Bayesian Hierarchical Finite Mixture Models of Reading Times: A Case Study

Abstract

This theoretical note presents a case study demonstrating the importance of Bayesian hierarchical mixture models as a modelling tool for evaluating the predictions of competing theories of cognitive processes. This note also contributes to improving current practices in data analysis in the psychological sciences. As a case study, we revisit two published data sets from psycholinguistics. In sentence comprehension, it is widely assumed that the distance between linguistic co-dependents affects the latency of dependency resolution: the longer the distance, the longer the time taken to complete the dependency (e.g., Gibson 2000). An alternative theory, direct access (McElree, 2000), assumes that retrieval times are a mixture of two distributions (Nicenboim & Vasishth, 2017): one distribution represents successful retrievals and the other represents an initial failure to retrieve the correct dependent, followed by a reanalysis (McElree, 1993) that leads to successful retrieval. Here, dependency distance has the effect that in long-distance conditions the proportion of reanalyses is higher (due to similarity-based interference). We implement both theories as Bayesian hierarchical models and show that the direct-access model fits the Chinese relative clause reading time data better than the dependency-distance account. This work makes several novel contributions. First, we demonstrate how the researcher can reason about the underlying generative process of their data, thereby expressing the underlying cognitive process as a statistical model. Second, we show how models that have been developed in an exploratory manner to represent different underlying generative processes can be compared in terms of their predictive performance, using both K-fold cross validation on existing data, and using completely new data. Finally, we show how the models can be evaluated using simulated data; this is a method that is standardly used in Bayesian statistics, but remains unutilized in data analysis within the psychological sciences.