On Prediction and the Power Transformation Family

Abstract

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Predictive Margins with Survey Data

“…a Observed incidence is based on a sample-weighted Fleming-Harrington estimator of the cause-specific survival distribution (4) In some applications, there is interest in the magnitude of the effects of different possible transformations of the dependent variable on group differences. These effects are difficult to interpret by examining regression coefficients (because they are on different scales with different transformations) but are easy to interpret with predicted quantities like predictive margins (Carroll and Ruppert, 1981).…”

Linear regression

“…Bickel and Doksum45 noticed that the variance of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\hat{\boldsymbol{\beta}}$ \end{document} associated with transformed model is inflated, relative to the estimate obtained with known λ . For prediction purposes, Carroll and Ruppert46 found that the prediction ŷ obtained by transforming ŷ ( λ ) back to its original scale does not have such a problem. Box and Cox47 suggested employing their method to estimate λ , and then estimating β by treating \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\hat{\lambda}$ \end{document} as fixed.…”

Book Reviews

“…This material is well presented and includes a summary of the likelihood theory needed for the m r e test. Atkinson includes a short recapitulation of the BoxCox-Bickel-Doksum-Carroll-Ruppert dispute over the appropriate measure of variability of estimates of the regression parameters made when using the Box-Cox transformation family (Bickel and Doksum 1981;Box and Cox 1982;Carroll and Ruppert 1981) and decides in favor of Box and Cox. Chapter 7 covers some similar transformation families for percentages and proportions, including the folded power, GuerreroJohnson, and Aranda-Ordaz transformations.…”