Bayesian factor and structural equation models, issues in identification and estimation
Keynote address by Peter Congdon, Department of Geography and Centre for Statistics, Queen Mary College, University of London, UK.
Chair: Tim Croudace, Wednesday 22nd July, 8.45 - 9.45, Palmeston Lecture Theatre, Fisher Building.
This presentation considers some questions concerning Bayesian estimation of models involving continuous latent variables, and presents illustrative applications in health statistics. Bayesian estimation of factor and structural equation models via MCMC repeated sampling from the posterior p(q|y) offers potential for extended inference as compared to “classical” approaches based on multivariate normality. These include the ease of deriving inferences for model related functions of parameters that are problematic in classical approaches. Specification and fitting of correlated factor structures (e.g. spatially correlated factor scores when the units of observation are areas) is also straightforward. However, distinct problems occur such as ensuring consistent labelling of factors during repeated MCMC sampling and also derivation of Bayesian model fit criteria for the larger sample sizes typical of survey applications.
Two applications of Bayesian SEM are considered which exemplify the benefits, possible drawbacks and the extra constraints that a realistic Bayesian analysis may involve. The first is an analysis of the impact of social capital (a latent variable) on psychiatric caseness using data from the 2006 Health Survey for