Application of hierarchical linear models to assessing change.

Developments over the past 10 years in the statistical theory of hierarchical linear models (HLMs) now enable an integrated approach for (a) studying the structure of individual growth and estimating important statistical and psychometric properties of collections of growth trajectories; (b) discovering correlates of change factors that influence the rate at which individuals develop; and (c) testing hypotheses about the effects of on or more experimental or quasi-experimental treatments on growth curves. The approach is based on a two-stage hierarchical model. An example based on Head Start data illustrated key analytic uses of HLMs; (a) describing the structure of the mean growth trajectory; (b) estimating the extent and character of individual variation around mean growth; (c) assessing the reliability of measures for studying both status and change; (d) estimating the correlation between subjects entry status and rates of growth; (e) estimating correlates of both status and change; (f) assessing the adequacy of between-subjects models by estimating reduction in unexplained parameter variance (reduction in uncertainty about the individual growth parameters as distinguished from errors in their estimation); and (g) predicting future individual growth. HLMs can be applied in experimental and quasi-experimental settings. The HLM approach requires multi-time point data. The special strengths of HLMs in individual prediction are remarkable. The study of growth curves using HLMs requires special care to distributional assumptions covariance assumptions and the metric of measurement. HLMs seem broadly applicable to the study of change and are likely to extend substantially the empirical research on change. To the extent that HLMs enrich the class of testable hypotheses about the structure of growth it may also encourage a broadened discussion about the nature of change itself.