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A Further Note on “Finite Markov Processes in Psychology”

Published online by Cambridge University Press:  01 January 2025

Leo A. Goodman
Leo A. Goodman*
Affiliation:
The University of Chicago
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Abstract

In his interesting article “Finite Markov Processes in Psychology,” G. A. Miller derived a “least-squares estimate” for a matrix of transitional probabilities (I). However, the mathematical proof seems to be unclear. Since this proof is considered invalid (2), we shall present a somewhat clearer version of the proof of this result. We shall also examine the general problem in some detail.

In the proof we shall assume that the reader is familiar with matrix notation, which enables a considerably shorter presentation. We shall follow the matrix conventions and the terminology adopted by Miller (I).

Type
Original Paper
Information
Psychometrika , Volume 18 , Issue 3 , September 1953 , pp. 245 - 248
Copyright
Copyright © 1953 The Psychometric Society

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Footnotes

*

This report was prepared in connection with research supported by the Office of Naval Research.

References

Miller, G. A. Finite Markov processes in psychology. Psychometrika, 1952, 17, 149–167.CrossRefGoogle Scholar
Kao, Richard. Note on Miller's “Finite Markov processes in Psychology. Psychometrika, 1953, 18, 241–243.CrossRefGoogle Scholar
Kempthorne, Oscar. The design and analysis of experiments, New York: John Wiley and Sons, Inc., 1952.CrossRefGoogle Scholar
Wilks, S. S. Mathematical statistics, Princeton: Princeton Univ. Press, 1944.Google Scholar