Weight function for non-linear transformation of regression equations
2002
Nilson, A. (Estonian Agricultural University, Tartu (Estonia). Department of Forest Management)
Non-linear transformation of output variables has been quite common in forest model building during many decades. The illusion of a good fit of initial values based on the nice picture of a logarithmic or semi-logarithmic paper in the past or the seemingly good multiple coefficient of correlation today has been, and often still is, quite common as well. Sometimes and somehow, the author of the model can recognise the danger of the non-linear transformation bias in such cases; however, there is rather little help in terms of the literature and computer software to estimate, avoid or minimise it. Regression analysis is the most popular tool for model developers in forestry. Linear regression analysis programs are fast and reliable for mass production of models whereas non-linear ones are often sensitive to initial values and parameter correlations and result in failure. The least-squares estimates for non-linear transformation of output values (dependent variables in the case of regression analysis) are not, as a rule, OLSE for initial values; however, non-linear transformation attractive in many cases to simplify the model for reliable and uncomplicated linear regression analysis. There is no difference in the non-linear transformation bias regardless of whether we use linear or non-linear regression analysis programs if these cannot respond adequately to the non-linear transformation of the dependent variable used
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