An introduction to Bayesian structural equation modelling

Bayesian statistical modelling is on a sharp rise in the social science. Its philosophical basis rests on estimating the probability of parameter estimates given data, rather than the probability of data given a model (referred to as null-hypothesis statistical testing, NHST).

It is a very feasible technique for situations in which (1) large-sample assumptions for Maximum Likelihood do not hold, (2) models are complex resulting in misbehaved parameters (e.g., Heywood cases, negative residuals, correlations > 1), or (3) the data-structure is complex (e.g., cross-classified data structure, or dynamic time-lagged). Bayesian techniques have been implemented in a range of freeware (e.g., R) and commercial software (e.g., SPSS, Mplus). I will provide a gentle introduction to the modelling logic and examples of Bayesian structural equation models (BSEM), from our on-going research.