Efficient Bayesian marginal likelihood estimation in generalised linear latent trait models

Abstract

The term latent variable model (LVM) refers to a broad family of models which are used tocapture abstract concepts (unobserved / latent variables or factors) by means of multipleindicators (observed variables or items). The key idea is that all dependencies among pobserved variables are attributed to k unobserved ones, where k << p. That is, the LVMmethodology is a multivariate analysis technique which aims to reduce the dimensionality,with as little loss of information as possible. Most importantly, the LVMs accountfor constructs that are not directly measurable, as for instance individuals’ emotions,traits, attitudes and perceptions. In the current thesis, the LVMs are studied within theBayesian paradigm, where model evaluation is conducted on the basis of posterior modelprobabilities. A key role in this comparison is played by the models’ marginal likelihood,which is often a high dimensional integral, not available in closed form. The propertiesof the LVMs are implemented here in order to efficiently approximate the marginallikelihood.