Multivariate hierarchical linear modeling in randomized field experiments

The hierarchical linear model (HLM) is now commonly accepted as a useful modeling approach for multilevel data resulting from randomized field experiments. When multiple outcomes of interest exist, a multivariate extension of the conventional univariate HLM offers advantages over the usual application of separate HLM analyses for each of the outcomes. In this article, the authors review these advantages, discuss the device that allows the univariate HLM procedure to model multiple outcomes, and present a series of multivariate models that would be useful in addressing typical questions in field experiments. In addition to the multivariate multilevel versions of basic analysis of variance (ANOVA) or analysis of covariance (ANCOVA) designs, the authors present more complex models that allow the testing of moderation and mediation of the treatment effect. The various analyses are illustrated with computer generated data for a hypothetical scenario.