Latent variable models for partially ordered responses and trajectory analysis of anger-related feelings

A general framework is presented for the analysis of partially ordered set (poset) data. The work is motivated by the need to analyse poset data such as multi-componential responses in psychological measurement and partially accomplished cognitive tasks in educational measurement. It is shown how the generalized loglinear model can be used to represent poset data that form a lattice and how latent-variable models can be constructed by further specifying the canonical parameters of the loglinear representation. The approach generalizes a class of latent-variable models for completely ordered data. We apply the methods to analyse data on the frequency and intensity of anger-related feelings. Furthermore, we propose a trajectory analysis to gain insight into the response function of partially ordered emotional states.