Coupled Hidden Markov models for Categorization

One intuition in the categorization literature is that how we assign a stimulus to a given category depends on the assignment of other stimuli that we have encountered in the past. In other words, it is assumed that stimulus–stimulus interactions can affect categorization decisions. Nevertheless, categorization models typically avoid modeling this feature by either considering the “true” category assignment for the stimulus, for a fixed experimental design, or by taking some function of a participants’ previous responses. A consequence of these assumptions is that learning about the associations between a specific stimulus and the categories can only occur on trials when that stimulus is presented. Coupled Hidden Markov models (CHMM) allow stimulus-stimulus interactions in categorization to be modeled directly, so that association to categories are continuously updated The key idea under this approach is that the category (state) that a given stimulus (chain) is assigned to on a trial is a function of its assignment on the previous trial and the category that all other stimuli are inferred to be in. In other words, category assignments are updated continuously by a latent process based on participants’ trial-by-trial choices. We present a Bayesian implementation of a CHMM on two classic categorization tasks: Lewandowsky’s (2011) replication of the Shepard et al. (1961) Type VI category structures, and the extension of this task to ternary stimuli presented by Lee and Navarro (2002). We show that the CHHM model allows us to obtain posterior inferences about the category assignment (state) of each stimulus at every trial in the experiment.