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An Analysis of Some Conditions for Representing N State Markov Processes as General all or None Models

Published online by Cambridge University Press:  01 January 2025

Theodore E. Steiner
Affiliation:
University of Illinois
James G. Greeno
Affiliation:
University of Michigan

Abstract

Recently Markov learning models with two unidentifiable presolution success states, an error state, and an absorbing learned state, have been suggested to handle certain aspects of data better than the three state Markov models of the General All or None model type. In attempting to interpret psychologically, and evaluate statistically the adequacy of various classes of Markov models, a knowledge of the relationship between the classes of models would be helpful. This paper considers some aspects of the relationship between the class of General All or None models and the class of Stationary Absorbing Markov models with N error states, and M presolution success states.

Type
Original Paper
Copyright
Copyright © 1969 The Psychometric Society

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References

Atkinson, R. C., & Crothers, E. J. A comparison of paired-associate learning models having different acquisition and retention axioms. Journal of Mathematical Psychology, 1964, 1, 285315.CrossRefGoogle Scholar
Bernbach, H. A. A forgetting model for paired-associate learning. Journal of Mathematical Psychology, 1965, 2, 128144.CrossRefGoogle Scholar
Burke, C. J., & Rosenblatt, M. A Markovian function of a Markov chain. Annals of Mathematical Statistics, 1958, 29, 11121122.CrossRefGoogle Scholar
Goldberg, S. Introduction to difference equations, 1961, New York: Wiley & Sons, Inc..Google Scholar
Greeno, J. G. Paired-associate learning with short term retention: mathematical analysis and data regarding identification of parameters. Journal of Mathematical Psychology, 1967, 4, 430472.CrossRefGoogle Scholar
Greeno, J. G. Identifiability and statistical properties of two-stage learning with no successes in the initial stage. Psychometrika, 1968, 33, 173215.CrossRefGoogle ScholarPubMed
Greeno, J. G., & Steiner, T. E.. Markovian processes with identifiable states: General considerations and application to all or none learning. Psychometrika, 1964, 29, 309333.CrossRefGoogle Scholar
Greeno, J. G., & Steiner, T. E. Comments on “Markovian processes with identifiable states: General considerations and application to all or none learning. Psychometrika, 1968, 33, 169172.CrossRefGoogle ScholarPubMed
Jolley, L. B. W. Summation of series, 2nd ed., New York: Dover, 1961.Google Scholar
Kemeny, J. G., & Snell, J. L. Finite Markov Chains, 1960, Princeton: D. Van Nostrand Co..Google Scholar
Murdoch, D. C. Linear algebra for undergraduates, 1957, New York: John Wiley & Sons.Google Scholar
Polson, P. G., & Greeno, J. G. Nonstationary performance before all or none learning. Paper read at Midwestern Psychological Association, 1965.Google Scholar
Suppes, P., & Ginsberg, Rose A fundamental property of all or none models. Psychological Review, 1963, 70, 139161.CrossRefGoogle ScholarPubMed