Orthogonalizing parametric link transformation families in binary regression analysis

Claudia Czado, Thomas J. Santner

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


This paper studies the application of the orthogonalization technique of Cox and Reid (1987) to parametric families of link functions used in binary regression analysis. The explicit form of Cox and Reid's condition (4), for orthogonality at a point, is derived for arbitrary link families. This condition is used to determine a transform of a family introduced by Burr (1942) and Prentice (1975, 1976) which is locally orthogonal when the regression parameter is zero. Thus the benefits of having orthogonal parameters are limited to “small” regression effects. The extent to which approximate orthogonality holds for nonzero regression coefficients is investigated for two data sets from the literature. Two specific issues considered are: (1) the ability of orthogonal reparametrization to reduce the variability of the regression parameters caused by estimation of the link parameter and (2) the improved numerical stability (and hence interpretability) of regression estimates corresponding to different link parameters.

Original languageEnglish
Pages (from-to)51-61
Number of pages11
JournalCanadian Journal of Statistics
Issue number1
StatePublished - Mar 1992
Externally publishedYes


  • Key words and phrases
  • Logistic regression
  • binary regression
  • link family
  • transformation


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