Environmental Hazards and Structural Covariates of US Homicide Rates: Methodological Considerations When Investigating the “Ecology” of Violence

ABSTRACT

Environmental hazards such as air pollutants have increasingly been investigated as macro-level correlates of violent criminal activity, including rates of homicide across space. Such efforts highlight the growing appreciation in the social sciences of the interaction between humans and the natural environment, particularly within the subfields of environmental sociology and green criminology. However, while such investigations broaden the scope of relevant social scientific inquiry, they often fail to appreciate the theoretical and methodological contributions from prior crime and deviance scholars. Given the expansive history within the social sciences of investigating structural covariates of homicide rates, this effort seeks to determine whether differential levels of particulate matter with aerodynamic diameters smaller than 2.5 μm (PM_2.5) can be observed as unique predictor of lethal violence in the US after simplifying the dimensionality of the regressor space. Results indicate that while air pollution levels share covariate space with population size and density, their combined influence represents a robust predictor of county-level homicide rates in the various spatial econometric models estimated.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Broadly conceived, green behaviorism is a branch of green criminology that seeks to empirically examine the relationship between exposure to chemical pollutants and criminal behavior, given the vast collection of medical and epidemiological evidence linking such exposure to behavioral changes that generate increased levels of aggression and/or anxiety. Borrowing from psychological/radical behaviorism, which holds not only that human behavior is driven solely by responses to external stimuli, but that no reference needs to be made to psychological processes or mental states, Lynch and Stretsky (2014) argued that crime as a measurable behavioral response could be explained by way of the effect of environmental toxins on a subject’s physiology or physiological state. The green behaviorism position, according to the researchers, is theoretically and empirically useful for social scientists when analyzing the factors that generate criminal behavior and affect its distribution within the environment and/or population. While the current manuscript is engaged in the environmental hazard-homicide relationship at a more methodological level, attention will be given at the end of the work to theoretical explanations, much like Lynch and Stretsky’s “green behaviorism” position, for why an ecological relationship between air pollution and homicide may exist.

² Throughout this article, for the sake of parsimony, the term “air pollution” is considered synonymous, and used interchangeably, with particulate matter with aerodynamic diameters smaller than 2.5 μm (PM_2.5). However, it should be noted that prior air pollution-crime investigations have focused on alternative environmental hazards, either alone or in combination, such as sulfur dioxide, nitrogen dioxide, carbon monoxide, ozone, manganese, and particulate matter with aerodynamic diameters smaller than 10 μm, to represent differential levels of “air pollution” (e.g., Bondy, Roth, and Sager 2020, Burkhardt et al. 2019, 2020, Herrnstadt et al. 2021, Lu et al. 2018, Masters et al. 1998).

³ In terms of variation, regionally speaking, the Ohio Valley (i.e., IL, IN, KY, MO, OH, TN, WV) and Southeast (i.e., AL, FL, GA, NC, SC, VA) regions of the US have seen the largest percentage decreases in average ambient PM_2.5 concentrations over the 2000–2021 timeframe at 45%, while the Southwest (i.e., AZ, CO, NM, UT) region of the US has seen the smallest percentage decrease at 13% (United States Environmental Protection Agency 2022b).

⁴ Given the “pitfalls” that arise when utilizing regression for areal-based data (e.g., Gordon 1967, 1968), Land et al. (1990) believed that their model had fallen trap to the partialing fallacy (i.e., the explained variance attributable to a particular regressor, amongst an intercorrelated set, is allocated to the indicator with the highest correlation with the dependent variable). In such a case, wide confidence intervals and algebraically opposite coefficient signs are most likely produced. Stated succinctly by Farrar and Glauber (1967), “the mathematics, in its brute and tactless way, tells us that explained variance can be allocated completely arbitrarily between linearly dependent members of a completely singular set of variables, and almost arbitrarily between members of an almost singular set” (p. 93).

⁵ The population structure component consisted of the unit’s population size and density, while the resource deprivation/affluence component consisted of median family income, the percentage of families living in poverty, the Gini index, the percentage of black residents, and the percentage of households with only one parent.

⁶ Within Stretsky and Lynch (2004), the correlation matrix revealed that county-level air-lead levels had a larger intercorrelation coefficient with the population structure component (r = 0.92) than with the highest multiple correlation coefficients reported (i.e., R² = 0.447 for violent index crimes). For Farrar and Glauber (1967), “the most simple, operational definition of unacceptable collinearity … is established to constrain simple correlations between explanatory variables to be smaller than, say, r = .8 or .9” (p. 98). Relatedly, Monte Carlo simulations estimated by Hanushek and Jackson (1977) found that the variance surrounding estimated regression coefficients increased dramatically once the correlation between a set of independent variables exceeded r = 0.50. Therefore, the reported correlation between air-lead levels and population structure justifies concerns related to multicollinearity, and thus, potentially the inferences drawn by Stretsky and Lynch (2004). When multiple correlation coefficients are not reported, scholars have instead invoked Klein’s (1962) rule of thumb to single out indicators that have higher intercorrelations amongst themselves than with the dependent variable of interest (see Balkwell 1990, Land et al. 1990). Within Lu et al.’s (2018) correlation matrix, the composite air pollution measure: (1) had a larger correlation with percent Asian (r = 0.17), percent poverty (r = −0.15), and percent primary sector employee (r = −0.13) than with all the crime types investigated (correlations ranging from r = 0.07 to r = 0.10); and (2) had a larger correlation with population size (r = 0.08), median age (r = −0.08), percent Native American (r = −0.09), percent other races (r = 0.10), and percent male unemployed (r = −0.09) than with six of the seven crime types (minus motor vehicle theft). Even though these correlations are lower than the thresholds set above, Maddala (1977) warned that in regressions with “more than two variables, the simple correlations could all be low and yet multicollinearity could be very serious” (p. 185). Thus, the more relaxed form of Klein’s (1962) rule of thumb applied previously (e.g., Balkwell 1990, Land et al. 1990) appears justifiable for the arguments presented throughout this section.

⁷ As highlighted by Farrar and Glauber (1967), “as the number of variables extracted from the sample increases, each tends to measure different nuances of the same few basic factors that are present. The sample’s basic information is simply spread more and more thinly over a larger and larger number of increasingly multicollinear independent variables” (p. 94). As a result, according to Hanushek and Jackson (1977), “the more two variables covary or move together in a sample, the harder it is to ascertain the independent effect of one of them, holding the other constant. The sample simply does not contain enough information about the variations in Y associated with changes in each explanatory variables for constant values of the other exogenous variables to estimate these effects accurately” (p. 87). Therefore, if pollution exposure and ascriptive socioeconomic inequality are gauging the same phenomenon, the resulting coefficients estimated may be biased, thus questioning potential inferences drawn.

⁸ According to Lynch and Stretsky (2014), “one of the assumptions of green behaviorism that needs to be made clear is that the actions that produce exposure to environmental toxins capable of altering behavior have a sociologically relevant dimension, and that absent this dimension, there is little need for a green behaviorism of crime … [i.e.,] the effect of exposure to toxins that may impact criminal behavior can also be impacted by the social and economic structure of society. Without the connection between exposure, the biological effects of exposure, and the role social structure plays in mediating this process and potentially the outcomes, green behaviorism fails to contribute to the understanding of the factors that affect the production of crime or its distribution” (p. 112–113).

⁹ As originally argued by Land et al. (1990), given the historical variability within the structural covariates of crime literature concerning units of analysis, “a general theory of how structural covariates affect homicide rates also should be applicable at these [alternative] levels” (p. 933, fn. 13). Such statements have led social scientists to view the structural components/indicators stressed and analyzed by Land et al. (1990) as invariant across differing ecological and/or historical lenses (e.g., Baller et al. 2001, McCall et al. 2010, Pridemore and Trent 2010).

¹⁰ While US county-level crime data from the FBI’s UCR have been subjected to criticisms in the past (e.g., Maltz and Targonski 2002), recent exploration by DeLang et al. (2022) has shown that estimates of US county-level crime data results in less bias than estimates derived utilizing US agency-level data and multiple imputation by chained equations with a random forest algorithm, thus increasing confidence in the employed criminal homicide data.

¹¹ According to Kim and Mueller (1978), principal components analysis falls under the umbrella of factor analysis, with the primary objective seeking to “represent a set of variables in terms of a smaller number of hypothetical variables” (p. 9; see also Tabachnick and Fidell 2007). Likewise, according to McCall et al. (2010), components are “dimensions in the vector space spanned by the columns or rows of the variance-covariance or correlation matrix of the regressors accounting for substantial variance in the regressor space and having substantial component loadings for two or more regressors” (p. 223–224). Readers are directed to Brown’s (2009a, 2009b, 2009c) work for non-technical definitions and recommendations for conducting principal components analyses themselves.

¹² Varimax rotation was employed during the estimation of the principal components analysis, given its increased efficiency in producing independent/orthogonal (i.e., uncorrelated) components. Following the recommendations of Tabachnick and Fidell (2007), a 0.32 cutoff point was utilized for classification into a particular component.

¹³ Notably for the first component, the factor loadings are lower than the 0.50 cutoff rule employed by Land et al. (1990)—the percentage of families below the poverty line was the only regressor approaching this threshold. One explanation for this occurrence may be the increased sample size of the current study – both Land et al. (1990) and McCall et al. (2010) investigated the theory at the city-level, reporting sample sizes of 528 to 904 and 699 to 932, respectively. Given the importance of reducing isolated entities during the construction of the spatial weight matrices utilized within areal spatial data analysis (e.g., Chi and Zhu 2019), estimating this factor analysis amongst all counties in the contiguous US may have produced statistically dissimilar, but theoretically similar, components.

¹⁴ A ten-nearest neighbor spatial weight matrix was utilized to estimate each spatial model. In their spatial extension of Land et al.’s (1990) invariant structural covariates of crime theory, Baller et al. (2001) contended that having a fixed number of neighbors reduced methodological concerns that could arise if the constructed neighborhood structure was allowed to vary from county to county (see also Anselin 2002, Chi and Ho 2018, Ho et al. 2018).

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Notes on contributors

Jessie Slepicka

Jessie Slepicka is a doctoral candidate in the Department of Sociology and Criminology at The Pennsylvania State University. His research interests include criminological and sociological theory, green criminology and environmental sociology, comparative social science, spatial analysis, and quantitative research methods.