seasonal change of property crime and suggested that parks and eating and drinking establishments are related to additional seasonal variation of crime. Haberman et al. (2018) also focused on how the effect of specific facilities on street robbery changes across seasons. They examined what types of facilities affected crime during all seasons or only in some seasons. Sorg and Taylor (2011) incorporated both socioeconomic variables and local facilities to account for the temperature effect on street robbery using a multilevel growth model. They concluded that high-status neighborhoods, area with more commercial land use, and areas with a subway are likely to have a more rapid increase in street robbery with increasing temperature. Their modeling approach deals with space–time data soundly, but focuses only on street robbery, not assault. To sum up, while the existing studies suggested various models to incorporate both spatial and temporal variations and observed some regional conditions that were related to seasonal patterns of crime, spatiotemporal analysis of violent crime remains lacking compared with property crime and focuses only on limited variables such as neighborhood status or local facilities.

It can be of practical interest for effective policing to find areal characteristics interacting with temperature on the level of crime. Especially for crime prevention, knowing which areas become riskier than others when the temperature increases will be beneficial to design strategies for police patrol. Unfortunately, the effects of areal characteristics on dynamic change of crime are somewhat contradictory. While some studies report that low socioeconomic status (SES) areas show more distinctive increase in assaults in the summer than other areas (Harries et al., 1984), other studies show that low-SES areas have less fluctuation of crime than other areas (Hipp, Curran, Bollen, & Bauer, 2004). On crime-related facilities, while some authors argued that facilities such as parks and restaurants (Quick et al., 2017) or alcohol-selling establishments (Harries et al., 1984) are positively associated with the dynamic change of crime levels, others reported minimal effect of seasonal change in criminogenic facilities on the level of crime (Haberman et al., 2018). Although the contrasting results may be due to the different scopes of study areas or crime types, the mixed conclusions suggest continued but expanded work on the relation between temperature or seasonal changes and level of crime. Along the process, smaller and more homogeneous areal sampling and meticulous selection of crime type may lead to results that can be better explained by theoretical explanation and be more relevant for policy decisions. In this regard, there may be a higher likelihood of detecting a relationship between assaults and temperature (seasonal changes) as it is more supported by theories than property crime (Quick et al., 2017) or street robbery (Haberman et al., 2018; Sorg & Taylor, 2011).

Current Study

The purpose of this study was to examine the relationship between weather conditions (temperature and precipitation) and assault within small areal units in Seoul, South Korea. Two important features of our study are worth noting. First, we use a week as the temporal resolution (whereas most prior studies used broader intervals of time such as months and seasons). Second, our unit of spatial aggregation is “dong,” which is somewhat larger than a census tract but smaller than a city. The weekly and subcity level aggregation results in less aggregated spatiotemporal data with more homogeneity within a space–time range.

Data and Method

Study Region and the Unit of Analysis

The site of our study is the city of Seoul, the capital of South Korea. The overall area calculated by the given geographical data is 606.43 km² (234.14 mi²), which is bigger than Chicago (227.3 mi²) but smaller than New York City (301.5 mi²). The estimated population of Seoul is 9,904,312 (Korea National Statistics Office, 2015), which is greater than that of the New York City (8,175,133 in the 2010 census), residence-wise. As a result, Seoul is a good site because of its sufficient number of subdistricts (424) and high population density (16,332.15/km²).

The spatial unit of analysis is a subdistrict called “dong” which is the minimum administrative unit in Seoul. In 2015, Seoul comprised 424 subdistricts where major statistics are produced. The average area of a subdistrict is 1.43 km² (0.55 mi²) and its mean population is 23,359. The present study focuses on a relatively small aspect of the study site where weather conditions can be assumed to be universal over the whole study site. The large population and the resultant large number of crimes in each subarea enabled us to obtain sufficient criminal acts in each area at each time even after total occurrences of crime were divided by both area and time (424 area × 51 weeks = 21,624 units).

The year 2015 was chosen as the study period because it was the most recent census year. Among the time-variant data aggregated or averaged by week, the data from the first and the last week of the year were excluded from the analysis because they did not complete a week. Thus, crime and weather data from January 4, 2015, to December 26, 2015, were counted and aggregated.

Dependent Variable

The dependent variable is weekly number of assaults at 424 subdistricts in 2015. The data were provided by the Korean National Police Agency. The original data contained the type of crime, the date and time of crime, and the coordinates of crime. For this study, the counts of assaults were aggregated by weeks and subdistricts for analysis. Therefore, the observations of the dependent variable were 21,624 for weekly count of assaults.

As crimes in South Korea are classified by the articles of the criminal law, there can be some disagreement with global classification of crime (www.unodc.org/unodc/en/data-and-analysis/statistics/iccs.html) or the Uniform Crime Reports (UCR: https://ucr.fbi.gov/additional-ucr-publications/ucr_handbook.pdf/), both of which are based on criminal behavior (see National Academies of Sciences, 2016). For example, the article of assault in the Korean Criminal Law describes the different levels of assaults, including both attempted assault and assault resulting in death, which would be categorized separately in the UCR. However, as the provided data only contain the top classification of crime, we aggregated the count of assaults without further differentiating the levels of assault.

Independent Variables

The weather data in Seoul 2015 were downloaded from the Korean Meteorological Administration (http://www.kma.go.kr/eng). Among the various indicators of weather, the weekly mean temperature (TEMP) and the weekly sum of precipitation (PREC) were selected for the analysis. The temperature in this study was measured in Celsius, and the precipitation was measured in millimeter. Because the observed weather data were originally constructed by day, TEMP is calculated by averaging the daily mean temperature of the week and PREC is calculated by summing all the daily precipitation of the week. Adopting the criteria from prior research (DeFronzo, 1984), we acknowledge the day with more than 0.25 precipitation as a day of precipitation and aggregated those while counting days of precipitation a week. As mentioned above, the weather conditions in the study area are assumed to be universal all over the space. That is, the entire subarea will receive the same values for weekly mean temperature (TEMP) and weekly total precipitation (PREC).

All other areal covariates were measured by 424 subdistricts and assumed to be time-invariant throughout the study period. Their selection followed the framework suggested by the theories of social disorganization and routine activities. First, the percentage of households receiving basic living security (AID) was used as a proxy of poverty in the areal unit. A higher rate of recipients suggests a larger proportion of households under the base living condition in the area. The data also include median value of apartments (APT.PR) and gross tax revenue (TAX) to indicate the economic level of the area.

The percentage of foreigners (FOREIGNER) represents the racial or ethnic heterogeneity, which is drawn from the percentage of registered foreigners among the total population. The city-wide proportion of foreigners in Seoul 2015 is dominated by Chinese (53,750) and Korean-Chinese (186,494) who comprise 71% of the whole foreigner population in Seoul. Divorce rate per 1,000 population (DIVORCE) was chosen to represent the family disruption of the area. Percentage of single-member household (SINGLE) can partially indicate family disruption and residential instability as well. In addition, the percentage of migrants (MIGRANT) can also indicate residential instability. One outlier area with the migrant percentage more than 100 is a newly redeveloped area. While people moved to the area with construction of a large apartment complex in late 2015, the census survey question did not reflect change, resulting in outlier observation.

Some other independent variables were chosen within the context of routine activity theory. For example, nonresidential commercial areas (NON-RESID) can be the places where offenders and victims of assault frequently encounter each other for their routine activities outside of their houses (Felson, 1987). We collected the geographic information system (GIS) general buildings data and summed the floor space by the authorized purpose of the buildings. The proportion of nonresidential commercial area was calculated by dividing the sum of nonresidential floor space by the total floor space for all general-purpose buildings in each area.

The proportion of high-rise apartment (APT.R) is another variable which has drawn attention with respect to situational crime prevention. Although it is not always the case, most high-rise apartments of South Korea are more expensive than low-rise apartments. Because the economy of size lowers the burden of investment for hiring personnel charged with managing the community environment and for installing access control devices or surveillance cameras, residents in high-rise apartments usually are expected to enjoy more guardianship than residents in a small-sized apartment or house (Jang et al., 2018).

Another important variable identified in previous research are alcohol-related facilities. Places selling alcohol such as bars, taverns, and other alcohol outlets can draw potential parties of assault incidents together at the same time that facilitates crime (Linz et al., 2004; Snowden & Pridemore, 2013; Zhu et al., 2004). We use the statistics for food and lodge services (FLS) to represent alcohol-related facilities as the facilities for entertainment such as restaurants and hotels tend to cluster around crowded nonresidential areas. The number of FLS facilities aggregated by dong is divided by the area of each dong, producing the density of food and lodging business per 0.01 km² (FLS). Descriptive statistics are listed in Table 1.

Table 1.

Descriptive Statistics of Variables.

	N	M	SD	Minimum	1st Quartile	3rd Quartile	Maximum
Weekly count of assault	21,624	1.91	2.19	0	0	3	47
Weekly mean temperature (TEMP, °C)	51	14.01	9.65	−1.84	3.04	23.47	27.90
Weekly total precipitation (PREC, mm)	51	1.88	1.34	0.00	1.00	23.60	139.50
Rate of household receiving basic livelihood security (AID, %)	424	4.23	3.32	0.05	2.15	5.31	26.28
Median price apartment (APT.PR, million won ≈ thousand dollars)	424	1.06	3.91	0.15	0.59	1.00	79.90
Total revenue of local tax (TAX, billion won ≈ million dollars)	424	29.41	48.40	3.43	10.10	28.76	510.31
Percentage of foreigner (FOREIGNER, %)	424	3.88	5.70	0.20	1.05	3.65	48.00
Rate of divorce (DIVORCE, per 1000 population)	424	1.98	1.55	0.12	1.22	2.36	24.13
Proportion of single-member household (SINGLE, %)	424	29.36	12.15	4.92	21.17	35.53	71.94
Proportion of migrants (MIGRANT, %)	424	17.33	6.61	8.95	14.65	18.75	126.57
Proportion of nonresidential area (NON-RESID, %)	424	36.36	20.01	0.78	21.89	46.72	99.89
Proportion of high-rise apartment among residential housing (APT.R, %)	424	53.83	30.16	0.00	29.24	79.95	100.00
Rate of FLS business (FLS, per 0.01 km²)	424	290.73	237.95	4.32	116.77	393.35	1,605.34
Total number of population (in thousands)	424	23.36	9.06	0.75	17.50	28.63	53.88
Total number of households (in thousands)	424	9.23	3.55	0.22	7.00	11.41	21.98

For the analyses, all the independent variables were z-transformed for three reasons. First, different scales often prevent the maximum likelihood estimation (MLE) process from converging, which results in an unreliable estimation of parameters. Second, the centered independent variables (with a mean of zero) can make the intercept of the model more meaningful such that the intercept represents the logged value of the expected crime rate for an average area whose independent variables are the mean in each item. Third, as some of the original scales such as Celsius, kilometer, and Korean currency may not be widely familiar, this study uses z-transformed variables to focus more on the relative magnitude of each effect on deciding the level of crime at each time and space.

Statistical Models

We conducted GLMMs using the R software. As mentioned earlier, the weather variables (TEMP, PREC) are measured by time-variant global observation ignoring the spatial variation, and the other covariates are measured by time-invariant local observation ignoring the temporal variation. The dependent variable, crime counts, is measured by spatiotemporal observation. The main advantage of GLMM is that it separates the levels of the models to account for the group effect nesting the lower level observations. In this study, areal units are treated as the second level which group sequential observations within the same area, and weather and crime are treated as repeated observations at the lower level. While the areal data are assumed to be time-invariant, the weather data are assumed to be universal over the whole study areas at a certain time point.

Model 1, the simplest model, will include only weather covariates and random intercepts:

\begin{matrix} \log (E [Y_{i t}]) = β_{0} + β_{1} \cdot {Temp}_{t} + β_{2} \cdot {Prec}_{t} \end{matrix},

(1.1)

\begin{matrix} β_{0} = u_{0 i} + \log (P_{i}) \end{matrix},

(1.2)

where $E [Y_{i t}]$ represents the number of crimes at area $i$ in week $t$ . ${TEMP}_{t}$ and ${PREC}_{t}$ represent z-transformed weekly temperature and proportion of rainy day at week $t$ , respectively. $P_{i}$ represents the population of area $i$ working as an offset, and $u_{0 i}$ represents the random effect of area $i$ on the intercept. Equations 1.1 and 1.2 specify the model where the random intercept ( $u_{0 i}$ ) defines the base level of assaults, while change in assault counts is influenced by weather covariates. Specifically, Equation 1.1 defines Level 1 (temporal structure), whereas Equation 1.2 defines Level 2 (areal characteristics).

If we do not assume the effect of temperature is universal over the whole study area, Model 2 includes a random slope term ( $u_{0 i}$ ) as Equation 2:

\begin{matrix} \log (E [Y_{i t}]) = u_{1 i} + \log (P_{i}) + u_{1 i} \cdot {Temp}_{t} + β_{2} \cdot {Prec}_{t} \end{matrix} .

(2)

$u_{0 i}$ and $u_{1 i}$ define the random effects on the intercept and the slope by the higher level, in this case spatial units i. While the random effect on the slope of temperature is intensively considered in this study, the coefficient of precipitation is assumed to be fixed. As the effect of precipitation on assault was not obvious, the precipitation variable is only used to control the effect of the temperature.

By adding more geographical covariates, Model 3 becomes more complex, and variation in response variables will be explained by fixed effects rather than random effects. We can explain the base level of assault by replacing the intercept part of Equation 1.2 with more areal covariates such as Equation 3:

\begin{matrix} β_{0} = γ_{00} + γ_{01} \cdot x_{1 i} + \dots + γ_{0, 10} \cdot x_{10 i} + \log (P_{i}) \end{matrix}

(3)

Compared with the specification of Equation 1.2, the unexplained random effect ( $u_{0 i}$ ) will become less in Equation 3 by adding the 10 geographical covariates. In Equation 3, the random effect $u_{0 i}$ captures the different levels of intercept due to the spatial unit but not fully explained by the covariates.

Model 4 can explain random slope by the areal covariates. Along with increasing temperature, some areas may show a rapid increase in crime while others may not. By specifying $β_{1}$ with geographical variables, the model aims to reduce the variance of random slope effects. Specification of the slope can be expanded as follows:

\begin{matrix} β_{1} = γ_{10} + γ_{11} \cdot x_{1 i} + \dots + r_{1, 10} \cdot x_{10 i} + u_{1 i} \end{matrix} .

(4.1)

Now, the variance of $u_{1 i}$ in Equation 4.1 will be smaller than that of $u_{1 i}$ in Equation 2 because its variation will be explained by 10 geographical variables ( $x_{1 i}$ to $x_{10 i}$ ). The expanded equation of Model 4 will be as follows:

\begin{matrix} \begin{array}{l} \log (E [Y_{i t}]) = \overset{Intercept}{\overset{︷}{γ_{00} + γ_{01} \cdot x_{1 i} + \dots + r_{0 k} \cdot x_{k i} + u_{0 i}}} \\ + \overset{slope}{\overset{︷}{(γ_{10} + r_{11} x_{1 i} + \dots + γ_{1 k} x_{k i} + u_{1 i})}} \cdot {Temp}_{t} \\ + \underset{slope}{\underset{︸}{β_{2}}} \cdot {Prec}_{t} \end{array} \end{matrix}

(4.2)

All of the right-hand side of Equation 4.2 except $u_{0 i}$ and $u_{1 i}$ specifies the fixed effect by the independent variables. The purpose of this model specification is to reduce the variance of random effects by adding fixed effects to explain the difference in base level of assaults and their increase with temperature.

The process of modeling assumes a Poisson distribution of the response variable because overdispersion is not a serious problem in the analysis. The comparison of the fit among various models utilized the Akaike information criterion (AIC), which is generally used to compare model quality with constraint of simplicity. To find the explanatory contribution of adding covariates in the mixed models, we also compared the variance of random effects. A reduction in the value of random effects represents more variation in the dependent variable and is explained by the selected variables (fixed effects).

Results

Exploratory Analysis

Exploratory data analysis shows a linear relationship between daily temperature and daily number of assaults over the study site (see Figure 1). However, the presence of precipitation does not indicate any significant relationship to the number of daily assaults.

Figure 1.

Daily total count of assaults on temperature and precipitation.

On the contrary, the trend of weekly temperature and the number of assaults show some corresponding trends except the hottest season of the year (see Figure 2). That trend can be suspected to show the plausibility of a negative affect escape model which asserts that extremely hot weather may reduce aggressive behavior. Or it can be understood in relation to the precipitation because the Korean monsoons usually occur in the summer. The sudden drop in assaults in the hottest weeks may be due to the rainy days during that season. Still, the bivariate exploration of precipitation and assault does not imply a meaningful relationship between those variables.

Figure 2.

Trends of assaults by temperature and days of precipitation.

GLMM

Figure 3 illustrates why the spatial components should be considered while analyzing the relationship between temperature and assaults. The maps represent the random intercepts and random slopes of Models 1 and 2. Without any geographical covariates, the base level of assaults and their increase by temperature vary over the spatial units. The left side of Figure 3 shows the map of average assault per 1,000 people when the fluctuation of the crime count is controlled by weather covariates and random slope terms. The right-side map of Figure 3 represents the relative risk of random slope, that is, how the effect of temperature on assault varies over the space. The blue areas represent where the increasing rate of assault by temperature is significantly lower than average (p < .05), whereas the red areas represent the areas with significantly more rapid increase than others (p < .05).

Figure 3.

The relative risk of random intercepts and slopes.

The results of all GLMMs (Models 1-4) are summarized in Table 2. In the model specification, temporal weather data are treated as Level 1 individual data, while the spatial data of socioeconomic and environmental variables are treated as Level 2 group data. The estimated effect of each variable is presented in relative risk (RR) and its significance is shown by its p-value. The 95% confidence intervals are also provided.

Table 2.

Results of Generalized Linear Mixed Models.

Fixed effects	Model 1		Model 2		Model 3		Model 4
Fixed effects	RR	95% CI	RR	95% CI	RR	95% CI	RR	95% CI
TEMP^z	1.101***	[1.09, 1.11]	1.113***	[1.09, 1.13]	1.106***	[1.09, 1.12]	1.114***	[1.10, 1.13]
PREC^z	0.974***	[0.96, 0.98]	0.974***	[0.96, 0.98]	0.974***	[0.96, 0.98]	0.974***	[0.96, 0.98]
AID^z					1.103***	[1.04, 1.17]	1.095***	[1.03, 1.16]
APT.PR^z					0.989	[0.94, 1.05]	0.988	[0.93, 1.05]
TAX^z					1.075**	[1.01, 1.15]	1.076**	[1.01, 1.15]
FOREIGNER^z					1.068*	[0.99, 1.14]	1.071**	[1.001.15]
DIVORCE^z					1.189***	[1.12, 1.26]	1.188***	[1.12, 1.26]
SINGLE^z					1.094*	[0.99, 1.20]	1.091*	[0.99, 1.20]
MIGRANT^z					1.059*	[0.99, 1.13]	1.058*	[0.99, 1.13]
NON-RESID^z					1.340***	[1.25, 1.44]	1.347***	[1.25, 1.45]
APT. Ra					0.994	[0.93, 1.07]	0.994	[0.93, 1.07]
FLS^z					1.171***	[1.09, 1.26]	1.182***	[1.10, 1.27]
Temp^z × AID^z							1.015***	[1.01, 1.03]
Temp^z × APT.PR^z							1.002	[0.99, 1.01]
Temp^z × TAX^z							1.001	[0.99, 1.01]
Temp^z × FOREIGNER^z							0.997	[0.99, 1.01]
Temp^z × DIVORCE^z							1.001	[0.99, 1.01]
Temp^z × SINGLE^z							1.005	[0.99, 1.02]
Temp^z × MIGRANT^z							1.004	[0.99, 1.02]
Temp^z × NON-RESID^z							0.989*	[0.98, 1.00]
Temp× APT. Ra							1.001	[0.99, 1.01]
Temp^z × FLS^z							0.986**	[0.97, 0.99]
Constant	0.066***	[0.06, 0.07]	0.066***	[0.06,0.07]	0.066	[0.06, 0.07]	0.066***	[0.06, 0.07]
Random effects
Var(Intercept)	0.682		0.684		0.330		0.330
Var(Slope)			0.001		0.001		0.000
Observations	21,624		21,624		21,624		21,624
Dispersion	1.126		1.126		1.124		1.126
Log-likelihood	–33,893.64		–33,886.28		–33,746.62		–33,733.26
Akaike information criterion	67,795.28		67,784.57		67,525.23		67,518.51

Note. RR = relative risk; CI = confidence interval.

z-transformed.

p < 0.1. **p < .05. ***p < .01.

The first column of the table (Model 1) is based on the specification of Equations 1.1 to 1.2 which includes the weather covariates and the random intercept in the model. The intraclass correlation coefficient (ICC) of .385 was calculated by dividing the variance of the random effect ( $σ_{α} = 0.682$ ) by the total variance ( $σ_{t} = σ_{α} + σ_{ϵ} = 1.773$ ). Thus, the spatial unit effects account for approximately 38.5% of the total variance of weekly assaults, which suggests nonnegligible areal (Level 2) effects on weekly assaults. It is also to be noted that with the introduction of a random intercept, temperature has significantly positive effects on weekly assaults and the days of precipitation have significantly negative effects.

The next model (Model 2) additionally includes a random slope term. If adding a random slope does not improve the model fit significantly, the interaction effect between temperature and geographical characteristics would be good to be ignored. However, the ANOVA test of log-likelihood (LL) indicates that Model 2 is significantly better than Model 1 ( $χ^{2} = 14.713, p < . 001)$ . AIC values also suggest better fit with random slope term (Model 2). This indicates the temporal changes of assaults by temperature are not applied to the area in the same manner.

The combined model (Model 3) includes both spatial and temporal variables. About half of the random effect (51.7%) is now explained by the spatial variables, and the fit values (LL and AIC) are also improved. The final model (Model 4) additionally includes the interaction term between spatial variables and temperature. The slope change cannot be compared with the effects of other variables because it is different from the effects of other variables in scale. However, the fixed effects of the intercept terms now explain 49% of the random slope variance, and the change in variance of slope was statistically significant (F = 2.03, p <.001).

Throughout the process of model specification, the following are observed. First, a positive effect of temperature and a negative effect of precipitation on assault were constant in the models. Second, a comparison across multiple GLMMs supports that additional variables can improve the model fit. Overall, the final model (Model 4) best describes the data among all the models. Third, adding more variables does not change the covariate estimates nor their significance values much, indicating that the relationships between covariates do not greatly alter the results.

The final model (Model 4) generally agrees with the prior expectations drawn by the theoretical perspectives. As mentioned earlier, the positive effect of temperature and negative effect of precipitation remained constant in the analysis. The effects of socioeconomic and environmental variables on the baseline level of assaults (the intercept term in regression) also seem reasonable. The rate of people in poverty (AID^z), racial heterogeneity (FOREIGNER^z), residential mobility (MIGRANT^z), family disruption (DIVORCE^z, SINGLE^z), and places for routine activities (NON-RESID^z, FLS^z) are all related to the increased level of assaults, although MIGRANT^z and SINGLE^z do not have very large effects. The positive effects by gross amount of tax (TAX^z) on assault also make sense because the variable indicates the gross size of the local economy, not the economic status at the individual level. The wealthy area may be linked to more commercial places and entities which draw people together in the same time and space. In this study, a significant relationship between the status of housing units (APT.PR^z and APT.R^z) and assaults is not observed. It may be because the data for those variables are less thorough or less representative than the sources for other variables or simply because the higher standards of living of some people may not work for reduced crime in the surrounding neighborhoods.

The coefficients of the interaction term do not indicate a direct effect of the covariates on the level of assaults but instead their indirect effect on the slope of assault due to temperature. The interaction terms show that poverty level (AID^z) has positive interaction with temperature on assault, while the proportion of nonresidential area (NON-RESID^z) and density of alcohol outlets (FLS^z) shows a negative interaction. It is interesting that the individual level of poverty will facilitate the increase of assault as temperature rises while it already has raised the baseline of assaults. Unfortunately, people lower in SES may not have many options while choosing their residential areas and as such tend to live in less developed/more distressed areas with lower living costs. Although not all those persons living in poverty receive the basic livelihood security, they may share similar options for residence or areas for their routine activities. Therefore, the positive interaction may imply that areas with people in lower SES are more vulnerable to the increased risk of assaults in hotter weeks.

At the same time, a higher rate of nonresidential buildings and higher density of alcohol-selling facilities showed negative interaction effects with increasing temperature. Yet, the milder increase in assaults by temperature in areas with higher NON-RESID^z or FLS^z may not indicate that those variables mitigate the increase in assaults by temperature, but simply that there is not much room for additional increases because they already have increased the baseline assault level significantly. In other words, assaults in those areas remain relatively stable at a high level throughout the year even with temperature fluctuation.

Discussion and Conclusion

This research has evaluated the relationship between weather conditions and weekly assaults in the spatiotemporal context of Seoul, Korea, in 2015. Several key findings emerged from our analysis. First, a curved relationship between temperature and assault was not observed. However, these results do not support the negative affect escape model (Bell, 1992; Cohn & Rotton, 2005; Rotton & Cohn, 2000). In the study areas, the maximum degree of the weekly mean temperature was 27.9°C (82.2°F). In addition, we averaged the daily mean temperatures by weeks to compare them with weekly assaults. Taking the mean of temperature and aggregating the count of weekly assault may cause extreme observation which may have been observed in the analysis of daily data.

Second, the effects of local socioeconomic and environmental variables on baseline level of assaults generally agree with theoretical expectations. The variables indicating social disorganization (e.g., poverty, racial heterogeneity, residential mobility, family disruption) and increased routine activities (e.g., nonresidential area, alcohol-selling business, the gross revenue of local tax) are all significantly related to the increased level of assault. However, a high individual standard of residence (e.g., the median price of apartments and the rate of high-rise apartment) did not significantly lower the level of assaults in the neighborhoods.

Finally, the interaction effect between temperature and areal characteristics deserves further discussion. First, the rate of households receiving basic livelihood security has a positive connection with the baseline of assaults in areas, as well as a dynamic increase in assaults by high temperature. This result coincides with that of Harries and colleagues where low-SES areas were related to a distinct peak of assault in the summer. The authors explained that the increased crime risks especially in low-SES areas may be due to the fact that people in those areas usually have limited air conditioning systems that can mitigate the heat stress in the summer (Harries et al., 1984). However, the results from similar studies carried out by Hipp et al. (2004) and Sorg and Taylor (2011) contradict the prior explanation.

The discordance between the result of the current study and the prior studies may be attributed to several reasons. First, aggregating the crime counts from the broad range of law enforcement (Hipp et al., 2004) may not reveal the true variability in the data within the area. For example, the weather pattern of cities in the west coast is greatly different from the southern part or the northern inland part of the United States. Also, it is very hard to control unexplained regional or cultural difference other than SES or weather conditions, which may have led to the confounded results. In addition, it may have been naïve to assume homogeneity of the city-level jurisdictions where UCR crime is reported. Second, regarding Sorg and Taylor’s (2011) study, the temperature condition in their study (1.6°C-31°C) may be less harsh compared with our temperature range (–1.6°C to 27°C). It may be that that the latter set of temperature represents the gradually changing conditions for outdoor activity, from the less desirable to the more desirable, while the former set of temperature defines both extreme conditions for outdoor activities. Thus, in the latter set of temperature, the increasing trend of crime might not be expected to bring about significant increases in crime. In addition, as Sorg and Taylor (2011) mentioned, robbery can happen more in the winter season in low-SES areas by people who have to take care of their daily needs in colder days, while the assaults investigated in the present study can happen more by emotional or opportunistic reasons whose dynamic change by temperature is more likely to be linked to the characteristics of the areas.

Overall, according to the results of our study, the interaction effect between temperature and areal SES may indicate that the underdeveloped conditions of residences where many poor people live are more vulnerable to an increased level of violence or that people in poverty are more likely to be involved in violence around their residing areas. Yet, the negative interactions between temperature and level of nonresidential land use and the density of alcohol-selling facilities imply that assault in those areas is relatively high throughout the year without much fluctuation by temperature. It can also be interpreted that the weekly assaults in those areas will not decrease with lowering temperature in the winter season as much as other areas. Nevertheless, the strength of these interaction effects was not very large, so caution should be exercised with their interpretation.

The dynamic changes of those variables with a significant interaction effect(s) offer some implications for crime prevention along with seasonal changes. Business areas and areas with dense alcohol-selling facilities should be considered as constantly risky areas of assaults even in the colder weeks when assaults generally decline. Therefore, focused policing in those areas may bring greater effect for reducing assault incidents. And with increasing temperatures, crime prevention efforts should treat conflicts in lower SES area more seriously because the assault levels of lower SES areas are generally high and are increasing faster than other areas with increasing temperature.

Some limitations of our study should be noted and would make for useful extensions. First, future work should focus on exploring the generalizability of our findings by applying the models to different areas of South Korea, particularly rural or suburban areas. In addition, the models could be improved by adding more local-level variables and weather-related variables which are possibly measured over repeated time points. It would be also interesting to investigate the association between weather and nonviolent crime to examine the distinctive impact of weather characteristics by different types of crimes. A multicountry comparative study highlighting unique weather and local characteristics in each country would also be useful to validate the theoretical robustness of the findings of this study in more general settings. Finally, individual-level perceptual studies would be useful to gather information about what individuals feel during hot (and cold) days and how this may relate to their (antisocial) behavior. Hopefully, the current study is the first of several to continue to focus on analyzing the spatiotemporal association between temperature and assaults, especially in an international context.

Footnotes

Appendix

Correlation Table Between Regional Variables.

	AID	APT.PR	TAX	FOREIGN	DIVORCE	SINGLE	MIGRANT	NON-RESID	APT.R	FLS
AID	1.00	0.00	−0.14	0.02	0.09	0.15	−0.07	−0.04	−0.06	−0.02
APT.PR	0.00	1.00	0.03	−0.02	0.01	0.01	0.04	0.08	0.05	−0.02
TAX	−0.14	0.03	1.00	0.14	−0.02	0.13	0.08	0.45	0.16	0.31
FOREIGN	0.02	−0.02	0.14	1.00	0.02	0.50	−0.10	0.37	−0.27	0.41
DIVORCE	0.09	0.01	−0.02	0.02	1.00	0.07	0.23	0.01	−0.12	0.09
SINGLE	0.15	0.01	0.13	0.50	0.07	1.00	0.20	0.49	−0.52	0.59
MIGRANT	−0.07	0.04	0.08	−0.10	0.23	0.20	1.00	0.05	−0.02	0.19
NON-RESID	−0.04	0.08	0.45	0.37	0.01	0.49	0.05	1.00	−0.10	0.39
APT.R	−0.06	0.05	0.16	−0.27	−0.12	−0.52	−0.02	−0.10	1.00	−0.30
FLS	−0.02	−0.02	0.31	0.41	0.09	0.59	0.19	0.39	−0.30	1.00

Declaration of Conflicting Interests

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

Funding

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

ORCID iD

Alex R. Piquero

Notes

Author Biographies

Yeondae Jung, MS, is a PhD student of Geospatial Information Science at the University of Texas at Dallas. He received an MS on criminology from Dongguk University at Seoul, Korea. His research interests are geospatial analysis crime and crime prevention.

Dohyeong Kim, PhD, is an associate professor of Public Policy and Geospatial Information Sciences at the University of Texas at Dallas. He received a PhD from the University of North Carolina at Chapel Hill and postdoctoral training at Duke University. His research efforts have been dedicated to develop statistical, economic, geospatial, and decision-analytic approaches to address a variety of health, environmental and safety concerns both in the US and internationally.

Alex R. Piquero is Ashbel Smith Professor of Criminology and Associate Dean for Graduate Programs in the School of Economic, Political and Policy Sciences at The University of Texas at Dallas. His research interests include criminal careers, criminological theory, and quantitative research methods. He is fellow of both the American Society of Criminology and the Academy of Criminal Justice Sciences. In 2014, he received The University of Texas System Regents’ Outstanding Teaching Award and in 2018 he was elected to The University of Texas System Academy of Distinguished Teachers. In 2019, he received the Academy of Criminal Justice Sciences Bruce Smith, Sr. Award for contributions to criminal justice.

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