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4 - Antecedents and contemporary counterparts

Published online by Cambridge University Press:  05 June 2012

William H. Greene
Affiliation:
New York University
David A. Hensher
Affiliation:
University of Sydney
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Summary

McKelvey and Zavoina's proposal is preceded by several earlier developments in the statistical literature. The chronology to follow does suggest, however, that their development produced a discrete step in the received body of techniques. The obvious starting point was the early work on probit methods in toxicology, beginning with Bliss (1934a) and made famous by Finney's (1947b) classic monograph on the subject. The ordered choice model that we are interested in here appears in three clearly discernible steps in the literature: Aitchison and Silvey's (1957) treatment of stages in the life cycle of a certain insect, Snell's (1964) analysis of ordered outcomes (without a regression interpretation), and McKelvey and Zavoina's (1975) proposal of the modern form of the “ordered probit regression model.” Some later papers, e.g., Anderson (1984) expanded on the basic models. Walker and Duncan (1967) is another discrete step in the direction of analyzing individual data.

The origin of probit analysis: Bliss (1934a), Finney (1947a)

Bliss (1934a) tabulated graphically the results of a laboratory study of the effectiveness of an insecticide. He plotted the relationship between the “Percent of Aphids Killed” on the ordinate and “Milligrams of Nicotine Per 100 ML of Spray” on the abscissa of a simple figure, reproduced here as Figure 4.1. The figure loosely traces out the familiar sigmoid shape of the normal CDF, and in a natural fashion provides data on what kill rate can be expected for a given concentration of nicotine.

Type
Chapter
Information
Modeling Ordered Choices
A Primer
, pp. 111 - 135
Publisher: Cambridge University Press
Print publication year: 2010

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