The purpose of this article is to compare four different levels of aggregation to assess their utility as areal units in child maltreatment research. The units examined are county, zip code, tract, and block group levels. Each of the four levels is analyzed to determine which show the strongest effects in modeling the correlation between poverty and child maltreatment report rates. Tract-level aggregation appears to be the most generally robust level, with other levels of aggregation being more vulnerable to different kinds of threats. Some zip codes contain very few people, raising reliability issues, but if weighting or minimum population cutoffs are used, this problem is minimized, and zip codes become an attractive choice. County-level data are less homogeneous than other levels, introducing validity concerns. The smaller populations commonly present in block groups also invoke reliability problems, reducing their utility, especially when rare events are examined.
KEY WORDS: child maltreatment; geography; neighborhood; poverty
Neighborhood effects on child maltreatment are an important area of study. Many studies of child maltreatment use geographically aggregated data to represent neighborhood-level constructs in statistical models. Levels of aggregation can range from the state or county level to zip codes, neighborhoods, tracts, block groups, or even smaller geographically defined areas (Sampson, Morenoff, & Gannon-Rowley, 2002). Contextual measures of poverty are also often used as control variables in studies using individual-level data. For the current research, aggregate data is defined as means, percentages, or similar values derived from and representing a geographic area.
The modifiable areal unit problem (MAUP) is well known in many fields (King, 1997) and has recently received attention in the child maltreatment literature (Lery, 2008, 2009).The MAUP is an issue encountered when arbitrary geographic areas are established. Should the area be small, events within the area may be rare, and reliability can suffer because of poor signal-to-noise ratios. Should the area be large and not homogeneous with regard to key factors, then any aggregate measure of those factors will not represent the area well (Nakaya, 2000). An ideal areal unit would be one in which the area is large enough to create stable (reliable) counts of the variables of interest and also sufficiently homogenous on all key variables to minimize error due to conflation of dissimilar subareas. For child welfare research, it would be best to use geographic boundaries that are large enough to provide stable counts of maltreatment but small enough to encompass families that are generally similar to each other on key factors, especially poverty, a key construct relative to child maltreatment (Drake & Zuravin, 1998).
An obvious practical question confronting child welfare researchers and agencies involves which levels of aggregation to use for different purposes. This article presents data to assist academic and agency researchers in answering that question. For each of four geographic levels, data are presented showing observed correlations between poverty and child maltreatment reporting rates. Correlations obtained at each level of analysis are presented side by side so that the relative strengths and significance of the correlations can be observed. To the degree that each level of analysis fosters reliability (stability) and validity (homogeneity within each unit of analysis), error will be reduced, and the observed correlations will be correspondingly higher (Nakaya, 2000). This is, perhaps, the most straightforward way of demonstrating the relative utility of different levels of aggregation, at least relative to poverty and its relationship to maltreatment. To maximize utility and generalizability, a simple and important construct (poverty), a very basic statistical operation (correlation), and the four most universally available levels of aggregation (county, zip code, tract, and block group) are used.
Contextual and Compositional Variables
Seldom encountered in the child maltreatment literature, descriptions of variables as contextual or compositional are commonly found in the health and social capital literatures (Subramanian, Lochner, & Kawachi, 2002; Veenstra, 2005). For example, income can be measured at the individual level, generally using survey questions. This is termed a compositional variable, one that directly describes an individual-level characteristic. Aggregate measures of income (median, mean, percentage below poverty level in a given area) are contextual variables representing the economics or other features of a geographic area in which individuals five. A random sampling of individuals in a given area will provide a set of compositional measures that can be used to derive a contextual measure. Full or near-full sampling of individuals within areas (for example, census data) provide another source for contextual data. Compositional and contextual variables are therefore computationally related but remain theoretically quite distinct. Compositional variables provide measures of individual subjects, whereas contextual variables describe the communities in which subjects live. If a geographic area is relatively homogeneous, there will be correspondingly little variation between contextual and compositional measures.Theoretically, if an area is entirely homogenous, then the contextual and compositional measures will be identical.
Neighborhood Context as a Subject of Inquiry
There is a long tradition of empirical exploration in this area (Coulton, Korbin, & Su, 1999; Drake & Pandey, 1996; Garbarino & Sherman, 1980).Various neighborhood characteristics, from cohesion to mobility to density to income (Freisthler, 2004, Lery, 2009), have been identified as contributing to child maltreatment. Much of the work in this area is essentially deductive, testing for anticipated relationships between theoretically derived neighborhood characteristics and observed maltreatment rates. The unit of analysis is generally the geographic area, for example, tracts (Coulton, Korbin, Su, & Chow, 19%). These studies often do not use weighted data, as their purpose is to test theory, not to apply findings back to (generalize to) state or national populations. Only contextual variables are used in studies of this type, as analyses are performed using areas as the unit of analysis.
Neighborhood Context as a Statistical Control
Both individual and community income have been shown to be strongly associated with child maltreatment (Drake & Zuravin, 1998; Sedlak & Broadhurst, 1996). Models and analyses that do not include some measure of income or poverty invite massive threats to their content validity. Content validity is the methodological requirement that a study attend to all variables that may powerfully influence the model being tested (Drake & Jonson-Reid, 2008). For example, if income is not controlled for, African American race will generally appear to be a powerful predictor of maltreatment, when this relationship is, in fact, largely a spurious result of the uneven distribution of income across racial groups (Ards, Myers, Chung, Malkis, & Hagerty, 2003; Drake, Lee, & Jonson-Reid, 2009). To address this problem, multivariate models attempting to explain child maltreatment must include income or poverty variables as controls. These variables can be either compositional (for example, Sedlak & Broadhurst, 1996) or contextual (for example, Drake, Jonson-Reid, Way, & Chung, 2003).
Many child maltreatment data sets do not include individual (compositional) measures of income. Some data sets, particularly administrative data sets, do include addresses that can be geocoded and then fixed within neighborhoods. In conjunction with census data, this allows for a (contextual) measure of the relative wealth or poverty of areas in which individuals live (Drake et al., 2003; Freisthler, 2004). When such steps are taken, the researcher must be clear that neighborhood-level indicators of poverty do not stand as representative of the individual subject's income level, as this would constitute an ecological fallacy. It is valid, however, to use such measures as an indicator of the neighborhood context in which the child lives. This is often the best available way to attempt to control for the powerful effects of socioeconomic status in models of child maltreatment. The same lack of individual-level income data confronts medical researchers. One study directly addressed this problem by comparing individual measures of income with neighborhood (block group) income data (Krieger, 1992), with findings indicating that "census-level and individual-level socioeconomic measures were similarly associated with the selected health outcomes" (p. 703).
Levels of Aggregation in Child Welfare Research
Prior work looking at neighborhood context and maltreatment has been done at block group (Friesthler, Needell, & Gruenewald, 2005), tract (Coulton et al., 1995), zip code (Drake & Pandey, 1996), and county (Garbarino, 1976) levels. Beyond child welfare, a recent overview of studies examining neighborhood effects in social...