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Leslie Blaha, Tamaryn Menneer, Michael Wenger, Jennifer L. Bittner; Correlation Analysis for Multidimensional Signal Detection Evaluation and Comparison with Standard Analyses. Journal of Vision 2013;13(9):1028. doi: https://doi.org/10.1167/13.9.1028.
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© ARVO (1962-2015); The Authors (2016-present)
We evaluated tetrachoric and polychoric correlation analyses as candidate techniques for modeling data in studies employing general recognition theory (GRT). GRT is a multidimensional signal detection theory that provides a rigorous framework for distinguishing among perceptual and decisional effects when perceptual dimensions interact, such as in perceptual configurality (e.g., Cornes et al., 2011). The traditional methods for GRT modeling (Townsend & Ashby, 1986; Kadlec & Townsend, 1995; 1999) employ a set of marginal and non-parametric methods to indirectly estimate the configuration of underlying probability models. Within GRT, violations of some model constructs, like perceptual independence, can be represented theoretically as non-zero correlations in the covariance structure for individual stimuli; the marginal methods do not directly estimate these correlations but instead infer them indirectly. We developed four new applications of correlation estimates, marginal and conditional tetrachoric and polychoric correlations, to examine correlations for the multivariate representation of each stimulus and within responses given between stimuli. The novel correlation and standard marginal analyses were applied to simulated data from known GRT configurations to determine the relative frequency of correct and incorrect inferences made by the two types of analyses. The results show that the marginal methods are very conservative with respect to detecting correlations within perceptual distributions (violations of perceptual independence), and those inferences are corroborated by the conditional tetrachoric correlation estimates. Additionally, the marginal correlation estimates are able to detect response correlations that can result from violations of decisional separability and perceptual separability, such as violation through mean shift integrality. Taken together the four new analyses illustrate various patterns of correlations within identification-confusion responses that can augment traditional signal detection analyses. This simulation study suggests ways in which the two approaches may be combined (as sources of converging evidence) to support inferences regarding multidimensional signal detection models.
Meeting abstract presented at VSS 2013
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