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Regression Estimation Following the Square-Root Transformation of the Response

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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: 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.

Keywords: back-transformation bias; nonlinearity

Document Type: Research Article

Publication date: 2008-10-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

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    June 1, 2016 to Feb. 28, 2017

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