@article {Gregoire:2008:0015-749X:597,title = "Regression Estimation Following the Square-Root Transformation of the Response",
journal = "Forest Science",
parent_itemid = "infobike://saf/fs",
publishercode ="saf",
year = "2008",
volume = "54",
number = "6",
publication date ="2008-10-01T00:00:00",
pages = "597-606",
itemtype = "ARTICLE",
issn = "0015-749X",
url = "http://www.ingentaconnect.com/content/saf/fs/2008/00000054/00000006/art00004",
keyword = "nonlinearity, back-transformation bias"
author = "Gregoire, Timothy G. and Lin, Qi Feng and Boudreau, Johnathan and Nelson, Ross",
abstract = "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: {\^E}[Y 2|x ] = y|x 2 + V( y|x 2). Its performance is compared against that of two biased estimators: {\^E}b [Y 2|x ] = y|x 2 + and {\^E}p [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.",
}