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

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.

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.

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.

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.