# Defining neighborhood boundaries in studies of spatial dependence in child behavior problems

Margaret O’Brien Caughy1*, Tammy Leonard2, Kurt Beron2 and James Murdoch2

Author Affiliations

1 University of Texas School of Public Health, Dallas Regional Campus, 5323 Harry Hines Blvd, BL10.204, Dallas, TX, 75390-9655, USA

2 University of Texas at Dallas, Department of Economics, School of Economics, Political & Policy Sciences, 800 West Campbell Road, GR31, Richardson, TX, 75080-3021, USA

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International Journal of Health Geographics 2013, 12:24  doi:10.1186/1476-072X-12-24

 Received: 30 January 2013 Accepted: 25 April 2013 Published: 3 May 2013

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

#### Background

The purpose of this study was to extend the analysis of neighborhood effects on child behavioral outcomes in two ways: (1) by examining the geographic extent of the relationship between child behavior and neighborhood physical conditions independent of standard administrative boundaries such as census tracts or block groups and (2) by examining the relationship and geographic extent of geographic peers’ behavior and individual child behavior.

#### Methods

The study neighborhood was a low income, ethnic minority neighborhood of approximately 20,000 residents in a large city in the southwestern United States. Observational data were collected for 11,552 parcels and 1,778 face blocks in the neighborhood over a five week period. Data on child behavior problems were collected from the parents of 261 school-age children (81% African American, 14% Latino) living in the neighborhood. Spatial analysis methods were used to examine the spatial dependence of child behavior problems in relation to physical conditions in the neighborhood for areas surrounding the child’s home ranging from a radius of 50 meters to a radius of 1000 meters. Likewise, the spatial dependence of child behavior problems in relation to the behavior problems of neighborhood peers was examined for areas ranging from a radius 255 meters to a radius of 600 meters around the child’s home. Finally, we examined the joint influence of neighborhood physical conditions and geographic peers.

#### Results

Poor conditions of the physical environment of the neighborhood were related to more behavioral problems, and the geographic extent of the physical environment that mattered was an area with a radius between 400 and 800 meters surrounding the child’s home. In addition, the average level of behavior problems of neighborhood peers within 255 meters of the child’s home was also positively associated with child behavior problems. Furthermore, these effects were independent of one another.

#### Conclusions

These findings demonstrate that using flexible geographies in the study of neighborhood effects can provide important insights into spatial influences on health outcomes. With regards to child behavioral outcomes, specifically, these findings support the importance of addressing the physical and social environment when planning community-level interventions to reduce child behavior problems.

##### Keywords:
Neighborhood; Child behavior problems; Peer relationships

### Background

#### Analysis of the impact of neighborhood physical condition on child behavior problems

We estimated equation (1) with ordinary least squares varying the condition index from 50 meters to 1000 meters while including in each model all previously described covariates. In all OLS regressions, robust standard errors are reported that also were adjusted for clustering of children within families. Neighborhood condition in the 400-, 600-, and 800- meter circles were statistically significant.

We tested the three significant circle sizes using a Wald test to determine if their estimated magnitudes were the same. We found the null of equality across the three parameter estimates could not be rejected, χ2 (2) = 2.73, p = .26. Similarly, we tested the other two significant variables across the three regressions with the significant circle sizes and found no statistical evidence that female, χ2 (2) = 3.40, p = .18, or income greater than \$30 thousand, χ2 (2) = 1.81, p = .41, were different at the three geographies. As a robustness check, we also tested whether the parameter estimate of the (non-significant) circle size at 200 meters was the same as that of the 400 meter circle size and rejected the null hypothesis of equality, χ2 (1) = 4.83, p = .03. We also tested 1000 meters which, while having a non-significant parameter estimate, still was indistinguishable statistically in value to smaller sizes down to 400 meters.

Thus, with evidence that the 400 meter and larger circles were statistically equivalent, we report the 400 meter model results in Table  2. Our findings, then, based on OLS, were that a one standard deviation increase in negative physical conditions in the neighborhood was expected to lead to about a one-quarter standard deviation increase in the BPI at the 400-meter and above circle geography.

Table 2. OLS results for 400-meter radius circle size (n = 208)

#### Analysis of the impact of geographic neighborhood peers on child behavior problems

The first step in analyzing the impact of geographic neighborhood peers was specifying a weight matrix that determined the relevant geographic peer group. As before, we tested multiple geometries for the spatial weights matrix to correspond with neighborhood definitions at varying distances from the child’s home. Because the spatial weights matrix must be specified such that every observation in the sample has at least one neighbor in the sample, the smallest neighborhood geometry that we could specify for the spatial weights matrix was a circle with a 255-meter radius. For larger geometries, we used the same conventions as before (400 m, 600 m and 800 m).

We first tested for spatial correlation in the errors of the previous ordinary least-squares regression models by calculating Moran’s I statistics [61]. The Moran’s I statistic is a measure of spatial correlation. A statistically significant Moran’s I in our study indicates that the residuals of nearer observations are more likely to be similar than observations located further apart. As condition at 400 m, 600 m and 800 m were found to be statistically significant and have similar associations with child BPI, we focused on these models. In this application, the spatial weights matrix defines the geographic scope over which the spatial correlation is hypothesized to occur. Table  3 presents the Moran’s I statistic, and the associated p-value for each of the different combinations of neighborhood condition geography and weight matrix geography. Two interesting results emerged. First, when we did not control for neighborhood physical condition, the Moran’s I statistic was statistically significant for each of the different weight matrix geographies. However, when we did control for the neighborhood physical condition, we found that only the weight matrix based on a 255 meter radius resulted in a statistically significant Moran’s I. Thus, for spatial weights matrices based on larger neighborhood definitions, we failed to reject the null hypothesis that there was no spatial correlation remaining in the model’s residuals once we controlled for the neighborhood physical condition. This suggests the influence of geographic peers is present after accounting for the exogenous neighborhood effect only for very near geographic peers.

Table 3. Moran'sIstatistic for different definitions of neighborhood geography

Next we estimated (2) and (3) with maximum likelihood algorithms [62] for each of the neighborhood definitions for which the Moran’s I test rejected the hypothesis of no spatial correlation. For (2) we did not control for neighborhood physical condition, and Moran’s I tests were statistically significant at all neighborhood geographies. The results for these models are presented in Table  4.

Table 4. Coefficient estimates for spatial autoregressive models without controls for neighborhood condition

The estimation results presented in Table  5 are based on (3). Here, we analyzed average neighborhood BPI for the 255 m neighborhood only as indicated by the Moran’s I tests. Model 1 included the neighborhood physical condition using the 400 m radius and spatial peers defined over a 255 meter radius; Model 2 examined the neighborhood physical condition using the 600 m radius and spatial peers at a 255 meter radius; and finally Model 3 examined a 800 m radius for neighborhood physical condition with spatial peers at a 255 meter radius. When examining the exogenous (neighborhood physical condition) and endogenous (neighborhood peers) effects in the model, we found that in all cases, neighborhood physical condition was statistically significant. The coefficient estimates for geographic peers are positive in each model and statistically significant in Models 2 and 3. Interestingly, as the coefficient estimate for the geographic peers increased in magnitude and statistical significance, the coefficient estimated for the neighborhood condition variable decreased in magnitude and statistical significance. There is likely some trade-off occurring as we vary the geographic scope over which we measured the neighborhood characteristics. Likelihood ratio tests were performed to test the joint significance of controlling for the relationship between neighborhood physical and social characteristics (both the neighborhood condition and the effects of neighborhood peers) for each of the models estimated in Table  5. In all cases the likelihood ratio statistics were statistically significant. The statistical tests indicate that both the neighborhood physical condition and the average behavior problems of geographically close peers are statistically important correlates of child BPI.

Table 5. Coefficient estimates for spatial autoregressive models with all covariates

#### Sensitivity analyses

We conducted several analyses to examine the robustness of the findings to alternate model specifications. First, we examined whether there were differences between boys and girls and the relation between conditions and the behavior problem index (BPI) across all geographies. The gender interaction term was non-significant at every circle size. A more rigorous set of constraints was imposed to see whether there was evidence that separate models for girls and for boys were warranted, with the result being that pooling across sex could not be rejected at any circle size. Therefore, all multivariate models are pooled across child gender.

In addition, because the primary dependent variable in the model is standardized child BPI, about 14% of the observed BPI values are zero. As a robustness check, we accounted for the 14 percent pileup at our lowest BPI value by re-estimating our final models using Tobit. The estimated coefficients on our condition indices as well as covariates were almost identical.

Finally, there is also concern that neighborhood socio-economic status may be an important correlate with child BPI that is also correlated with both neighborhood condition and average neighborhood BPI. To examine this potential source of endogeneity, we estimated spatial Durbin models [63] that directly control for average neighborhood income, race, parental education, and health status. The results from these models were very similar to the estimation results reported in Tables  4 and 5 and are available from the authors upon request.

### Discussion

We examine the contemporaneous correlated, exogenous and endogenous effects of child behavior problems for children living in a low-income, ethnic minority neighborhood. Our results suggest an important role for all three paths of influence. The correlated effects indicate that dis-amenities in the physical environment of the neighborhood in which children reside are related to more behavioral problems, and the geographic extent of the physical environment that matters is an area with radius between 400 and 800 meters surrounding the child’s home. Finally, the endogenous effects—measured as the average level of behavior problems of neighborhood peers within 255 meters of the child’s home—are positively associated with child BPI.

These findings provide important policy insights. The vast majority of interventions to prevent or treat child behavior problems have focused on individual and family correlates [7-9,12]. The results of this study support the importance of considering the community context as suggested by Dodge [14] in that significant levels of negative physical conditions in the area surrounding a child’s home are related to higher levels of child behavior problems. Interventions for children living in distressed neighborhoods would do well to coordinate with community-level environmental improvement efforts and/or include assessment of neighborhood conditions in the evaluation of potential treatment moderation effects. Likewise, our results demonstrate the importance of geographic peer-network effects for child behavior problems in the neighborhood, which is another outcome that should be included in program evaluations. The existence of geographic peer effects indicate that “untreated” children likely benefit from living in close proximity to “treated” children.

Additionally, the analysis uncovered important findings regarding the geographic definition of neighborhood that mattered for each type of effect. The boundaries for the physical environment that mattered for child behavior encompassed a much broader area than those for the neighborhood peer (e.g., the social environment). This suggests that policies aimed at improving the neighborhood physical environment should target a larger geography. On the other hand, it also means that improvements to a highly concentrated area of neighborhood environment features that need rehabilitation might provide benefits to residents at a fairly large distance.

The geographic scope over which we found evidence of the endogenous impact of neighborhood peers was much smaller (255 meters). Using the estimates from Model 3, a decrease in the average BPI score of geographic peers within this area by one standard deviation is associated with a reduction in child BPI of .18. Although this effect size would be considered modest [64], it is consistent with the effect sizes for the relation of sensitive parenting with child behavioral competence reported by others [65]. However, this effect size does not account for the social multiplier effect, or the reciprocal influence between a child and his geographic peers. The total effect of a reduction of the average BPI of a child’s geographic peers can be calculated as (1-ρ)-1 times the direct effect [66] or 1.23. Thus, the total effect size for a one standard deviation change in average behavior problems of geographic peers is 1.23 for all peers within a 255 meter radius. This is significantly larger than effect sizes reported for behavior problem interventions, which range between .30 and .89 [8,12].

Evidence of the simultaneous endogenous and exogenous effects is highly important for policy analysis and implementation, but the results here should be considered within the limitations of our study. First, the sample is from a single neighborhood, so although our results are supported by numerous studies examining either the neighborhood physical environment [15,19,20,67] or social peers in isolation [68-70] and the development of child behavior problems, the external validity of our contemporaneous estimation of the two types of effects is unknown. Additionally, due to data limitations, our enumeration of the geographic peer network is incomplete. There are many more children in the neighborhood that are not enrolled in our study, and the school peer group of children (for which we do not have complete data) is likely another highly important reference group. We hypothesize inclusion of a more complete peer network would improve the strength of the endogenous effects, but this hypothesis is not testable with our current data. Further, a more complete peer network may cause the exogenous effects of the neighborhood physical environment to diminish. These are important questions for future research.

### Conclusions

Despite these limitations, our study presents some important considerations for both research on neighborhoods as well as for policies aimed at improving child behavior outcomes. With regards to research implications, our findings support the importance of carefully considering the geographic unit of analysis in studies of neighborhood effects on health. Although there have been limited attempts to examine the different geographic neighborhoods, most has relied upon existing administrative boundaries as the smallest geographic unit, be it census tracts in Canada [44,71], enumeration districts in the United Kingdom [72], or census blocks in the United States [73]. Only Chaix and colleagues in Sweden [43] examined the utility of a neighborhood definition that was completely independent from existing administrative boundaries. More research is needed to systematically compare neighborhood definitions and their relation to a variety of health outcomes. Recent advances in the use of such technology as Google Street View [74] may provide an opportunity for replicating this work in a range of urban and rural settings in different parts of the world.

Our findings also have implications for policies related to community-level interventions to reduce child behavior problems. In particular, failure to account for the three simultaneous paths of influence correctly may result in underestimation of the benefits of interventions. Our results indicate if the influence of neighborhood physical conditions and peer networks are accounted for, the potential economic impact of community-based parenting programs to prevent child behavior problems such as “Triple-P” [51] might be misestimated. A more comprehensive assessment of program impact is critical if policy makers are to compose informed decisions on how to improve population behavioral health in children and youth.

### Competing interest

The authors declare that they have no competing interests.

### Authors’ contributions

MC, TL, and JM were responsible for the conceptualization and design of the study, and TL was responsible for overseeing data collection. MC, TL, and KB were responsible for the analysis and interpretation of data and for drafting the manuscript. JM provided final approval of the manuscript. All authors read and approved the final manuscript.

### Acknowledgements

This research was funded by the National Science Foundation (NSF grant #: 0827350, PI J. Murdoch). The National Science Foundation had no role in the design of the study, the collection, analysis or interpretation of data, or the preparation of this manuscript for publication.

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