Understanding beliefs, values, and preferences of patients is a tenet of contemporary health sciences. This application was motivated by the analysis of multiple partially ordered set (poset) responses from an inventory on layman beliefs about diabetes. The partially ordered set arises because of two features in the data-first, the response options contain a Don't Know (DK) option, and second, there were two consecutive occasions of measurement. As predicted by the common sense model of illness, beliefs about diabetes were not necessarily stable across the two measurement occasions. Instead of analyzing the two occasions separately, we studied the joint responses across the occasions as a poset response. Few analytic methods exist for data structures other than ordered or nominal categories. Poset responses are routinely collapsed and then analyzed as either rank ordered or nominal data, leading to the loss of nuanced information that might be present within poset categories. In this paper we developed a general class of item response models for analyzing the poset data collected from the Common Sense Model of Diabetes Inventory. The inferential object of interest is the latent trait that indicates congruence of belief with the biomedical model. To apply an item response model to the poset diabetes inventory, we proved that a simple coding algorithm circumvents the requirement of writing new codes such that standard IRT software could be directly used for the purpose of item estimation and individual scoring. Simulation experiments were used to examine parameter recovery for the proposed poset model.