Book contents
- Frontmatter
- Contents
- List of tables
- List of figures
- Preface
- 1 Introduction: random utility and ordered choice models
- 2 Modeling binary choices
- 3 A model for ordered choices
- 4 Antecedents and contemporary counterparts
- 5 Estimation, inference and analysis using the ordered choice model
- 6 Specification issues and generalized models
- 7 Accommodating individual heterogeneity
- 8 Parameter variation and a generalized model
- 9 Ordered choice modeling with panel and time series data
- 10 Bivariate and multivariate ordered choice models
- 11 Two-part and sample selection models
- 12 Semiparametric and nonparametric estimators and analyses
- References
- Index
4 - Antecedents and contemporary counterparts
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- List of tables
- List of figures
- Preface
- 1 Introduction: random utility and ordered choice models
- 2 Modeling binary choices
- 3 A model for ordered choices
- 4 Antecedents and contemporary counterparts
- 5 Estimation, inference and analysis using the ordered choice model
- 6 Specification issues and generalized models
- 7 Accommodating individual heterogeneity
- 8 Parameter variation and a generalized model
- 9 Ordered choice modeling with panel and time series data
- 10 Bivariate and multivariate ordered choice models
- 11 Two-part and sample selection models
- 12 Semiparametric and nonparametric estimators and analyses
- References
- Index
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 ChoicesA Primer, pp. 111 - 135Publisher: Cambridge University PressPrint publication year: 2010