Extending multinomial processing tree models to measure the relative speed of cognitive processes.

Multinomial processing tree (MPT) models account for observed categorical responses by assuming a finite number of underlying cognitive processes. We propose a general method that allows for the inclusion of response times (RTs) into any kind of MPT model to measure the relative speed of the hypothesized processes. The approach relies on the fundamental assumption that observed RT distributions emerge as mixtures of latent RT distributions that correspond to different underlying processing paths. To avoid auxiliary assumptions about the shape of these latent RT distributions, we account for RTs in a distribution-free way by splitting each observed category into several bins from fast to slow responses, separately for each individual. Given these data, latent RT distributions are parameterized by probability parameters for these RT bins, and an extended MPT model is obtained. Hence, all of the statistical results and software available for MPT models can easily be used to fit, test, and compare RT-extended MPT models. We demonstrate the proposed method by applying it to the two-high-threshold model of recognition memory.