Multilevel Structural Equation Modeling

Anders Skrondal, London School of Economics

Sophia Rabe Hesketh, University of California

Structural equation models (SEMs) extend conventional regression models to allow for (1) latent variables measured with error and (2) structural relations or paths between variables. In multilevel SEM latent variables are allowed to vary at different hierarchical levels. Conventional multilevel SEM partitions the covariance matrix of level-1 variables into between and within components and specifies separate models for each level. Two limitations of this approach are that no cross-level effects of latent variables are permitted and that latent variables can only be measured by variables at level-1. We describe a modelling framework which overcomes these limitations and accommodates a wide range of response types.

Books
Rabe-Hesketh, S. and Skrondal, A. (2005). Multilevel and Longitudinal Modeling using Stata http://www.stata.com/bookstore/mlmus.html . College Station, TX: Stata Press.

General Information

http://www.gllamm.org

Hierarchical models for combining multiple data sources measured at individual and small area levels

Nicky Best and Christopher Jackson, Imperial College

Administrative data from censuses and registers can be used to study area-level variations in health, but individual-level inference can be subject to ecological bias or confounding. Conversely, survey or cohort data on small samples of individuals can be used for direct individual-level inference, but have low power to study area-level variations. By combining administrative and survey data under suitable hierarchical models, each data source can borrow strength from the other. These principles will be illustrated with a study of traffic-related air pollution and low birth weight.

Latent categorical effects in multilevel models

Jon Rasbash and Kelvyn Jones, University of  Bristol

Often in multilevel models the assumption of continuous Normally distributed random effects is unreasonable and between unit variation is better modelled by a set of latent categories, possibly allowing further latent group specific between unit variances. For example we wish to model repeated measures data with continuous Normal random effects at the occasion level and set of M latent groups at the person level, where each latent group has a group specific growth curve(or trajectory). We can also model within group between person variability using Normal random effects. Applications of these models will be discussed and generalisations to more complex population structures (in terms of further crossed and nested classifications) will be covered.

4.15 - 5.00

General Discussion