Hierarchical Hidden Markov Models for Response Time Data

Abstract

Psychological data, particularly measurements obtained sequentially in experiments designed to test theories of human cognition, are often treated as independent and identically distributed samples from a single distribution that describes the cognitive process. This assumption is made for mathematical and analytic convenience; it is widely appreciated that such data are in fact mixtures from two or more processes, only a subset of which are associated with the cognitive process of interest. Our modeling framework describes response times (RTs) as arising from a mixture of three distinct distributions. Transitions across the distributions are governed by a hidden Markov structure whose states produce either fast, average, or slow RTs. This process is nested within a second hidden Markov structure, producing an “environment” process that allows the distribution of the response modes to evolve due to both internal factors (such as fatigue and distractions) and external factors (such as changing task demands). We performed a detection experiment designed to elicit responses under three environments that mimic external conditions that influence latent response modes. We present our hierarchical model and demonstrate its fit on the experimental data. We also demonstrate the model’s fit in the case when external conditions were not manipulated as part of the experimental process.