Regression Estimation Following the Square-Root Transformation of the Response
In a variety of regression situations, there is interest in predicting the value of Y 2, yet it is useful to model it using a square root transformation, such that Y rather than Y 2 is regressed on one or more covariates. The back-transformation bias of the square root transformation of the response variable of interest is presented in detail. An unbiased estimator is presented: Ê[Y 2|x ∗] = y|x∗ 2 + − V( y|x∗ 2). Its performance is compared against that of two biased estimators: Êb [Y 2|x ∗] = y|x∗ 2 + and Êp [Y 2|x ∗] = y|x∗ 2. The first two moments of these estimators are derived analytically and verified by means of a simulation study. Both biased estimators have lower mean square errors than the unbiased estimator. An example wherein aboveground biomass is the response variable is presented for illustration.
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