Modeling when people quit: Bayesian censored geometric models with hierarchical and latent-mixture extensions

People often interact with environments that can provide only a finite number of items as resources. Eventually a book contains no more chapters, there are no more albums available from a band, and every Pokémon has been caught. When interacting with these sorts of environments, people either actively choose to quit collecting new items, or they are forced to quit when the items are exhausted. Modeling the distribution of how many items people collect before they quit involves untangling these two possibilities, We propose that censored geometric models are a useful basic technique for modeling the quitting distribution, and, show how, by implementing these models in a hierarchical and latent-mixture framework through Bayesian methods, they can be extended to capture the additional features of specific situations. We demonstrate this approach by developing and testing a series of models in two case studies involving real-world data. One case study deals with people choosing jokes from a recommender system, and the other deals with people completing items in a personality survey.