Analysis of clustered data in community psychology: With an example from a worksite smoking cessation project

Abstract

Although it is common in community psychology research to have data at both the community, or cluster, and individual level, the analysis of such clustered data often presents difficulties for many researchers. Since the individuals within the cluster cannot be assumed to be independent, the use of many traditional statistical techniques that assumes independence of observations is problematic. Further, there is often interest in assessing the degree of dependence in the data resulting from the clustering of individuals within communities. In this paper, a random-effects regression model is described for analysis of clustered data. Unlike ordinary regression analysis of clustered data, random-effects regression models do not assume that each observation is independent, but do assume data within clusters are dependent to some degree. The degree of this dependency is estimated along with estimates of the usual model parameters, thus adjusting these effects for the dependency resulting from the clustering of the data. Models are described for both continuous and dichotomous outcome variables, and available statistical software for these models is discussed. An analysis of a data set where individuals are clustered within firms is used to illustrate features of random-effects regression analysis, relative to both individual-level analysis which ignores the clustering of the data, and cluster-level analysis which aggregates the individual data.

Fidelity Criteria: Development, Measurement, and Validation

“…Researchers have seen this as a problem when relating fidelity scores to outcomes, because a large number of programs had to be studied, in order to achieve the necessary power (Clarke, 1998). Newer multilevel or hierarchical approaches (cf., Hedeker et al, 1994;Raudenbush & Bryk, 2001) afford much greater flexibility, allowing analysis of relationships between program-level variables and characteristics of the individual participants that are nested within each program (e.g., individual-level outcomes or participants' reports about program operations). These methods appropriately model the dependencies inherent in data from participants in the same program while maximizing statistical power to identify cross-level relationships.…”

Statistical and Substantive Inferences in Public Health: Issues in the Application of Multilevel Models

“…These trials are experiments in which randomization is implemented at the group level, but outcome variables are measured at the individual level. Numerous cluster-randomized trials have been conducted in public health, with randomization of cities (12,13,45,47,56,74), housing developments (139), schools (63,89,157), classrooms (136), and worksites (54,64,69). The natural question that arises in such studies is, Did the intervention make a difference?…”

Multilevel Analysis in Public Health Research

“…The groups or contexts investigated using multilevel analysis have included countries, states, regions, neighborhoods or communities, schools, families, workplaces, and health care providers (see for example 24,25,29,32,43,87,92,100 (31,43), and the study of addictions (98,100). Multilevel models have also been used increasingly in the investigation of the social determinants of health.…”

“…Thus the two assumptions of standard regression (independence and equal variance) are violated, and special estimation methods must be used. The parameters of the above equations (fixed effects, random group effects, variances of the random effects, and residual variance) are simultaneously estimated using iterative methods (4,36,43,56). Multilevel models allow investigation of a variety of interrelated research questions.…”