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The Average Error of a Learning Model, Estimation and Use in Testing the Fit of Models

Published online by Cambridge University Press:  01 January 2025

Helena Chmura Kraemer
Helena Chmura Kraemer*
Affiliation:
Stanford University
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Abstract

A measure of the discrepancy between observed transition frequencies and those predicted by a learning model, an “average error” of a learning model, is presented. The maximum-likelihood estimator of the average error is derived and its use in a modified test of goodness of fit is demonstrated.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 3 , September 1965 , pp. 343 - 352
Copyright
Copyright © 1965 Psychometric Society

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References

Abdel-Aty, S. H. Approximate formulae for the percentage points and the probability integral of the non-centralx 2-distribution. Biometrika, 1954, 41, 538–540.Google Scholar
Anderson, T. W. and Goodman, L. A. Statistical inference about Markov chains. Ann. math. Statist., 1957, 28, 89–110.CrossRefGoogle Scholar
Arrow, K. J. Decision theory and the choice of a level of significance for thet-test. In Olkin, I. et al. (Eds.), Contributions to probability and statistics, Stanford, Calif.: Stanford Univ. Press, 1960.Google Scholar
Bulmer, M. G. Confidence intervals for distance in the analysis of variance. Biometrika, 1958, 45, 360–369.CrossRefGoogle Scholar
Goodman, L. S. Statistical methods for analyzing processes of change. Amer. J. Soc., 1962, 68, 57–78.CrossRefGoogle Scholar
McLachlan, N. W. Bessel functions for engineers, Cambridge, Eng.: Claredon Press, 1934.Google Scholar
Onoe, M. Tables of modified quotients of Bessel functions of the first kind for real and imaginary arguments, New York: Columbia Univ. Press, 1958.Google Scholar
Patnaik, P. B. The non-centralx 2- and F-distributions and their applications. Biometrika, 1949, 36, 202–232.Google ScholarPubMed
Pearson, E. S. and Hartley, H. O. Biometrika tables for statisticians, Volume I, Cambridge: University Press, 1962.Google Scholar
Severo, N. C. and Zelen, M. Normal approximation to the chi-square and non-centralF probability functions. Biometrika, 1960, 47, 411–416.CrossRefGoogle Scholar
Suppes, P. and Atkinson, R. C. Markov learning models for multiperson interactions, Stanford, Calif.: Stanford Univ. Press, 1960.Google Scholar
Suppes, P., Rauanet, H., Levine, M., and Frankman, R. W. Empirical comparison of models for a continuum of responses with non-contingent bimodal reinforcement. In Atkinson, R. C. (Eds.), Studies in mathematical psychology, Stanford, Calif.: Stanford Univ. Press, 1964.Google Scholar
Suppes, P. and Schlag-Rey, M. Test of some learning models for double contingent reinforcement. Psychol. Rep., 1962, 10, 259–268.CrossRefGoogle Scholar
Suppes, P. and Schlag-Rey, M. Test of some learning models for double contingent reinforcement: A correction. Psychol. Rep., 1964, 14, 482–482.CrossRefGoogle Scholar
Tukey, J. W. Approximations to the upper 5% points of Fisher'sB distribution and non-centralx 2. Biometrika, 1957, 44, 528–531.Google Scholar
Whittaker, E. T. and Watson, G. N.. A course in modern analysis (Chapter XVII), New York: MacMillan, 1943.Google Scholar

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