State-trace analysis can be an appropriate tool for assessing the number of cognitive systems: a reply to Ashby (2014).

Ashby (2014) has argued that state-trace analysis (STA) is not an appropriate tool for assessing the number of cognitive systems, because it fails in its primary goal of distinguishing single-parameter and multiple-parameter models. We show that this is based on a misunderstanding of the logic of STA, which depends solely on nearly universal assumptions about psychological measurement and clearly supersedes inferences based on functional dissociation and the analysis of interactions in analyses of variance. We demonstrate that STA can be used to draw inferences concerning the number of latent variables mediating the effects of a set of independent variables on a set of dependent variables. We suggest that STA is an appropriate tool to use when making arguments about the number of cognitive systems that must be posited to explain behavior. However, no statistical or inferential procedure is able to provide definitive answers to questions about the number of cognitive systems, simply because the concept of a "system" is not defined in an appropriate way.