We found it more informative to use a geostatistical rather
than a lattice formulation (45) of the spatial correlation
structure (34): defining the correlation between neighborhoods
as a decreasing function of the spatial distance between
them enabled us to estimate the spatial range of
correlation (34).
First, the hierarchical geostatistical model is of heuristic
interest. Since many contextual factors have a strong spatial
structure, disentangling spatially structured variability from
other more chaotic sources of neighborhood variation may
allow researchers to generate hypotheses on contextual
mechanisms (35). Following recommendations in the literature
(46), we compared the spatially structured variations
in mental health (figure 4) with the geographic distribution
of neighborhood income (figure 1) to gain preliminary insight
into the association between deprivation and mental
disorders.
Second, rather than being a nuisance parameter, the parameter
/ for correlation decay allowed us to make inferences
about the scale of spatial variations, showing that
variations in substance-related disorders occurred on a larger
scale than that of the neighborhood. As a public health
implication, coordinating interventions between administrative
neighborhoods close to each other may be an effective
strategy. If recent developments in local regression techniques
are used (47), one possible analytical refinement
may consist of moving from a global to a local perspective
in which the spatial autocorrelation parameter could vary
over space.
Measuring contextual factors across continuous space
around residences of individuals
In many instances, relying on administrative boundaries
to define contextual factors may be restrictive. We found
a much stronger relation between contextual deprivation
and prevalence of disorders when we measured the factor
in local areas of smaller size than administrative neighborhoods.
Therefore, this association may operate on a more
local scale than the neighborhood scale commonly used in
contextual studies.
Contextual income was measured within spatially adaptive
areas, that is, circles of variable width and fixed population
size centered on residences of individuals. Using
these areas appeared to be the only way to investigate
whether contextual deprivation operated on a local scale,
since measuring contextual income within areas having
a small, fixed radius results in missing values or unreliable
measurements in sparsely populated areas (39, 40). Theoretically,
this approach that considers surrounding population
rather than surrounding space may be particularly
appropriate when considering contextual factors aggregating
individual characteristics (e.g., income) rather than features
of the physical environment.
In our cross-sectional study, causal mechanisms for the
association between contextual deprivation and substancerelated
disorders may operate in both directions. On the one
hand, although not yet definitely confirmed by quantitative
studies, selective migration processes may contribute to the
clustering of substance-related disorders in the mostdeprived
neighborhoods (15). On the other, deprivation
may have an independent negative impact on mental wellbeing
(14). Despite such uncertainty, an issue that has yet to
be addressed in a longitudinal study, our findings show that
interventions focused on individuals with substance-related
disorders may be particularly useful in hot spots of contextual
deprivation identified on a smaller scale than that of
administrative neighborhoods.
In conclusion, beyond important geographic variations in
the prevalence of substance-related disorders, our spatial
analytical perspective showed that the spatial scale of variations
was much larger than that of administrative neighborhoods.
However, apart from such large-scale variations
due to the clustering of poor socioeconomic circumstances
in northern Malmo¨, we also found more local variations in
prevalence that were attributable to differences in the intensity
of deprivation.
We are aware that multilevel models may be appropriate
when the context is defined in a way that is not strictly