Clarifying the use of aggregated exposures in multilevel models: self-included vs. self-excluded measures. 2012

Etsuji Suzuki, and Eiji Yamamoto, and Soshi Takao, and Ichiro Kawachi, and S V Subramanian
Department of Epidemiology, Okayama University Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama, Japan. etsuji-s@cc.okayama-u.ac.jp

BACKGROUND Multilevel analyses are ideally suited to assess the effects of ecological (higher level) and individual (lower level) exposure variables simultaneously. In applying such analyses to measures of ecologies in epidemiological studies, individual variables are usually aggregated into the higher level unit. Typically, the aggregated measure includes responses of every individual belonging to that group (i.e. it constitutes a self-included measure). More recently, researchers have developed an aggregate measure which excludes the response of the individual to whom the aggregate measure is linked (i.e. a self-excluded measure). In this study, we clarify the substantive and technical properties of these two measures when they are used as exposures in multilevel models. METHODS Although the differences between the two aggregated measures are mathematically subtle, distinguishing between them is important in terms of the specific scientific questions to be addressed. We then show how these measures can be used in two distinct types of multilevel models-self-included model and self-excluded model-and interpret the parameters in each model by imposing hypothetical interventions. The concept is tested on empirical data of workplace social capital and employees' systolic blood pressure. RESULTS Researchers assume group-level interventions when using a self-included model, and individual-level interventions when using a self-excluded model. Analytical re-parameterizations of these two models highlight their differences in parameter interpretation. Cluster-mean centered self-included models enable researchers to decompose the collective effect into its within- and between-group components. The benefit of cluster-mean centering procedure is further discussed in terms of hypothetical interventions. CONCLUSIONS When investigating the potential roles of aggregated variables, researchers should carefully explore which type of model-self-included or self-excluded-is suitable for a given situation, particularly when group sizes are relatively small.

UI MeSH Term Description Entries
D007564 Japan A country in eastern Asia, island chain between the North Pacific Ocean and the Sea of Japan, east of the Korean Peninsula. The capital is Tokyo. Bonin Islands
D008297 Male Males
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D001794 Blood Pressure PRESSURE of the BLOOD on the ARTERIES and other BLOOD VESSELS. Systolic Pressure,Diastolic Pressure,Pulse Pressure,Pressure, Blood,Pressure, Diastolic,Pressure, Pulse,Pressure, Systolic,Pressures, Systolic
D005260 Female Females
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D013599 Systole Period of contraction of the HEART, especially of the HEART VENTRICLES. Systolic Time Interval,Interval, Systolic Time,Intervals, Systolic Time,Systoles,Systolic Time Intervals,Time Interval, Systolic,Time Intervals, Systolic
D016000 Cluster Analysis A set of statistical methods used to group variables or observations into strongly inter-related subgroups. In epidemiology, it may be used to analyze a closely grouped series of events or cases of disease or other health-related phenomenon with well-defined distribution patterns in relation to time or place or both. Clustering,Analyses, Cluster,Analysis, Cluster,Cluster Analyses,Clusterings
D017132 Workplace Place or physical location of work or employment. Job Site,Work Location,Work Place,Work-Site,Worksite,Job Sites,Location, Work,Work Locations,Work Places,Work Site,Work-Sites,Workplaces,Worksites
D055361 Multilevel Analysis The statistical manipulation of hierarchically and non-hierarchically nested data. It includes clustered data, such as a sample of subjects within a group of schools. Prevalent in the social, behavioral sciences, and biomedical sciences, both linear and nonlinear regression models are applied. Analyses, Multilevel,Analysis, Multilevel,Multilevel Analyses

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