Decisional separability, model identification, and statistical inference in the general recognition theory framework

Abstract

Recent work in the general recognition theory (GRT) framework indicates that there are serious problems with some of the inferential machinery designed to detect perceptual and decisional interactions in multidimensional identification and categorization (Mack, Richler, Gauthier, & Palmeri, 2011). These problems are more extensive than previously recognized, as we show through new analytic and simulation-based results indicating that failure of decisional separability is not identifiable in the Gaussian GRT model with either of two common response selection models. We also describe previously unnoticed formal implicational relationships between seemingly distinct tests of perceptual and decisional interactions. Augmenting these formal results with further simulations, we show that tests based on marginal signal detection parameters produce unacceptably high rates of incorrect statistical significance. We conclude by discussing the scope of the implications of these results, and we offer a brief sketch of a new set of recommendations for testing relationships between dimensions in perception and response selection in the full-factorial identification paradigm.

Categorization training increases the perceptual separability of novel dimensions

“…1 GRT-wIND solves a number of problems that have been recently identified in traditional GRT models. Importantly, while traditional GRT models have problems dissociating perceptual and decisional forms of separability in the 2 Â 2 identification design (e.g., Mack, Richler, Gauthier, & Palmeri, 2011;Silbert & Thomas, 2013), we have shown that GRT-wIND does not suffer from these problems (see appendix of Soto et al, 2015).…”

“…Recent work (Mack et al, 2011;Silbert & Thomas, 2013) has shown that decisional separability is not identifiable in traditional GRT models for the 2 Â 2 identification design. In some cases, perceptual separability might also show identifiability problems.…”

“…A less general problem with the 2 Â 2 design is that under some conditions a model without perceptual separability can be transformed into an equivalent model with perceptual separability (Silbert & Thomas, 2013). Although all the conditions required to observe this non-identifiability have not been worked out, one condition that is absolutely necessary is illustrated in Fig.…”

“…The most serious issue was identified by Silbert and Thomas (2013) regarding decisional separability. These authors showed that any traditional GRT model for the 2 Â 2 identification design without decisional separability can be transformed into a model with decisional separability without affecting the predicted response probabilities.…”

Perception of voicing and place of articulation in labial and alveolar English stop consonants

“…Although this may seem to be a very strong assumption, in the standard 2 × 2 GRT model (i.e., the model of stimuli defined by the factorial combination of two levels on each of two dimensions), deviations from this assumption are not identifiable (Silbert and Thomas 2013); it is useful to think of the decision bounds as both partitioning the perceptual space into response regions and (implicitly) defining the axes of the perceptual space. Figure 1 shows four illustrative 2 × 2 Gaussian GRT models, each defined with respect to the stops [p], [b], [t], and [d], which consist of the factorial combination of place of articulation (labial vs. alveolar) and voicing (voiced vs. voiceless).…”