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Tamaryn Menneer, Michael Wenger, Leslie Blaha; Inferential challenges for General Recognition Theory: Mean-shift Integrality and Perceptual Configurality. Journal of Vision 2010;10(7):1211. doi: 10.1167/10.7.1211.
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General recognition theory (GRT) provides clear definitions and distinctions for the way in which perceptual and decision processes can interact across dimensions. As perceptual configurality is often defined in terms of feature or processing interactions (Wenger & Townsend, 2001), GRT provides a conceptual framework for assessing perceptual configurality. However, there are a variety of different quantitative and statistical methodologies available for relating data to theory. One of the challenges for these methods is to address issues of model identifiability that can arise when there is a one-to-many mapping from empirical data to the GRT framework. Mean shift integrality is such a situation, under which inferential errors can occur because there are multiple solutions in GRT. A mean shift integrality arises when changing one dimension of a multidimensional stimulus shifts the perceptual representation of all other dimensions. We have developed two techniques that can facilitate identification of a mean shift. The first is a collection of probit models that can be estimated simultaneously across two dimensions (DeCarlo, 2003), allowing bivariate correlations with perceptual distributions to be directly estimated. When a mean shift in distributions is accompanied by a continuous decision bound, the probit models identify bivariate correlations of the same sign and similar magnitude across all distributions. They also identify any shift in decision bound relative to the distributions. The second approach is an application of polychoric and tetrachoric correlations both within and across all distributions. Tetrachoric correlations applied to data sampled from mean-shift distributions accompanied by a continuous decision bound shift revealed significant non-zero correlations in the response space. These estimates are sensitive to the magnitude of the mean shift. Results from the two approaches are contrasted with more traditional multidimensional signal detection theory approaches (Kadlec, 1995; 1999).
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