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Keywords:

  • logistic regression;
  • quantal response;
  • discriminant analysis;
  • case-control study

A review is given of the development of logistic regression as a multi-purpose statistical tool.

A historical introduction shows several lines culminating in the unifying paper of Cox (1966), in which theory as developed in the field of bio-assay is shown to be applicable to designs as discriminant-analysis and case-control study. A review is given of several designs all leading to the same analysis. The link is made with epidemiological literature.

Several optimization criteria are discussed that can be used in the case of more observations per cell, namely maximum likelihood, minimum chi-square and weighted regression on the observed logits. Recent literature on the goodness of fit problem is reviewed and finally, comments are made about the non-parametric approach to logistic regression which is still in rapid development.