Multilevel regression models are now well established and widely applied in analyses of hierarchical data – typically to account for variation in only one univariate response variable at level 1. However, many substantive research questions call for more complex models. For the analyses of hierarchical data with multivariate outcomes, multilevel mean and covariance structure modelling in the structural equation modelling framework offers great flexibility and modelling opportunities. This paper describes the basic concepts of two-level mean and covariance structure analysis of hierarchical data, and showcases application examples. The paper focuses on fitting possible models requiring multilevel applications and highlight: (a) the statistical modelling opportunities afforded by latent variable modelling, and (b) the utility of the structural equation modelling framework. The models discussed include: multilevel path models; multilevel factor models with multiple-group comparisons; latent growth curve models with multiple processes; and mediational models. The examples are based on analyses of hierarchical educational and psychosocial data. The statistical modelling methodology will be discussed in terms of implications for both research and practice.
Available at: http://works.bepress.com/siek_toon_khoo/32/