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As the data had individual and aggregate level variables, we used random effect multi-level generalised linear models to identify the influence of these variables on ACSCs [ 47].
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Although this alternative method of scale construction makes it difficult to compare the results with previous studies, the approach is preferable to the conventional method of aggregating individual level variables.
An aggregate level socioeconomic status (SES) variable was derived from 2000 census data as previously described [ 19].
This treatment abstracts radically from the details of the causal processes involving particular individual molecules and instead focuses on identifying higher level variables that aggregate over many individual causal processes and that figure in general patterns that govern the behavior of the gas.
Group level variables considered were aggregate income, education, income inequality, and unemployment.
No significant changes were observed due to oversampling in the main variables at the aggregate level.
To compensate, it is possible to link Census variables at an aggregate level to the administrative data.
Fourth, because this study was based on aggregate data, it should be noted that an association among variables at an aggregate level does not necessarily mean that the association exists at the individual level[ 38].
Secondly, all ecological studies have a potential limitation of ecological fallacy, which is an association observed between the study variables on an aggregate level, not necessarily representing the association that exists at an individual level.
If, however, there is significant heterogeneity in the areas used, then the aggregate measures can result in ecological fallacy when an association observed between variables at an aggregate level does not represent the association that exists at an individual level[ 7].
The last of these was the only variable measured at aggregate level and was derived by linking patient postal codes to the 2007 Lower Super Output Area Index of Multiple Deprivation 26 (higher quintiles represent greater socio-economic deprivation).
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