Academic journal article Psychonomic Bulletin & Review

Decisional Separability, Model Identification, and Statistical Inference in the General Recognition Theory Framework

Academic journal article Psychonomic Bulletin & Review

Decisional Separability, Model Identification, and Statistical Inference in the General Recognition Theory Framework

Article excerpt

Published online: 23 October 2012

© Psychonomic Society, Inc. 2012

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.

Keywords Math modeling * Perceptual categorization and identification * Signal detection theory * Decision making

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The structure of general recognition theory

General recognition theory, or GRT, is a multidimensional model of perception and response selection (Ashby & Townsend, 1986; Kadlec & Townsend, 1992a, 1992b; Silbert, Townsend, & Lentz, 2009; Thomas, 2001b; Wenger & Ingvalson, 2003). It was originally developed to unify a disparate set of concepts in the psychological literature and provide a rigorous mathematical foundation for the analysis of interactions between psychological dimensions in perception and response selection. GRT has been applied extensively to two-choice categorization (often under the name decision bound theory, and with a focus on various properties of response selection, rather than the presence or absence of dimensional interactions; see, e.g., Ashby & Gott, 1988; Ashby & Maddox, 1990) and has been related to a variety of other psychological constructs (e.g., similarity, Ashby & Perrin, 1988; same-different judgments, Thomas, 1996). As was established in the original article (Ashby & Townsend, 1986), the power of GRT as a tool for testing dimensional interactions is most evident in the so-called feature-complete factorial identification experimental protocol, in which stimuli consist of the factorial combination of each level on each dimension of interest.

For example, consider one of the stimulus sets used by Thomas (2001b). Four face stimuli were constructed by combining two levels of distance between the eyes with two levels of nose length. In the associated identification protocol, a oneto- one mapping between stimuli and responses is established, and the data consist of a four-by-four identification-confusion matrix. Although this approach can be extended to more than two levels on more than two dimensions (e.g., Ashby & Lee, 1991; see also Kadlec & Townsend, 1992b), the two-by-two case (two levels on each of two dimensions) is by far the most frequently used. For the sake of clarity, we restrict our attention to the two-by-two case here, although much of what we say applies more generally (e.g., to N-by-M or threedimensional factorial identification).

GRT relies on two basic assumptions to account for factorial identification data: (1) random perceptual effects and (2) deterministic decision bounds that exhaustively partition perceptual space. Over time, random perceptual effects produce multivariate perceptual distributions, and predicted response probabilities are determined by the proportion of perceptual distributions within each response region. …

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