A Cautionary Note on Scaling Variables That Appear Only in Products in Ordinary Least Squares
نویسندگان
چکیده
Variables may be used as products in a regression model to correct or adjust for the effects of other variables. Such variables may be transformed to become indices; for example, to be constrained to be between 0 and 1. We provide a theoretical and a practical demonstration that the choice of transformation can affect the statistical significance of tests associated with estimates of effects and coefficients unless the variables are included in the model as well as their products. This is the strong-heredity principle of Nelder (1988). We demonstrate the effects with a case study of the middle-infrared correction to the Normalized Difference Vegetation Index to improve predictions of leaf area index.
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