Introduction to Categorical Data Analysis

328 A HISTORICAL TOUR OF CATEGORICAL DATA ANALYSIS ∗
(Section 2.6.2) based on his experience at an afternoon tea break while employed
at Rothamsted Experiment Station. Other CDA-related work of his included showing
how to (i) find ML estimates of parameters in the probit model (an iterative weighted
least squares method today commonly called Fisher scoring), (ii) find ML estimates
of cell probabilities satisfying the homogeneous association property of equality of
odds ratios between two variables at each level of the third, and (iii) assign scores to
rows and columns of a contingency table to maximize the correlation.
11.3 LOGISTIC REGRESSION
The mid-1930s finally saw some model building for categorical responses. For
instance, Chester Bliss popularized the probit model for applications in toxicology
dealing with a binary response. See Chapter 9 of Cramer (2003) for a survey of the
early origins of binary regression models.
In a book of statistical tables published in 1938, R. A. Fisher and Frank Yates
suggested log[π/(1 − π)] as a possible transformation of a binomial parameter for
analyzing binary data. In 1944, the physician and statistician Joseph Berkson introduced
the term “logit” for this transformation. Berkson showed that the logistic
regression model fitted similarly to the probit model, and his subsequent work did
much to popularize logistic regression. In 1951, Jerome Cornfield, another statistician
with a medical background, showed the use of the odds ratio for approximating
relative risks in case–control studies with this model.
In the early 1970s, work by the Danish statistician and mathematician Georg Rasch
sparked an enormous literature on item response models. The most important of these
is the logit model with subject and item parameters, now called the Rasch model
(Section 10.2.5). This work was highly influential in the psychometric community of
northern Europe (especially in Denmark, the Netherlands, and Germany) and spurred
many generalizations in the educational testing community in the United States.
The extension of logistic regression to multicategory responses received occasional
attention before 1970, but substantial work after that date. For nominal responses,
early work was mainly in the econometrics literature. In 2000, Daniel McFadden
won the Nobel Prize in economics for his work in the 1970s and 1980s on the
discrete-choice model (Section 6.1.5). Cumulative logit models received some attention
starting in the 1960s and 1970s, but did not become popular until an article by
Peter McCullagh in 1980 provided a Fisher scoring algorithm for ML fitting of a more
general model for cumulative probabilities allowing a variety of link functions.
Other major advances with logistic regression dealt with its application to case–
control studies in the 1970s and the conditional ML approach to model fitting for
those studies and others with numerous nuisance parameters. Biostatisticians Norman
Breslow and Ross Prentice at the University of Washington had a strong influence on
this. The conditional approach was later exploited in small-sample exact inference in
a series of papers by Cyrus Mehta, Nitin Patel, and colleagues at Harvard.
Perhaps the most far-reaching contribution was the introduction by British statisticians
John Nelder and R. W. M. Wedderburn in 1972 of the concept of generalized