Joseph Berkson

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Joseph Berkson (1899 – 1982) was initially trained as a physicist. Later in his career he became primarily concerned with studying statistics.[1] In 1950, while working at the Division of Biometry and Medical Statistics, Mayo Clinic, Rochester, Minnesota, (1899 – 1982), Berkson wrote a key paper entitled Are there two regressions?.[2] In this paper Berkson proposed an error model for regression analysis that contradicted the classical error model until that point assumed to generally apply and this has since been termed the Berkson error model. Whereas the classical error model is statistically independent of the true variable, Berkson's model is statistically independent of the observed variable.[3] Carroll et al. (1995)[4] refer to the two types of error models as follows:

  • error models including the Classical Measurement Error models and Error Calibration Models, where the conditional distribution of W given (Z, X) is modeled — use of such a model is appropriate when attempting to determine X directly, but this is prevented by various errors in measurement.
  • regression calibration models (also known as controlled-variable or Berkson error models), where the conditional distribution of X given (Z, W) is modeled.

Berkson is also widely recognised as the key proponent in the use of the logistic in preference to the normal distribution in probabilistic techniques.[1] Berkson is also credited with the introduction of the logit model in 1944[5], and with coining this term. The term was borrowed by analogy from the very similar probit model developed by Chester Ittner Bliss in 1934.

[edit] Notes

  1. ^ a b Lecture notes for Economics students at Sussex university. Online resource: [1]
  2. ^ Berkson J (1950). "Are there two regressions?" ([dead link] – Scholar search). J Am Stat Assoc 45: 164–180. doi:10.2307/2280676. 
  3. ^ Heid IM, Kuchenhoff H, Miles J, Kreienbrock L, Wichmann HE (2004). "Two dimensions of measurement error: Classical and Berkson error in residential radon exposure assessment". J Exp Anal and Env Epi 14: 365–377. doi:10.1038/sj.jea.7500332. 
  4. ^ Carroll RJ, Ruppert D, Stefanski LA (1995). Measurement Error in Nonlinear Models. Chapman & Hall. 
  5. ^ Berkson J (1944). "Application of the logistic function to bio-assay". J Am Stat Assoc 39: 357–65. doi:10.2307/2280041.