A PRINCIPAL COMPONENTS ANALYSIS OF MODELS AND MEN

Abstract

ABSTRACT One consequence of stimulus sampling theory is the prediction of probability matching as the asymptotic response probability. That is, subjects tend to choose each alternative with the frequency of its reinforcement. This prediction has been tested in many experiments and the boundaries within which it holds have been delineated. However, the experiments which find probability matching have been criticized for doing one or more of several inappropriate things. It should be noted that probability matching is not a “rational” solution, in the sense that the behavior which maximizes gain would be always to choose the more frequently reinforced response. Some investigators have found it possible to devise experimental situations in which the subjects do come closer to maximizing behavior. This study attempts to differentiate the conditions which lead to “matching” behavior from those which lead to “maximizing” and to develop a mathematical model for this behavior. The experimental results indicate that the prediction of probability matching does not obtain. Therefore, it would seem to be probable that the stimulus sampling theory which predicts this behavior also does not apply. One of the axioms of stimulus sampling theory has been generalized. An effect of this revision is to allow for the prediction of nonprobability matching behavior. This model has been fitted to the data previously gathered, and described the data far better than any previous stimulus sampling model. It is concluded that probability matching is not a general learning law as Estes proposed in 1957, but, rather, that it is a special case of a more general phenomenon, just as previous stimulus sampling models are special cases of the model developed here. The major analytic tool in this study was a principal components analysis of the learning data. The inter‐factor plot of factor scores was used to compare the relative fit of the various forms of stimulus sampling models studied.

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