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Comment on ‘The Estimation of Proportions in M Groups’

Published online by Cambridge University Press:  01 January 2025

Tom Leonard
Tom Leonard*
Affiliation:
University of Warwick
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Abstract

Novick, Lewis and Jackson [1973] propose an interesting Bayesian method for the simultaneous estimation of the probabilities of several binomial distributions. They utilise arc-sine transformations and normal approximations and then refer to the normal theory method of Lindley [1972] which utilises the novel concept of ‘exchangeability’. The posterior estimates for the probabilities shrink the usual proportions towards a central value based on collateral information, and should provide substantial improvements.

The purpose of our comment is to discuss the relative merits of other methods which are available whenever exchangeability of the probabilities is appropriate, The main methods are

(1) The Logistic Approach: Leonard [1972a] uses logistic transformations of the parameters and proposes a simple exact method of estimation which is valid even if some of the cell frequencies are zero. This is because the logistic transformations are to the parameters and not to the observed frequencies. The exact posterior modal estimates replace the usual observed logits in such a way that difficulties involving zeros are removed. The are-sine approximation is of course inaccurate in such cases.

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 4 , December 1974 , pp. 521 - 523
Copyright
Copyright © 1974 The Psychometric Society

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References

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