Abstract
Transformations of many kinds are used in statistical method and theory including simple changes of unit of measurement to facilitate computation or understanding, and the linear transformations underlying the application and theory of multiple regression and the techniques of classical multivariate analysis. Nevertheless the word transformation in a statistical context normally brings to mind a non-linear transformation (to logs, square roots, etc.) of basic observations done with the objective of simplifying analysis and interpretation. The present entry focuses on that aspect.
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Bibliography
Bartlett (1943) gives an excellent account of the early work; Box and Cox (1964) discuss the estimation of transformations via the likelihood and Bayesian methods. Butter and Verbon (1982) describe economic applications in some depth. Bickel and Doksum (1981) and Box and Cox (1982) give opposing views of estimation following a transformation.
Bartlett, M.S. 1947. The use of transformations. Biometrics 3: 39–52.
Bickel, P.J., and K.A. Doksum. 1981. An analysis of transformations revisited. Journal of the American Statistical Association 76: 296–311.
Box, G.E.P., and D.R. Cox. 1964. An analysis of transformations. Journal of the Royal Statistical Society, Series B 26: 211–243.
Box, G.E.P., and D.R. Cox. 1982. An analysis of transformations revisited, rebutted. Journal of the American Statistical Association 77: 209–210.
den Butter, F.A.G., and H.A.A. Verbon. 1982. The specification problem in regression analysis. International Statistical Review 50: 267–283.
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Cox, D. (2018). Transformation of Statistical Variables. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1826
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DOI: https://doi.org/10.1057/978-1-349-95189-5_1826
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