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Social Science & Medicine 58 (2004) 19611967
Commentary
The relevance of multilevel statistical methods for identifying
causal neighborhood effects
S.V. Subramanian*
Harvard School of Public Health, Department of Society, Human Development and Health, 677 Huntington Avenue,
KRESGE, 7th floor, Boston, MA 02115-6096, USA
Introduction
Our current understanding of, and continued interest
in, the social determinants of health is in large part due
to the important empirical contributions that in the last
10 years have consistently shown an association between
neighborhood factors and individual health (for an
excellent review of these works, see Diez Roux, 2001;
Ellen, Mijanovich, & Dillman, 2001; Pickett & Pearl,
2001; Sampson & Morenoff, 2002; OCampo, 2003).
Three aspects underscore the importance of these
empirical studies. First, the impact of neighborhood
characteristics, independent of individual factors, has
been shown to exist across a range of public health
outcomes (e.g., all-cause mortality, cardiovascular mor-
tality, infant and child health, womens health, chronic
diseases, mental health, health behaviors, health percep-
tions, delinquency, violence). Second, multiple aspects of
neighborhood (e.g., deprivation, inequality, neighbor-
hood ties, social control, institutional resources) have
been shown to be associated with public health out-
comes. Finally, much of this research utilizes some form
of multilevel statistical methodsan improved quan-
titative methodology especially suited to modeling
neighborhood clustering and variationin order to
estimate neighborhood effects. Does the multilevel
empirical evidence for independent neighborhood ef-fects, accumulated over the last 10 years across a range
of public health outcomes measuring a range of
neighborhood factors, provide a basis to conclude that
neighborhoods matter for health?
In this issue, Oakes (2003) reviews the capability of
multilevel regression models to identify and estimate
neighborhood effects. Notably, Oakes presents four
conceptual/methodological issues that threaten the
ability of multilevel models to detect the causal effects
of neighborhoods on health, thereby casting doubt onthe trustworthiness of existing multilevel empirical
evidence. The alternative strategy (to multilevel model-
ing), Oakes argues, lies in community trials. Oakes
concludes that multilevel methods, while having en-
riched the etiological discussion on the linkages between
neighborhoods and health, are incapable of producing
valid estimates of neighborhood effects: we do not
know yet (whether there is an independent effect of
neighborhoods on health or not), but now we know that
our methodology must change if we wish to find out.
In this commentary, I argue that Oakes position is
rather extreme and overly pessimistic. In the interest of a
more vigorous discussion, this commentary scrutinizes
the claims and conclusions of Oakes essay. In the spirit
of this timely reflection on the usefulness of multilevel
methods, the commentary makes an attempt to raise the
level of awareness on issues related to designing,
conducting and interpreting a multilevel analysis.
The (mis)estimation of neighborhood effects: a critique
In an essay that otherwise raises key methodological
challenges for research on neighborhoods and health,
the motivation and background to the discussion ismisplaced. At the outset, the essay fails to recognize that
issues of causality are one of substantive subject matter
and not one of statistical methodologies. To add to this,
Oakes mixes up the issues that are intrinsic to study
design as compared to those that pertain to metho-
dological/modeling strategies in order to make a
confusing case against the application of both multilevel
methods and observational data. The confusing nature
of the claim is evident in his proposal for randomized
community trials as an alternative to multilevel ana-
lysis. Since the alternative is proposed after painstak-
ingly rehearsing the multilevel regression methodology
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as it relates to identifying neighborhood effects, followed
by a passionate criticism of it (and not after critiquing
the limits of cross-sectional observational data-design-
based inferences), Oakes seems to imply that rando-
mized community trials are an alternative to multilevel
methods. In order to evaluate Oakess claims (especially
as they relate to multilevel methods), the distinctionbetween methodological strategies and study design
is critical.
The framework of randomized community trials,
which is not without it merits, is completely independent
of the advantages or shortcoming of multilevel modeling
strategies. Importantly, even when we have data from
randomized community trials, a multilevel analytical
framework would still provide the most appropriate
statistical strategy to analyze the data for detecting and
describing neighborhood effects, besides offering other
substantive advantages (Subramanian, Jones, & Dun-
can, 2003). Analysis of cluster trials (regardless of thelevel of randomization) either involving schools or
clinics or workplaces are good analogy to Oakes
alternative of neighborhood-based community trials;
and the relevance of multilevel methods to identify
causal cluster effectsbe it schools (De Vries et al.,
1994) or clinics (Bach et al., 1995) or workplaces
(Hedeker, McMahon, Jason, &Salina, 1994)are well
recognized (Donner, 1998). Indeed, an acknowledgment
of this would make any potential basis to discourage the
use of multilevel methods less compelling. The proposal
for community trials, therefore, is not only compatible
with multilevel methods, rather multilevel methods with
its ability to model treatment-based clustering and
treatment heterogeneity would arguably be the most
appropriate methodology to analyze community trial
data.
Moreover, randomized study designs are probably
best suited when we have a single exposure of interest.
While Oakes recognizes the limitations to community
trials paradigm, he is almost silent about certain
fundamental drawbacks (Sorensen, Emmons, Hunt, &
Johnston, 1998). For instance, often community-level
interventions are beset with contamination problems
(e.g., changing secular trends in background factors, or
a moving target in the control community, or theprocess of what and who defines communities and
neighborhoods). Conversely, with community-based
interventions, the more specific the intervention (e.g.,
building a playground to encourage exercise), the less
generalizable it is and the less it represents the
constellation of societal determinants that shape popu-
lation distribution of health, including its geographic
variability. Surely, it would not be a practicable social
epidemiology to design and test every potential com-
munity variable in this manner. For Oakes to state that
the observational evidence on neighborhood effects is
not trustworthy, but still suggest that we go ahead and
conduct randomized experiments across communities is
ethically questionable both from a research and from a
policy intervention perspective.
The core issue of Oakes essay is about the limits of
observational data designs as they relate to the
intellectual and practicable project of identifying causal
neighborhood effects. Crucially, the central tenets ofOakes essay, therefore, stand independent of the rather
exhaustive (and well-known) discussion of multilevel
methods and as such Oakes claim that no one appears
to haveconceptually developedthe multilevel model with
an eye on causal inference is incorrect (see among
othersJones, 1991;Duncan, Jones,&Moon, 1993, 1996;
Jones & Moon, 1993; Jones & Duncan, 1995, 1996;
Subramanian, Kawachi, & Kennedy, 2001; Subrama-
nian et al., 2003). While researchers may not have
specifically chosen to use the term causal, a reading of
these would reveal that the motivation for the metho-
dological exposition of multilevel models is indeed tounderstand the causal role of contexts. The appropriate
framework for Oakes to discuss the important issues
would have been a detailed background critique on the
limits of cross-sectional observational data-design-based
inferences. Notwithstanding this shortcoming, Oakes
identifies four obstacles to detecting causal neighbor-
hood effects. The remainder of this commentary
scrutinizes each of the claims and will argue that
there is nothing in these claims that would force us
to abandon a sensible application of multilevel statis-
tical techniques, especially for a practicable social
epidemiology.
The first obstacle, according to Oakes, is the
feasibility of identifying true neighborhoods differ-
ences. Applied multilevel research relies on partitioning
the individual-compositional effects while estimating
the true contextual differences between neighbor-
hoods. The notion of partitioning, however, contradicts
the foundational idea that people make places and
places make people; an idea germane to neighborhoods
and health, and much of social epidemiological,
research. Oakes argues that the process of social
stratification will generate complete confounding
between the background attributes of persons in a given
neighborhood and (approximately) complete separationbetween the background attributes of people in other
neighborhoods. Given this, in a perfectly specified
individual-compositional model (or selection model
to use Oakes phrase) the neighborhood differences
would move towards zero and as such eliminate the
possibility of explaining the neighborhood differences.
While social stratification complicates neighborhood
comparisons, the extent to which they confound the
comparisons is an interesting empirical question. More-
over, for this claim to hold, the process through which
people select neighborhoods would have to be comple-
telynon-random atalltimes. Indeed, if we believe this to
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1. Importantly, the structure weights the amount of time
that individual 25 spent in her current neighborhood
residence (20% between times 1 and 2) and 80% in her
previous neighborhood residence. Importantly, such a
repeated measure, multiple membership should allow
an estimation of changing neighborhood effects, con-trolling for the changing population composition and
thus offer some mileage in addressing the endogeneity in
neighborhood exposures. Other such creative modifica-
tions can be adopted for analyzing causal neighborhood
effects. The general issue of endogeneity has certain
unique implications for multilevel models and it is useful
to take cognizance of some of the methodological work
underway to address this challenge (Spencer, 2002). The
problem of endogeneity while by no means entirely
surmountable to everybodys satisfaction can none-
theless be addressed in some practicable manner within
a multilevel framework.
The third obstacle identified by Oakes is the issue of
extrapolation. Oakes suggestion that contexts (and
individuals living in them) are unique and hence not
comparable clearly cannot be a basis for invalidating the
method. Instead, the uniqueness of neighborhoods raises
empirical challenges for measuring these contexts and to
understand why they are different. Also, at issue is
preponderance of effect; if, in general, people in poor
areas have the worst health, then even though each poor
area may be unique in some way, there is still an over-
riding effect of impoverishment.
It is also worth underscoring that multilevel models
are not about modeling specific neighborhoods (asOakes describes) even though they do allow posterior
predictions for specific neighborhoods. Rather, the
neighborhood-specific differences are viewed as a ran-
dom sample of differences that are derived from a
population of neighborhoods that can be modeled as
a function (constant, linear, quadratic) of individual as
well as neighborhood exposures (Subramanian et al.,
2003). Quite clearly then, researchers need to consider
the assumption of exchangeability not simply in
relation to who lives in these neighborhoods, but more
importantly whether the sampled neighborhoods are
representative of the population of the neighborhoods
for which we wish to make inferences (Stoker& Bowers,
2002). It is of course critical that extrapolations and
predictions are not made outside the range of possible
predictor variables and to that extentallstatistical models
need to ensure that both individuals and neighborhoods
are drawn from a population to which we wish to makeinference and predictions and as such have exchange-
able properties with sufficient sample size.
The final obstacle of disequilibria, Oakes argues, is a
consequence of failing to recognize that a treatment
given to one person does not affect (the treatment given
to) another person. Such an assumption appears to be
fundamentally inconsistent with the very basis of
investigating a community effect, which assumes that
diseases and health outcomes are clustered in the
population (not just in the data sample). One can see
the partial relevance of this assumption in conditions
where the intervention involves moving (poor) in-
dividuals to (rich) neighborhoods and thereby chan-
ging the equilibrium of the recipient neighborhoods.
Even here, from a causal perspective our interest is in the
underlying association and it is hard to see how that
might change; while the rich neighborhood may no
longer be rich but that does not mean that the
underlying association between area deprivation and
health has changed. If we shift our focus to neighbor-
hood-level treatment (rather than moving individuals),
arguably, the Stable Unit Treatment Value Assumption
should hold. For instance, the health effects on residents
of one neighborhood to having a playground will not be
different depending on whether another neighborhooddoes or does not have a playground. Indeed, considering
the complex issues of proximity and access that may not
respect neighborhood boundaries raises challenges for
estimating valid neighborhood effects, in general. How-
ever, a fair discussion of this issue is contingent on
access to a host of details through which such
interventions are designed and without knowledge of
these conditions it is hard to comment on the relevance
of this issue for observational attempts to detect
neighborhood effects. Moreover, this issue does not
demonstrate anything that invalidates the multilevel
methodology.
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1 25
1
1 50
25
1 30
50
0.40.8
Level-1: Time
Level-2: Individuals
Level-3:Neighborhoods
0.60.2 0.6 0.4
21 21 21 21 2121
Fig. 1. Multilevel structure of repeated measurements of individuals over time across neighborhoods with individuals having multiple
membership to different neighborhoods across the time span.
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Challenges in multilevel analysis
The preceding commentary was not intended to
present an unconditional defense of multilevel models.
Indeed, echoing Harvey Goldstein, multilevel models
are not a panacea and like all statistical methods, need
to be used with care and understanding (Goldstein,2003). Given the complexity in the parameterization of
multilevel models, caution must be exhibited at both
design and analysis stage in the form of conceptual
justification and rigorous diagnostics, respectively.
Meanwhile, research on neighborhoods and health,
fueled by the relatively easy access to multilevel
modeling procedures, clearly risk making questionable
inferential leaps. Indeed, Oakes essay serves this general
purpose rather well. In the interest of raising the level of
awareness of multilevel applications in public health
research, I outline three critical issues for multilevel
analysis.The first relates to issues of multilevel designs and
structures. This relates to the issue of delimiting
neighborhood and identifying neighborhood boundaries
for empirical research (Sampson & Morenoff, 2002),
and importantly recognizing other multiple spatial and
non-spatial contexts within and around which neighbor-
hoods operate (Subramanian et al., 2003). Indeed,
current applications have failed to recognize this multi-
plicity of neighborhood contexts and as such do not go
beyond the two-level conceptualizations of individuals
at lower level hierarchically nested within neighbor-
hoods at a higher level. While it is now possible to
implement complex hierarchical as well as non-hier-
archical structures (Leyland & Goldstein, 2001) under
substantially realistic and sophisticated assumptions
(Browne, 2002), there is a need to develop clearer
methodological and applied understanding on combin-
ing multilevel data designs (e.g., multivariate, repeated
measures and cross-classified with multiple member-
ships) and thus reducing the knowledge gap between
statistical advances and applied quantitative research.
An immediate concern, meanwhile, for interpreting
the multilevel structures is the identification of appro-
priate levels (such as households, or other larger macro-
levels within which neighborhoods operate) or conver-sely, the implication of missing levels. Identifying true
neighborhood differences also requires identifying
true neighborhoods; an aspect on which much of
the applied work, including Oakes essay, is entirely
silent.
The second relates tomultilevel model specificationfor
making causal inferences. The flexibility to specify and
estimate complex parameters also means that multilevel
models, by definition, are highly conditional and
sensitive to model specification. Much of the existing
application of multilevel research continues to focus
largely on the fixed parameters; stated differently, the
average effects of a particular exposure (be it individual
or neighborhood) on the individual outcome. However,
in multilevel models the same fixed part of the statistical
model can be estimated under a range of random part
specifications (Subramanian et al., 2003). Consequently,
a clear understanding and justification for specifying the
within-neighborhood (level 1) and the between-neighborhood (level 2) model, especially in the random
part, is completely lacking in the current applications.
Specifically, this relates to the variancecovariance
structures that can be specified at each of the desired
level. While the notion of complex variance structures is
recognized, the assumption of homoskedastic variances
continues to prevail (at levels 1 and 2) and this has
critical implications in terms of making inferences about
neighborhood differences as well as about average
predictive role of exposures. In addition, of course,
there is also the issue of specifying the explanatory
(substantive) within-neighborhood or the individual-level model in the fixed part of the multilevel statistical
model. Typically, the tendency is to over-specify or
exhaustively control the individual model in order to
either ensure a perfect specification of the within-
neighborhood model (Oakes, 2003) or to be conservative
and cautious while estimating neighborhood differences.
Either way, there are substantive issues that relate to
model specifications, especially so in multilevel models.
One general framework would be to conduct sensitivity
analysis to ascertain the extent to which findings are
robust to alternate model specifications.
Finally, there are critical issues to interpreting multi-
level coefficients. Researchers rarely report or discuss
any diagnostic testing of the models fitted. While
diagnostic procedures are being implemented and
methodological work in this area is underway (Langford
& Lewis, 1998), applications of these methods need to
routinely report and discuss the extent to which different
models satisfy the statistical assumptions underlying
these models. Specifically, for multilevel neighborhoods
research, these could include: testing for the assumptions
of normality for random coefficients at higher and lower
levels; and testing of the assumptions related to
independence of residuals at different levels and of the
random part to the fixed part. A related concern whileinterpreting multilevel neighborhood studies is the issue
of power (Snijders& Bosker, 1993; Snijders, 2001). For
instance, how many neighborhoods and individuals
within neighborhoods do we need in order to model
the average effects of a neighborhood exposure that is
hypothesized to have a differential effect on the outcome
depending upon individual SES. Or, how many neigh-
borhoods are required to estimate the differential effect
of individual SES that is seen to vary across neighbor-
hoods. Such questions, and others, compel researchers
to consider power issues while designing, modeling and
interpreting multilevel coefficients.
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Concluding remarks
The clear strength of multilevel models for a causal
analysis of neighborhood effects lies in its ability to
model complex heterogeneities such that individual as
well as neighborhood exposures are not simply con-
ceptualized in terms of their average effect but rather interms of their true population heterogeneity. Modeling
heterogeneity is not only more realistic, and therefore a
better basis for a practicable social epidemiology, but
also provides important feedback loop to reframe our
questions related to average causal effects. Indeed, as
mentioned at the outset, the issue of validating causal
effects are essentially one of subject matter and less so of
the statistical methods employed.
The aim of this commentary was to balance Oakes
pessimism with a message that realistically complex
multilevel models (Best, Spiegelhalter, Thomas, &
Brayne, 1996) are crucial to not only answering theoriginal research questions but also to motivate new
causal questions, the empirical answers to which are less
well understood. While multilevel applications on
observational data-sets must be grounded in substantive
theories with careful consideration of what to measure,
specify and how to be critical of findings, it is clear that
the multilevel modeling approach can bring extra
predictive power, description and precision to our
efforts to understand causal neighborhood effects. We
have little evidence, as yet, to believe otherwise.
Acknowledgements
I am grateful to Harvey Goldstein and William
Browne for their insights on issues related to modeling
and interpreting higher-level variances. I thank Kim
Lochner, Stephen Gilman, Maria Glymour and Nancy
Krieger for their helpful comments on an earlier version
of this commentary.
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