The Box-Cox Transformation: Computational and Interpretation Features of the Parameters
Recently attention has returned in spatial statistics and spatial econometrics to the Box-Cox and Box-Tidwell families of power transformations (e.g., van Gastel and Paelinck, 1995; Kobayashi and McAleer, 1995). In part this renewed interest anses from geo-referenced data sets almost always falling under the heading of small sample theory. In such cases design-based inference cannot rely upon the conventional central limit theorem, and model-based inference risks confusing specification and sampling error. Power transformations offer a remedy for retaining the symmetry, constant spread, and linearity assumptions typifying conventional statistical analyses. These transformations often preserve the target parameter, and produce a change in measurement scale that better characterizes the population under study. Power transformations are monotone--changing only the distance between successive numbers along a measurement scale--tend to offer modest gains in statistical efficiency and to introduce no difficulties with the consistency of inferences.
KeywordsSpatial Autocorrelation Measurement Scale Power Transformation Spatial Econometric Bivariate Regression
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