Abstract
Fitting multiple regression models by the method of least squares is one of the most commonly used methods in statistics. There are a number of challenges to the use of least squares, even when it is only used for estimation and not inference, including the following. Fitting multiple regression models by the method of least squares is one of the most commonly used methods in statistics. There are a number of challenges to the use of least squares, even when it is only used for estimation and not inference, including the following.
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How should continuous predictors be transformed so as to get a good fit?
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Is it better to transform the response variable? How does one find a good transformation that simplifies the right-hand side of the equation?
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3.
What if Y needs to be transformed non-monotonically (e.g., | Y − 100 | ) before it will have any correlation with X?
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Notes
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A disadvantage of transform-both-sides regression is this difficulty of interpreting estimates on the original scale. Sometimes the use of a special generalized linear model can allow for a good fit without transforming Y.
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Beware that use of a data–derived transformation in an ordinary model, as this will result in standard errors that are too small. This is because model selection is not taken into account. 186
References
P. C. Austin, J. V. Tu, P. A. Daly, and D. A. Alter. Tutorial in Biostatistics:The use of quantile regression in health care research: a case study examining gender differences in the timeliness of thrombolytic therapy. Stat Med, 24:791–816, 2005.
L. Breiman and J. H. Friedman. Estimating optimal transformations for multiple regression and correlation (with discussion). J Am Stat Assoc, 80:580–619, 1985.
N. Duan. Smearing estimate: A nonparametric retransformation method. J Am Stat Assoc, 78:605–610, 1983.
J. J. Faraway. The cost of data analysis. J Comp Graph Stat, 1:213–229, 1992.
T. Hastie and R. Tibshirani. Generalized Additive Models. Chapman and Hall, London, 1990.
R. Koenker and G. Bassett. Regression quantiles. Econometrica, 46:33–50, 1978.
R. Tibshirani. Estimating transformations for regression via additivity and variance stabilization. J Am Stat Assoc, 83:394–405, 1988.
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Harrell, F.E. (2015). Transform-Both-Sides Regression. In: Regression Modeling Strategies. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-19425-7_16
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