A multivariate model for discrimination methods |
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| Institution: | 1. Department of Psychology, Center for Neuroscience, University at Albany, State University of New York, Albany, New York, USA;2. Neurosciences Program, University of Southern California, Los Angeles, California, USA;1. Rotman Institute of Philosophy, University of Western Ontario, London, Ontario, N6A 5B8, Canada;2. Department of Philosophy, University of Manchester, Oxford Road, Manchester, UK;3. Cognition and Philosophy Lab, Department of Philosophy, Monash University, Victoria, Australia;4. The Brain and Mind Institute, University of Western Ontario, London, Ontario, N6A 5B7, Canada |
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| Abstract: | We describe a multivariate model for a certain class of discrimination methods in this paper and discuss a multivariate Euclidean model for a particular method, the triangular method. The methods of interest involve the selection or grouping of stimuli drawn from two stimulus sets on the basis of attributes invoked by the subject. These methods are commonly used for estimation and hypothesis testing concerning possible differences between foods, beverages, odorants, tastants and visual stimuli.Mathematical formulation of the bivariate model for the triangular method is provided as well as extensive Monte Carlo results for up to 10-dimensional cases. The effect of correlation structure and variance inequality are discussed. Results from these methods (as probability of a correct response) are not monotonically related to the distance between the means of the stimulus sets from which the stimuli are drawn but depend in a particular way on dimensionality, correlation structure, and the relative orientation of the momentary sensory values in a multidimensional space. The importance of these results to the validity of these methods as currently employed is discussed and the possibility of developing a new approach to multidimensional scaling on the basis of this new theory is considered. |
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