The statistical accuracy and theoretical status of discrete-state MPT models: reply to Batchelder and Alexander (2013).

In "A Critical Comparison of Discrete-State and Continuous Models of Recognition Memory: Implications for Recognition and Beyond," Pazzaglia, Dube, and Rotello (2013) explored the threshold multinomial processing tree (MPT) framework as applied to several domains of experimental psychology. Pazzaglia et al. concluded that threshold MPT analyses require assumptions at the representation and measurement levels that are contradicted by existing data in several domains. Furthermore, they showed that this flaw in the threshold MPT framework produces systematic errors in data interpretation. Pazzaglia et al. suggested measures derived from the empirically validated unequal-variance signal detection theory framework as a viable alternative and provided a simple tutorial for implementing such measures in an Excel spreadsheet. In their reply, Batchelder and Alexander (2013) disputed the conclusions advanced by Pazzaglia et al. Their arguments consisted of a small number of strong assertions, some of which were accompanied by references and/or data. In this reply, we demonstrate that both types of assertions--those with and without supporting references and/or data--are, at best, contradicted by several existing studies (many of which were already discussed in Pazzaglia et al., 2013) and, at worst, patently false. We conclude that the conclusions of Pazzaglia et al. are valid.