Learning models for a continuum of sensory states reexamined

Dorfman and Biderman evaluated an additive-operator learning model and some special cases of this model on data from a signal-detection experiment. They found that Kac's pure error-correction model gave the poorest fit of the special models when the predictions were generated from the maximum likelihood estimates and the initial cutoffs were set at an a priori value rather than estimated. First, this paper presents tests of an asymptotic theorem by Norman, which provide strong support for Kac's model. On the final 100 trials, every subject but one gave probability matching, and the response propcrtions appropriately normed were approximately normally distributed with variance π(1 ? π). Further analyses of the Dorfman-Biderman data based upon maximum likelihood and likelihood-ratio tests suggest that Kac's model gives a relatively good, but imperfect fit to the data. Some possible explanations for the apparent contradiction between the results of these new analyses and the original findings of Dorfman and Biderman were explored. The investigations led to the proposal that there may be nonsystematic, random drifts in the decision criterion after correct responses as well as after errors. The hypothesis gives a minor modification of the conclusions from Norman's theorem for Kac's model. It gives asymptotic probability matching for every subject, but a larger asymptotic variance than π(1 ? π), which agrees with the data. The paper also presents good Monte Carlo justification for the use of maximum likelihood and likelihood-ratio tests with these additive learning models. Results from Thomas' nonparametric test of error correction are presented, which are inconclusive. Computation of Thomas' p statistic on the Monte Carlo simulations showed that it is quite variable and insensitive to small deviations from error correction.