The TRANSREG Procedure

Overview

The Box-Cox (1964) transformation has the form

$(y^\lambda - 1) / \lambda & \hspace*{1in} & \lambda \neq 0 \ \log(y) & & \lambda=0$

This family of transformations of the positive dependent variable y is controlled by the parameter $\lambda$ . Transformations linearly related to square root, inverse, quadratic, cubic, and so on are all special cases. The limit as $\lambda$ approaches 0 is the log transformation. More generally, Box-Cox transformations of the following form can be fit:

$((y + c)^\lambda - 1) / (\lambda g) & \hspace*{.4in} & \lambda \neq 0 \ \log(y + c) / g & & \lambda=0$

By default, c = 0. The parameter c can be used to rescale y so that it is strictly positive. By default, g = 1. Alternatively, g can be $\dot{y}^{\lambda - 1}$ where $\dot{y}$ is the geometric mean of y.

The new BOXCOX transformation in the TRANSREG procedure can be used to perform a Box-Cox transformation of the dependent variable. You can specify a list of power parameters using the LAMBDA= transformation option. By default, LAMBDA=-3 TO 3 BY 0.25. The procedure chooses the optimal power parameter using a maximum likelihood criterion (Draper and Smith 1981, pp. 225-226). You can specify the PARAMETER=c transformation option when you want to shift the values of y, usually to avoid negatives. To divide by $\dot{y}^{\lambda - 1}$ , specify the GEOMETRICMEAN transformation option. For example,

   proc transreg;
      model BoxCox(y / lambda=-2 to 2 by 0.1
                       parameter=2 geometricmean) =
            identity(x1-x5);
      output out=results;
      run;

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