Modeling ordinal data through bayesian sem

Abstract

Structural equation modeling (SEM) is a flexible statistical technique used to model complex relationships between a set of observable and unobservable variables, where each variable may be either dependent or independent. A SEM consists of a measurement model, catering for the relationships between the observable and latent variables, and a structural model, a simultaneous equation indicating how the latent variables in the model are related to each other. Once an appropriately identified SEM has been specified, the step to follow is that of estimating the unknown parameters in the model. As an estimation technique, the Bayesian approach has become increasingly popular in the field of SEM particularly when dealing with small samples. On using this approach, the unknown model parameters are estimated through the technique of data augmentation and the Markov Chain Monte Carlo (MCMC) methods. Once estimates are obtained, the goodness-of-fit of the model is assessed through the posterior predictive p-value, a Bayesian alternative to the classical p-value. The Bayesian SEM strategy will be applied to examine the relationship between a set of observable and latent variables in a dataset related to invasion of privacy, risk taking and security concerns of a person when using the internet.