Modeling contextual effects using individual-level data and without aggregation: an illustration of multilevel factor analysis (MLFA) with collective efficacy

Population health scientists increasingly study how contextual-level attributes affect individual health. A major challenge in this domain relates to measurement, i.e., how best to measure and create variables that capture characteristics of individuals and their embedded contexts. This paper presents an illustration of multilevel factor analysis (MLFA), an analytic method that enables researchers to model contextual effects using individual-level data without using derived variables. MLFA uses the shared variance in sets of observed items among individuals within the same context to estimate a measurement model for latent constructs; it does this by decomposing the total sample variance-covariance matrix into within-group (e.g., individual-level) and between-group (e.g., contextual-level) matrices and simultaneously modeling distinct latent factor structures at each level. We illustrate the MLFA method using items capturing collective efficacy, which were self-reported by 2,599 adults in 65 census tracts from the Los Angeles Family and Neighborhood Survey (LAFANS). MLFA identified two latent factors at the individual level and one factor at the neighborhood level. Indicators of collective efficacy performed differently at each level. The ability of MLFA to identify different latent factor structures at each level underscores the utility of this analytic tool to model and identify attributes of contexts relevant to health. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12963-015-0045-1) contains supplementary material, which is available to authorized users.