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Analogical transfer in perceptual categorization

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Abstract

Analogical transfer is the ability to transfer knowledge despite significant changes in the surface features of a problem. In categorization, analogical transfer occurs if a classification strategy learned with one set of stimuli can be transferred to a set of novel, perceptually distinct stimuli. Three experiments investigated analogical transfer in rule-based and information-integration categorization tasks. In rule-based tasks, the optimal strategy is easy to describe verbally, whereas in information-integration tasks, accuracy is maximized only if information from two or more stimulus dimensions is integrated in a way that is difficult or impossible to describe verbally. In all three experiments, analogical transfer was nearly perfect in the rule-based conditions, but no evidence for analogical transfer was found in the information-integration conditions. These results were predicted a priori by the COVIS theory of categorization.

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Notes

  1. In all three experiments, each participant was randomly assigned to a condition. Note that this practice led to small sample-size differences across conditions.

  2. For example, if we assume a noise variance equal to the mean estimated noise variance from the GLC model (see the Appendix) across all Experiment 1 participants for whom the GLC provided the best fit to the training data, then an ideal observer (with noise) would achieve 93.7% correct in Experiment 1 and 99.8% correct in Experiment 2.

  3. Although to our knowledge no previous research has addressed the question of whether pigeons show analogical transfer in perceptual categorization, we predict that pigeons run in the present experiments would show little or no transfer in either condition. This is because pigeons presumably have at most a limited rule-learning system.

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Correspondence to Michael B. Casale.

Appendix

Appendix

A variety of different decision bound models were fit to the responses of each individual participant. Included in this list were three models that assumed an RB decision strategy (two one-dimensional models and a model that assumed a conjunction rule), one that assumed an II strategy (the general linear classifier), and two that assumed random guessing. For more details, see Ashby (1992) or Maddox and Ashby (1993).

Models assuming an RB strategy

The one-dimensional classifier

This model assumes that participants set a decision criterion on a single stimulus dimension. For example, a participant might base his or her categorization decision on the following rule: “Respond ‘A’ if the bar width is small, otherwise respond ‘B’.” Two versions of the model were fit to the data. One version assumed a decision based on bar width, and the other assumed a decision based on orientation. These models had two parameters: a decision criterion along the relevant perceptual dimension, and a perceptual noise variance.

The general conjunctive classifier (GCC)

This model assumes that the rule used by participants is a conjunction of two one-dimensional classifiers (e.g., “Respond ‘A’ if the bar width is small AND the orientation is >45°, otherwise respond ‘B’.”). Although several different versions of the model could be fit to the present data, only the version that seemed plausible based on a visual inspection of the response data was fit. The GCC has three parameters: one for the single decision criterion placed along each stimulus dimension (one for orientation and one for bar width), as well as a perceptual noise variance.

Models assuming an II strategy

The general linear classifier (GLC)

The GLC assumes that participants divide the stimulus space using a linear decision bound. One side of the bound is associated with an “A” response, and the other side is associated with a “B” response. These decision bounds require linear integration of both stimulus dimensions, thereby producing an II decision strategy. The GLC has three parameters: the slope and intercept of the linear decision bound, and a perceptual noise variance.

Random guessing models

Two models assumed that the participant guessed randomly on every trial. One version assumed that each response was equally likely to be selected. This model had no free parameters. A second model assumed that the participant guessed response “A” with probability p and guessed “B” with probability 1 – p, where p was a free parameter. This model is useful for identifying participants who are biased toward pressing one response key.

Goodness-of-fit measure

Model parameters were estimated >using the method of maximum likelihood, and the statistic used for model selection was the Bayesian information criterion (BIC; Schwarz, 1978), which is defined as BIC = r ln N – 2 ln L, where r is the number of free parameters, N is the sample size, and L is the likelihood of the model given the data. The BIC statistic penalizes models for extra free parameters. To determine the best-fitting model within a group of competing models, the BIC statistic is computed for each model, and the model with the smallest BIC value is the winning model.

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Casale, M.B., Roeder, J.L. & Ashby, F.G. Analogical transfer in perceptual categorization. Mem Cogn 40, 434–449 (2012). https://doi.org/10.3758/s13421-011-0154-4

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