a comparison of foster care entry risk at three

8/12/2019 A Comparison of Foster Care Entry Risk at Three

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Substance Use & Misuse, 43:223237

Copyright 2008 Informa Healthcare USA, Inc.

ISSN: 1082-6084 (print); 1532-2491 (online)

DOI: 10.1080/10826080701690631

A Comparison of Foster Care Entry Risk at ThreeSpatial Scales

BRIDGETTE LERY

Chapin Hall Center for Children, University of Chicago, Chicago, Illinois, USA

This study addresses the problem of operationalizing neighborhood boundaries by inves-tigating foster care entry risk at three spatial scales. Foster care entries from a Californiacounty between 2000 and 2003 (n = 3,311) are geocoded to each of the three scales(N =46 zip codes, 320 census tracts, and 983 block groups). Exploratory spatial dataanalysis is used to compare spatial autocorrelation of entry rates among scales. Resultssuggest that depending on how neighborhoods are defined, the geographic pattern offoster care incidence changes. Implications for accurately targeting services to high-risk

neighborhoods and future research directions are noted.

Keywords spatial scale; child welfare; foster care; spatial analysis; modifiable arealunit problem; risk factors; high risk neighborhood

Introduction

The push for neighborhood-based child welfare and other social services demands bettertools to investigate the role of location in child and family outcomes. Geographic infor-

mation systems (GIS) and spatial analysis are now commonly used to map, for instance,

rates of child maltreatment in neighborhoods and to model its relationship to neighbor-

hood social conditions such as impoverishment or alcohol outlet density (Coulton, Korbin,

Su, and Chow, 1995; Freisthler, 2004). The spatial representation of social phenomena

on GIS maps exposes patterns and relationships that are not easily recognized using con-

ventional analytical procedures. However, there is a methodological gap between the de-

scriptive mapping of social data across geographic areas and the statistical inference of

the relationships of such variables across space. Most studies of neighborhood effects

on child maltreatment and subsequent policies promoting community-based interventions

have not considered the unique statistical biases that often arise in maps and models that use

geographic data.

The problem stems from the fact that there is no consensus on what is the best unit

of analysis to call neighborhood. Researchers chose administrative units such as census

tracts to represent neighborhoods in ecological studies out of convenience in the absence

of an available systematic method for doing so. This creates two related problems. For one,

administrative units are usually not very good proxies for neighborhoods. For another, the

variation of a phenomenon over a geographic area may change if the data are represented

over a different geographic scale (Coulton, Cook, and Irwin, 2004). These issues are known

as thezone problemand thescale problem, respectively, and fall within a larger definition

Address correspondence to Dr. Bridgette Lery, Chapin Hall Center for Children at the Universityof Chicago, 1313 East 60th Street, Chicago, IL 60637. E-mail: [email protected]

223

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224 Lery

of problems in ecological studies, the modifiable areal unit problem (MAUP; Openshaw

and Taylor, 1979; Robinson, 1950).

The zone problem refers to the fact that administrative units are typically poor rep-

resentations for neighborhoods because the concentration of a phenomenon in one spa-

tial unit will tend to spill over into adjacent units, making the relationships between the

units not independent. In other words, attributes of areal units may be correlated across

space. The strength of the correlation depends largely on where the unit boundaries are

drawn, and this correlation may bias the standard errors in multivariate ordinary least

squares regression models of ecological data, which assume independence among the

units of analysis (Bailey and Gatrell, 1995). Further complicating the matter of choos-

ing a reliable unit, neighborhood boundaries are permeable. People move in and out of

neighborhoods, making boundaries dynamic over time (Freisthler, Lery, Gruenewald, and

Chow, 2006).

Substance Use and Child Welfare in Spatial ContextThe explicit consideration of spatial scale makes a substantive difference when seeking to

understand how attributes of place may impact the risk of child maltreatment or foster care

entry and when designing interventions to reduce this risk. For example, there is ample

evidence that parental substance abuse* is a posited risk factor for child maltreatment and

that a large portion of children receiving child welfare services are from substance-using

families (Besinger, Garland, Litrownik and Landsverk, 1999). One recent study suggests

that integrating substance user and child welfare services might be an effective strategy

to increase the likelihood of reunification for children placed in out-of-home care (Ryan,

Marsh, Testa and Louderman, 2006). Coordinating the location of substance user treat-

ment programs nearby to maltreating parents is one way to do this (DAunno, 1997).However, in order to target the location of treatment services effectively and efficiently, it

is important to know which areas in a jurisdiction are at the highest risk of using foster

care.

From an ecological perspective, it is also important to know whether there is any

relationship between drug and alcohol availability in neighborhoods and risks to children,

beyond the known associations at the individual level. Freisthler (2004) found that the

availability of alcohol in neighborhoods is associated with rates of child maltreatment in

census tracts, suggesting that a solution could be to reduce the density of bars and other

alcohol outlets at that spatial scale. However, it is possible that the density of outlets, rates

of maltreatment, and therefore their relationship to each other changes depending on how

neighborhoods are defined.

Defining Neighborhoods

The child welfare literature offers little guidance on how to measure and define neigh-

borhoods and, as a consequence, the geographic unit chosen to represent neighborhoods

varies across studies. A neighborhood can be conceptualized as a geographic place where

residents share social networks and informal ties. However, such networks are not nec-

essarily tied to place, and the distinction between neighborhoods and communities can

become blurred (Newman and Small, 2001). In addition, residents perceptions of their

*The journals style utilizes the category substance abuseas a diagnostic category. Substancesare used or misused; living organisms are and can be abused. Editors note.

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A Comparison of Foster Care Entry Risk at Three Spatial Scales 225

neighborhoods are unlikely to correspond to administrative boundaries (Coulton, 2005;

Coulton et al., 2004; Coulton, Korbin, Chan, and Su, 1997). Since social networks and

residents perceptions are not reliable tools with which to measure homogenous neigh-

borhoods, researchers typically select either counties (Albert and Barth, 1996; Fryer and

Miyoshi, 1995; Spearly and Lauderdale, 1983), ZIP codes (Drake and Pandey, 1996), cen-

sus tracts (Coulton et al., 1995; Deccio, Horner, and Wilson, 1994; Ernst, 2001; Freisthler,

2004), or block groups (Coulton, Korbin, and Su, 1999; Young and Gately, 1988) as units

of analysis. Block groups or census tracts are sometimes grouped to model socialization

spaces that better represent neighborhoods than do individual units (Sampson, Raudenbush

and Earls, 1997). Census and geographic boundary data are readily available at all of

these levels of aggregation, allowing for the calculation of rates of social indicators such

as poverty and, when the data are accessible, rates of child maltreatment and foster care

entry.

In addition to the zone problem, administrative units may not represent the scale at

which the social processes of interest operate (Coulton, 2005). When the level of data

aggregation is too large, the spatial pattern is obscured (Can, 1993). Maps are merely amodel of reality and can misrepresent data and lead to poor assumptions about relationships

between variables. People are good at detecting patterns visually, but they also tend to

identify patterns that are not present (MacEachren, 1995).

Most neighborhood studies in child welfare limit analysis to one spatial scale without

formal consideration of the statistical bias that may occur due to spatial autocorrelation

among units of analysis. Recent evidence suggests that an outcome such as child maltreat-

ment risk may be affected by neighborhood characteristics differently at different scales

(Johnston et al., 2004). Chou (1991) found that Morans I (Moran, 1950)the most com-

monly used measure of spatial autocorrelationincreases systematically with the resolution

level. If resolution changes the degree to which units are correlated across space, which in

turn affects the level of bias in the statistical model, then the choice of which spatial scale

to use in a neighborhood analysis is a nontrivial one.

If neighborhoods can be defined in a variety of ways, then what criteria should be

used to examine the geographic distribution of a problem? While most previous studies

choose one spatial scale to approximate neighborhoods, this study systematically compares

foster care entry rates across three commonly used operational definitions of neighbor-

hood to address the question, How can we define neighborhoods operationally so that

researchers and administrators can choose an appropriate unit of analysis when evaluating

child welfare outcomes and designing interventions? A related goal is to demonstrate the

dangers of arbitrarily choosing units of analysis in neighborhood research. Determining

a practical and reliable unit of analysis to serve as a proxy for neighborhood will im-prove the reliability of research on neighborhoods and the efficiency of place-based service

allocation.

Method

Exploratory spatial data analysis (ESDA; Anselin, 2005) is used to compare spatial auto-

correlation in foster care entry rates at three geographic scales within Alameda County,

California. Counties are the administrative jurisdictions for child welfare agencies in Cali-

fornia. Foster care entry rates vary considerably within the county, making it an illustrative

choice for study. Table 1 shows foster care entries and child population by year for Alameda

County.

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226 Lery

Table 1

Alameda County first entries to foster care, child population, and entry rates per 1,000

children by year: 20002003

Total 2000 2001 2002 2003

First entries to foster care1 3,739 1,005 1,033 860 841

Child population


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inflated and are not shown. The purpose of the rates is to establish relative meaning within

and across geographic scales with respect to variation.

Independent Variable

Zip codes, census tracts, and block groups are the geographic units of analysis for compar-

ative study. Census block groups are nested within tracts, while zip codes are larger than

tracts but are not part of this hierarchy. Two of 48 zip codes, one of 321 census tracts, and

12 of 983 block groups are dropped from the analysis because these areas had zero child

population and therefore no risk of foster care entry. Foster care entries are particularly

infrequent at the block group scale. Thirty-one percent of block groups had zero entries

and 41% had between one and five entries over the study period. Figures 1a and 1b show

quartile maps of the distribution of child population and first entries to foster care across

the spatial scales. The presence and strength of spatial correlation of the measures across

neighborhoods at each spatial scale are assessed using ESDA.

Data Analysis

First, mapped foster care entry rates are explored at each spatial scale to examine variation

in risk within and between scales and to look for outliers. Second, the Morans I statistic

is calculated at each scale based on a neighbor matrix. The matrix assigns spatial weight

according to neighboring units that share lines and not vertices (referred to as rook cri-

teria), under the assumption that areas sharing a full boundary line are more alike (more

spatially dependent) than areas that do not (spatially independent). Griffith (1996) finds that

misspecification of the spatial weights matrix affects the quality of maximum likelihoodestimators, especially when N is small, and offers five rules of thumb for specifying the

weights matrix:

1. It is better to posit some spatial weights matrix than to assume independence among the

units (extreme underspecification).

2. It is best to use a partitioning that is in between a square and a hexagonal tessellation.

3. N should be greater than 30.

4. Low-order models are preferential to higher-order models.

5. It is generally better to use a somewhat underspecified than a somewhat overspecified

spatial weights matrix.

The choice of rook criteria in this study meets all of these suggestions.

It is predicted that each spatial scale will have a different Morans coefficient (MC)

because the distribution of entry rates will vary at different levels of aggregation. Attributes

of smaller units tend to have greater variances than do larger units because there are fewer

people to smooth out the mean. For example, the variance of foster care entry risk in a block

group is likely to exceed the variance in a zip code, which typically has many more people.

This will affect the value of the MC (Wong, 1996). The presence of significant positive

spatial autocorrelation at any spatial scale, as measured by the Morans I statistic indicates

that areas with high rates of foster care entry tend to be clustered together. If the level of

spatial autocorrelation varies across geographic scales, this will indicate that the pattern of

risk differs depending on which unit of analysis is chosen to map entry rates.

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228 Lery

Figure 1. Child population at three scales. (a) zip codes. (b) Census tracts. (c) Block groups. Foster

care entries at three scales. (d) zip codes. (e) Census tracts. (f) Block groups. (Continued)

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Figure 1. (Continued)

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230 Lery

Results

Figures 1d to 1f show quartile maps of aggregated 2000 through 2003 foster care entry rates

by zip code, census tract, and census block group for Alameda County. The distribution of

children across any spatial unit (Figures 1a1c) is not the same as the distribution of foster

care entry rates across that same unit (Figures 1d1f), indicating that many areas havedisproportionate rates of foster care entry. The relative rarity of foster care entry and low

population in some areasparticularly at the block group levelcreates unstable rates that

may be misleading on maps. This issue will be explored using ESDA techniques (Anselin

and Bao, 1997).

Exploratory Spatial Data Analysis (ESDA)

Zip Codes. The quartile map in Figure 1d shows aggregated foster care entry rates between

2000 and 2003 for Alameda County by zip code and is consistent with other, single-year

maps of this data. Areas with highest entry rates are in West Oakland, South Berkeley, andHayward. The lowest rates are in the more rural and suburban areas in the southern and

eastern parts of the county.

First-order contiguity spatial weights based on rook criteria produced significant global

spatial autocorrelation (I = .3445, p


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Figure 2. Univariate Moran scatterplots of foster care entry rates at each spatial scale. (a) Zip codes:

Morans I =.3445. (b) Census tracts, Morans I =.2446. (c) Block groups, Morans I =.1815.Note:Axis units are in standard deviations.

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232 Lery

weaker at this scale (I = .2446, p < .01), as shown in Table 2 and in the slope of the

Moran coefficient in Figure 2b. This is to be expected as neighborhoods are disaggre-

gated to smaller units. The Moran plot in Figure 2b centers the data around zero by sub-

tracting the mean, so the concentration of points along the y-axis indicates the preva-

lence of tracts with zero foster care entries. Positive and negative spatial autocorrelation

are present in the same general geographic areas as when entry rates were mapped in

zip codes. However, the finer level of granularity among tracts allows for the identifica-

tion of some different local spatial clusters, as can be seen by comparing Figure 2b to

Figure 2a.

Block Groups. The quartile map in Figure 1f shows aggregated foster care entry rates by

block group. The very fine resolution of this scale breaks up the north-south pattern visible

in the tract and zip code maps and highlights some new high-risk areas such as Livermore,

Castro Valley, Newark, and Dublin.

The Moran plot in Figure 2c shows significant spatial autocorrelation in entry ratesamong block groups. The spatial autocorrelation statistic remains significant at the block

group level (I =.1815, p < .01), although the difference in the slope coefficient between

tracts and block groups is smaller than between zip codes and tracts. This is partly because

in less populated areas tracts and block groups sometimes represent identical geographic

boundaries. The stacked values along the y-axis show that many of these small areas had

no foster care entries over the study period.

The analysis was repeated at each scale with a queen criteria spatial weights matrix

(units that share a line or a vertex border are considered contiguous spatial neighbors).

Results were consistent with the rook neighbor specification.

Discussion

This study investigates spatial dependence in foster care entry risk at three different spatial

scales and explores the extent to which risk spills over into adjacent areas depending on

how neighborhoods are aggregated. Results from ESDA suggest that indeed entry rates

in each of the three units of analysis used to represent neighborhoods are spatially au-

tocorrelated. In other words, depending on how neighborhoods are defined in this study,

the geographic pattern of foster care incidence changes. Zip codes possess the most spa-

tial dependence in this context, followed by census tracts and census block groups. This

pattern naturally occurs because, generally, zip codes are the largest geographic units andblock groups are the smallest. Therefore, neighborhood foster care entry risk varies the

least across zip codes and the most across block groups. This does not imply, however, that

zip codes best describe discreet, homogeneous neighborhoods as residents would define

them.

Zip Codes. Zip codes represent neighborhoods on a crude scale. Exploratory analysis re-

veals some initial patterns in the way that foster care entry rates are distributed across

Alameda County. Descriptive maps show clustering, with high rates concentrated in the

relatively urban areas and low rates grouped in the suburban and rural southern neighbor-

hoods. This pattern is supported by the significant Morans statistic as a global measure of

spatial dependence and by the local indicators of spatial association in the Morans plot.

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Census Tracts

Census tracts are generally smaller geographically than zip codes and when neighborhoods

are defined in this way, exploratory analysis yields somewhat different spatial patterning

that is confirmed by a significant Morans statistic. The finer resolution highlights more

specific high-rate neighborhoods within the broad areas on the zip code maps and onespecific high-rate tract stands out in the east-central part of the county that was hidden

when neighborhoods were aggregated to zip codes. Variance instability begins to emerge

at the smaller scales as the base population declines and this can create misleading visual

patterns of high rates in areas with very few children. In this case, the tract-level maps

expose at least one important area that is camouflaged in the zip code maps.

Block Groups

Census block groups, a subset of census tracts, are more homogenous and have less within-

unit variability than tracts. When neighborhoods are classified as block groups, the visualpattern of foster care entry across areas is different from the other two scales. Some different

high-risk neighborhoods newly emerge at this scale, but many neighborhoods have low

populations and only a few entries, causing the rates to be inflated. This is particularly

misleading in the geographically large block groups because they are the most striking

areas on the map. The significant global Morans statistic and the Morans plot support the

general trend of high entry rates clustering in the urban parts of the county.

Implications for Practice and Policy

Zip code representations of neighborhoods are useful when sharing maps with community

partners because they generally highlight the same highest risk areas as do the smaller

scale maps. They also are practical for child welfare service planning in rural areas where

population and resource densities are low and a census tract does not represent enough

children to produce a stable rate or an area large enough to capture available resources such

as foster homes or substance abuse treatment programs. Zip code-level data aggregation

may be the most useful for matching need with service because treatment facilities are likely

to serve clients from geographic areas larger than census tracts.

Block groups may be the best proxies for homogeneous neighborhoods but variance

instability makes them not ideal for estimation. Foster care entry is relatively rare within

these small areas so that nearly one third of the block groups had zero entries over the 4-year

study period and most areas had fewer than five entries. Census tracts, being smaller thanzip codes and larger than block groups, possess the strengths and limitations of both of the

other scales. Therefore, a best or least biased unit of analysis cannot be determined from

the study; rather, the analysis demonstrates benefits and drawbacks to each spatial scale.

Furthermore, the process by which spatial relationships and spatial scale are considered

strengthens the model-building process and offers a set of diagnostic and comparative

procedures that can be applied broadly to research on neighborhoods and other small areas.

A few limitations are noted. First, results may not be generalizable to other areas or time

periods. Other counties may have different demographic distributions and different spatial

and social configurations of neighborhoods. Second, foster care entry is a relatively rare

event compared to maltreatment, so the low number of entries in many areas makes it more

difficult to detect major differences in spatial dependence among the scales. Third, planning

for neighborhood-based foster care reform should be informed by more developed analyses

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234 Lery

that model the relationship between neighborhood characteristics and foster care entry risk.

Factors such as poverty and alcohol outlet density have been found to be related to child

maltreatment and foster care outcomes, and taking such factors into account at multiple

spatial scales would enrich our understanding of how the ecological environment may

influence risk for children (Coulton et al., 1995; Freisthler, 2004). Such design additions to

this study could be conducted in cities such as New York and Chicago, where neighborhoods

tend to be more discreet and homogenous than in California (and therefore where spatial

autocorrelation may be lower). This information can be used to guide the development

of geographically based resources and strategies such as foster parent recruitment or the

development of substance abuse programs for maltreating families in neighborhoods with

the highest need.

For instance, Freisthler (2004) found that the number of bars per 1,000 population

was positively related to child maltreatment rates in census tracts, adjusting for a very

high level of spatial autocorrelation (I = .5407) and neighborhood social characteristics.

When maltreatment reports, substantiations, and foster care entries were aggregated to the

zip code level and measured over time, Freisthler, Gruenewald, Remer, Lery, and Needell(2007) found a relationship between the concentration of off-premises alcohol outlets such

as convenience and liquor stores and increased risk for all three measured outcomes. The

persistent findings across scales suggest that an effective strategy for reducing risk to children

could be to limit the concentration of bars in neighborhoods.

As neighborhood-based services in child welfare and other social service fields become

increasingly popular, the accurate identification of high-risk neighborhoods becomes more

important. Administrators want to target the right areas, not just those that appear to have

high rates due to the MAUP. Planners using maps should take into account the spatial

relationships between areas because neighborhoods do not exist in isolation. As the positive

spatial autocorrelation in this study shows, phenomena in one neighborhood may, in fact,

spill over into adjacent areas. Agencies can use neighborhood maps at multiple spatial

scales to capture this artifact of mapping administrative units as proxies for neighborhoods,

and to eliminate the problems with viewing only one scale, such as over generalized zip

codes or variance instability across smaller areas. Maps can then be use to determine which

neighborhoods are most in need of interventions and then, separately, to consider spatial

scale in planning services at the scale most efficient for reaching the target population.

RESUME

Une comparaison des risques de placements sur trois echelles spatiales.

Letude aborde la question de loperationnalite des perimetres frontaliers / decoupages

par quartiers par lanalyse des risques dentree en placement sur trois echelles spatiales.

Entre 2000 et 2003 (n =3 311), les nouveaux placements ont ete geocodes selon trois

niveaux (N =46 codes postaux, 320 cas recenses et 983 groupes). Un systeme exploratoire

danalyse de donnees spatiales a ete utilise pour comparer les autocorrelations spatiales des

taux de placements sur differentes echelles.

Les resultats de letude demontrent que la facon dont les quartiers sont definis influence

la facon dont les placements sont effectues. Cette etude conclue en indiquant des pistes pour

mieux cibler les services a offrir dans les quartiers a haut risques. Des pistes de recherche

ulterieures sont aussi suggerees.

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RESUMEN

Una Comparacion de la Entrada al Sistema Acogida Temporal en Tres Escalas

Espaciales

Este estudio aborda el problema de la operacionalizacion de los lmites de vecindarios

a traves de la investigacion de la entrada al sistema de cuidado adoptivo temporal en tres

escalas espaciales. Entradas al sistema de acogida temporal de un condado de California

entre los anos 2000 y 2003 (n =3.311) han sido geo-codificadas para cada una de las tres

escalas (N =46 codigos postales, 320 subdivisiones de condado1 , 983 grupos de calles2 ).

El analisis exploratorio de datos espaciales es usado para comparar la autocorrelacion

espacial de las tasas de entrada entre las distintas escalas. Los resultados sugieren que

dependiendo de como los vecindarios son definidos, el patron geografico de la incidencia del

cuidado adoptivo temporal cambia. Se destacan implicaciones para concentrar los servicios

en vecindarios de alto riesgo y direcciones para futuras investigaciones.

THE AUTHOR

Bridgette Leryis a Researcher at the Chapin Hall Cen-

ter for Children at the University of Chicago. Much of

her work focuses on how location and neighborhood so-

cial structure impacts childrens involvement with the

child welfare system. She is particularly interested in how

neighborhoods can be better defined and targeted for so-cial service planning. Dr. Lery has an M.S. in Social Work

from Columbia University and a Ph.D. in Social Welfare

from the University of California, Berkeley.

Glossary

Neighborhood: can be conceptualized as a geographic place where residents share social

networks and informal ties.

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