The TRANSREG Procedure


Overview: TRANSREG Procedure

The TRANSREG (transformation regression) procedure fits linear models, optionally with smooth, spline, Box-Cox, and other nonlinear transformations of the variables. You can use PROC TRANSREG to fit a curve through a scatter plot or fit multiple curves, one for each level of a classification variable. You can also constrain the functions to be parallel or monotone or have the same intercept. PROC TRANSREG can be used to code experimental designs and classification variables prior to their use in other analyses.

The TRANSREG procedure fits many types of linear models, including the following:

The data set can contain variables measured on nominal, ordinal, interval, and ratio scales (Siegel; 1956). You can specify any mix of these variable types for the dependent and independent variables. PROC TRANSREG can do the following:

Transformations produced by the PROC TRANSREG multiple regression algorithm, requesting spline transformations, are often similar to transformations produced by the ACE smooth regression method of Breiman and Friedman (1985). However, ACE does not explicitly optimize a loss function (de Leeuw; 1986), while PROC TRANSREG explicitly minimizes a squared-error criterion.

PROC TRANSREG extends the ordinary general linear model by providing optimal variable transformations that are iteratively derived. PROC TRANSREG iterates until convergence, alternating two major steps: finding least squares estimates of the model parameters given the current scoring of the data, and finding least squares estimates of the scoring parameters given the current set of model parameters. This is called the method of alternating least squares (Young; 1981).

For more background on alternating least squares optimal scaling methods and transformation regression methods, see Young, de Leeuw, and Takane (1976), Winsberg and Ramsay (1980), Young (1981), Gifi (1990), Schiffman, Reynolds, and Young (1981), van der Burg and de Leeuw (1983), Israels (1984), Breiman and Friedman (1985), and Hastie and Tibshirani (1986). (These are just a few of the many relevant sources.)