ABSTRACT
This chapter refers to as the canonical psychometric model, an abstraction of the popular psychometric models. It introduces a distinction among different kinds of DAGs. Bayesian approaches are not the dominant paradigm in psychometric modelling, they have become widely used in certain applications, including some where there is apparent unanimous consent as to their propriety and advantages. The importance of structuring psychometric models via conditional independence relationships has long been recognized for its computational benefits. The psychometric or measurement model is the junction between the observable variables and the latent variables of inferential interest. If measurement model parameters are unknown, our probability model expands to accommodate them, specifying prior distributions for them, again often capitalizing on exchangeability assumptions. Conventional practices in various psychometric modeling paradigms vary in the extent to which Bayesian approaches are employed. Commonly, they depart from the fully Bayesian perspective by estimating parameters in stages, often treating point estimates from earlier stages.
