Latent Class Models (LCMs) are used to cluster multivariate categorical data, commonly used to interpret survey responses. We propose a novel Bayesian model called the Equivalence Set Restricted Latent Class Model (ESRLCM). This model identifies clusters who have common item response probabilities, and does so more generically than traditional restricted latent attribute models. We verify the identifiability of ESRLCMs, and demonstrate the effectiveness in both simulations and real-world applications.

Merging beliefs requires the plausibility of the sources of the information to be merged. They are typically assumed equally reliable when nothing suggests otherwise. A recent line of research has spun from the idea of deriving this information from the revision process itself. In particular, the history of previous revisions and previous merging examples provide information for performing subsequent merging operations. Yet, no examples or previous revisions may be available. In spite of the apparent lack of information, something can still be inferred by a try-and-check approach: a relative reliability ordering is assumed, the sources are integrated according to it and the result is compared with the original information. The final check may contradict the original ordering, like when the result of merging implies the negation of a formula coming from a source initially assumed reliable, or it implies a formula coming from a source assumed unreliable. In such cases, the reliability ordering assumed in the first place can be excluded from consideration. Such a scenario is proved real under the classifications of source reliability and definitions of belief integration considered in this article: sources divided in two, three or multiple reliability classes; integration is mostly by maximal consistent subsets but also weighted distance is considered.

Merging beliefs requires the plausibility of the sources of the information to be merged. They are typically assumed equally reliable in lack of hints indicating otherwise; yet, a recent line of research spun from the idea of deriving this information from the revision process itself. In particular, the history of previous revisions and previous merging examples provide information for performing subsequent mergings. Yet, no examples or previous revisions may be available. In spite of the apparent lack of information, something can still be inferred by a try-and-check approach: a relative reliability ordering is assumed, the merging process is performed based on it, and the result is compared with the original information. The outcome of this check may be incoherent with the initial assumption, like when a completely reliable source is rejected some of the information it provided. In such cases, the reliability ordering assumed in the first place can be excluded from consideration. The first theorem of this article proves that such a scenario is indeed possible. Other results are obtained under various definition of reliability and merging.