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. Many substantive psychological theories assume that observed behavior results from one or more latent cognitive processes. Because these hypothesized processes can often not be observed directly, measurement models are important tools to test the assumed cognitive structure and to obtain parameters quantifying the probabilities that certain underlying processing stages take place or not. Multinomial processing tree models (MPT models; Batchelder & Riefer, 1990) provide such a means by modeling observed, categorical responses as originating from a finite number of discrete, latent processing paths. MPT models have been successfully used to explain behavior in many areas such as memory (Batchelder & Riefer, 1986, 1990, decision making (Erdfelder, Castela, Michalkiewicz, & Heck, 2015;Hilbig, Erdfelder, & Pohl, 2010), reasoning (Klauer, Voss, Schmitz, & Teige-Mocigemba, 2007), perception (Ashby, Prinzmetal, Ivry, & Maddox, 1996), implicit attitude measurement (Conrey, Sherman, Gawronski, Hugenberg, & Groom, 2005;Nadarevic & Erdfelder, 2011), and processing fluency (Fazio, Brashier, Payne, & Marsh, 2015;Unkelbach & Stahl, 2009). Batchelder & Riefer (1999 and Erdfelder et al. (2009) reviewed the literature and showed the usefulness and broad applicability of the MPT model class. In the present paper, we introduce a simple but general approach to include information about response times (RTs) into any kind of MPT model.
KeywordsAs a running example, we will use one of the most simple MPT models, the two-high-threshold model of recognition memory (2HTM; Bröder & Schütz, 2009;Snodgrass & Corwin, 1988). The 2HTM accounts for responses in a binary recognition paradigm. In such an experiment, participants first learn a list of items and later are prompted to categorize old and new items as such. Hence, one obtains frequencies of hits (correct old), misses (incorrect new), false alarms (incorrect ol...