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Note on Miller's “Finite Markov Processes in Psychology”

Published online by Cambridge University Press:  01 January 2025

Richard C. W. Kao
Richard C. W. Kao*
Affiliation:
University of Michigan
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Extract

In his article “Finite Markov Processes in Psychology,”G. A. Miller derived a least-squares “estimate” for a matrix of transitional probabilities. However, the mathematical proof is found to be invalid.

On page 158, Miller defined by the equation

= N + C,

“where the elements of the matrix C are the corrections that must be added to the observed values in N to give the best estimate ”.

Type
Original Paper
Information
Psychometrika , Volume 18 , Issue 3 , September 1953 , pp. 241 - 243
Copyright
Copyright © 1953 The Psychometric Society

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References

* Psychometrika, 1952, 17, 149-167.

† For a valid mathematical proof of a least-squares estimate in this connection, see Goodman's “A Further Note on ‘Finite Markov Processes in Psychology.’” This issue, 245-248.

† tWe note here the distinction between Miller's matrix differentiation and that of Dwyer and Macphail, Symbolic matrix derivatives. Ann. math. Statist., 1948, 19, 517-534, esp. 523, 528-530.

* We note that this argument does not apply to Goodman's results, where M, N are column vectors.