Many small groups

Abstract

Hierarchical data from many small clusters arise by necessity and by design. They arise by necessity when the aim is to study married couples [1], identical twins [25], siblings [12], paired comparison tasks [2], cooperative learning groups [36], multiple informants of child social behavior [20], and studies of animal reproduction [35]. They arise by design in cross-sectional studies: cluster randomized trials [11, 18], multisite randomized trials [3, 6], and surveys that sample a small number of persons in each of many neighborhoods [14] or a small number of teachers in each of many schools [17]. In repeated measures studies, it is common to encounter small numbers of observations for each of many persons in short time-series designs, such as studies of student learning based on annual assessments [37], the extreme case being a pre-post design. In my experience teaching methods for multilevel data, students and other workshop participants have often expressed dismay that their data involve many clusters but few cluster members. However, there are often good reasons for such design choices. If the primary aim of a study is to estimate fixed regression coefficients (as opposed to variance components or realizations of random effects), a design that minimizes cluster size, n, and maximizes the number of clusters, J, may be optimal (cf. Chapter 4 in this volume; also [7, 26, 30, 38]). Optimal n per cluster depends on the cost of sampling at each level, the magnitude of variation at each level, and research question at hand. Choosing a small n is wise when little variability exists within clusters or when it is comparatively expensive to assess each individual within a cluster (relative to the cost of sampling clusters). Yet, under certain conditions, the small n, large J scenario can pose challenges to valid statistical inference and can create demanding computational tasks as well as problems of statistical precision. The problems are likely to be less challenging in the case of linear models with normal random effects at each level and more challenging when non-linear link functions and nonnormal data are involved. These problems are likely to be less challenging when the aim is to estimate fixed regression coefficients, and more challenging when the aim is to draw inferences about random regression coefficients (e.g., cluster-specific intercepts and slopes) or to estimate variance and covariance components at the second level of the hierarchy. I provide a brief overview of each scenario before considering each in more detail. © 2008 Springer Science+Business Media, LLC.