MODEL
<transform(dependents </ toptions>)><transform(dependents </ toptions>)…=> transform(independents </ toptions>)<transform(independents </ toptions>)…> </ aoptions> ;
The MODEL statement specifies the dependent and independent variables (dependents and independents, respectively) and specifies the transformation (transform) to apply to each variable. Only one MODEL statement can appear in PROC TRANSREG. The toptions are transformation options, and the aoptions are algorithm options. The toptions provide details for the transformation; these depend on the transform chosen. The toptions are listed after a slash in the parentheses that enclose the variable list (either dependents or independents). The aoptions control the algorithm used, details of iteration, details of how the intercept and coded variables are generated, and displayed output details. The aoptions are listed after the entire model specification (the dependents, independents, transformations, and toptions) and after a slash. You can also specify the algorithm options in the PROC TRANSREG statement. When you specify the DESIGN ooption, dependents and an equal sign are not required. The operators *, , and @ from the GLM procedure are available for interactions with the CLASS expansion and the IDENTITY transformation. They are used as follows:
Class(a * b ... c  d ... e  f ... @ n) Identity(a * b ... c  d ... e  f ... @ n)
In addition, transformations and spline expansions can be crossed with classification variables as follows:
transform(var) * class(group)
transform(var)  class(group)
See the section Types of Effects in Chapter 44: The GLM Procedure, for a description of the @, *, and  operators and see the section Model Statement Usage for information about how to use these operators in PROC TRANSREG. Note that nesting is not implemented in PROC TRANSREG.
The next three sections discuss the transformations available (transforms) (see the section Families of Transformations), the transformation options (toptions) (see the section Transformation Options (toptions)), and the algorithm options (aoptions) (see the section Algorithm Options (aoptions)).
In the MODEL statement, transform specifies a transformation in one of the following five families:
preprocess the specified variables, replacing them with more variables.
preprocess the specified variables, replacing each one with a single new nonoptimal, nonlinear transformation.
preprocess the specified variable, replacing it with a smooth transformation, fitting one or more nonlinear functions through a scatter plot.
replace the specified variables with new, iteratively derived optimal transformation variables that fit the specified model better than the original variable (except for contrived cases where the transformation fits the model exactly as well as the original variable).
are the IDENTITY and SSPLINE transformations. These do not fit into the preceding categories.
The transformations and expansions listed in Table 101.2 are available in the MODEL statement.
Table 101.2: Transformation Families
Transformation 
Description 

Variable Expansions 

Bspline basis 

set of coded variables 

elliptical response surface 

circular response surface & PREFMAP 

piecewise polynomial basis 

quadratic response surface 

Nonoptimal Transformations 

inverse trigonometric sine 

exponential 

logarithm 

logit 

raises variables to specified power 

transforms to ranks 

Nonlinear Fit Transformations 

BoxCox 

penalized Bsplines 

noniterative smoothing spline 

Optimal Transformations 

linear 

monotonic, ties preserved 

monotonic Bspline 

optimal scoring 

Bspline 

monotonic, ties not preserved 

Other Transformations 

identity, no transformation 

iterative smoothing spline 
You can use any transformation with either dependent or independent variables (except the SMOOTH and PBSPLINE transformations, which can be used only with independent variables, and BOXCOX, which can be used only with dependent variables). However, the variable expansions are usually more appropriate for independent variables.
The transform is followed by a variable (or list of variables) enclosed in parentheses. Here is an example:
model log(y) = class(x);
This example finds a LOG transformation of y
and performs a CLASS expansion of x
. Optionally, depending on the transform, the parentheses can also contain toptions, which follow the variables and a slash. Here is an example:
model identity(y) = spline(x1 x2 / nknots=3);
The preceding statement finds SPLINE transformations of x1
and x2
. The NKNOTS= toption used with the SPLINE transformation specifies three knots. The identity(y)
transformation specifies that y
is not to be transformed.
The rest of this section provides syntax details for members of the five families of transformations listed at the beginning of this section. The toptions are discussed in the section Transformation Options (toptions).
PROC TRANSREG performs variable expansions before iteration begins. Variable expansions expand the original variables into
a typically larger set of new variables. The original variables are those that are listed in parentheses after transform, and they are sometimes referred to by the name of the transform. For example, in CLASS(x1 x2
), x1
and x2
are sometimes referred to as CLASS expansion variables or simply CLASS variables, and the expanded variables are referred
to as coded or sometimes “dummy” variables. Similarly, in POINT(Dim1 Dim2
), Dim1
and Dim2
are sometimes referred to as POINT variables.
The resulting variables are not transformed by the iterative algorithms after the initial preprocessing. Observations with missing values for these types of variables are excluded from the analysis.
The POINT, EPOINT, and QPOINT variable expansions are used in preference mapping analyses (also called PREFMAP, external unfolding, ideal point regression) (Carroll, 1972) and for response surface regressions. These three expansions create circular, elliptical, and quadratic response or preference surfaces (see the section Point Models and Example 101.6). The CLASS variable expansion is used for maineffects ANOVA.
The following list provides syntax and details for the variable expansion transforms.
The nonoptimal transformations, like the variable expansions, are computed before the iterative algorithm begins. Nonoptimal transformations create a single new transformed variable that replaces the original variable. The new variable is not transformed by the subsequent iterative algorithms (except for a possible linear transformation with missing value estimation). The following list provides syntax and details for nonoptimal variable transformations.
Nonlinear fit transformations, like nonoptimal transformations, are computed before the iterative algorithm begins. Nonlinear fit transformations create a single new transformed variable that replaces the original variable and provides one or more smooth functions through a scatter plot. The new variable is not transformed by the subsequent iterative algorithms. The nonlinear fit transformations, unlike the nonoptimal transformations, use information in the other variables in the model to find the transformations. The nonlinear fit transformations, unlike the optimal transformations, do not minimize a squarederror criterion. The following list provides syntax and details for nonoptimal variable transformations.
Optimal transformations are iteratively derived. Missing values for these types of variables can be optimally estimated (see the section Missing Values). The following list provides syntax and details for optimal transformations.
If you use a nonoptimal, nonlinear fit, optimal, or other transformation, you can use toptions, which specify additional details of the transformation. The toptions are specified within the parentheses that enclose variables and are listed after a slash. You can use toptions with both the dependent and the independent variables. Here is an example of using just one toption:
proc transreg; model identity(y)=spline(x / nknots=3); output; run;
The preceding statements find an optimal variable transformation (SPLINE) of the independent variable, and they use a toption to specify the number of knots (NKNOTS=). The following is a more complex example:
proc transreg; model mspline(y / nknots=3)=class(x1 x2 / effects); output; run;
These statements find a monotone spline transformation (MSPLINE with three knots) of the dependent variable and perform a CLASS expansion with effects coding of the independents.
Table 101.3 summarizes the toptions available in the MODEL statement.
Table 101.3: Transformation Options
Option 
Description 

Nonoptimal Transformation 

Uses original mean and variance 

Parameter Specification 

Specifies miscellaneous parameters 

Specifies smoothing parameter 

Penalized BSpline 

Uses Akaike’s information criterion 

Uses corrected AIC 

Uses cross validation criterion 

Uses generalized cross validation criterion 

Specifies smoothing parameter list or range 

Specifies a LAMBDA= range, not a list 

Uses Schwarz’s Bayesian criterion 

Spline 

Specifies the degree of the spline 

Spaces the knots evenly 

Specifies exterior knots 

Specifies the interior knots or break points 

Creates n knots 

CLASS Variable 

Specifies CLASS coded variable name prefix 

Specifies a deviationsfrommeans coding 

Specifies a deviationsfrommeans coding 

Specifies CLASS coded variable label prefix 

Specifies order of CLASS variable levels 

Specifies an orthogonalcontrast coding 

Specifies CLASS coded variable label separators 

Specifies a standardizedorthogonal coding 

Controls reference levels 

BoxCox 

Specifies confidence interval alpha 

Specifies convenient lambda list 

Uses a convenient lambda 

Scales transformation using geometric mean 

Specifies power parameter list 

Other toptions 

Specifies operations occur after the expansion 

Specifies center before the analysis begins 

Renames variables 

Reflects the variable around the mean 

Specifies transformation standardization 

Standardizes before the analysis begins 
The following sections discuss the toptions available for nonoptimal, nonlinear fit, optimal, and other transformations.
The following toptions are available with the SPLINE, MSPLINE and PBSPLINE transformations and with the PSPLINE and BSPLINE expansions.
The following toptions are available only with the BOXCOX transformation of the dependent variable (see the section BoxCox Transformations and Example 101.2).
This section discusses the options that can appear in the PROC TRANSREG or MODEL statement as aoptions. They are listed after the entire model specification and after a slash. Here is an example:
proc transreg; model spline(y / nknots=3)=log(x1 x2 / parameter=2) / nomiss maxiter=50; output; run;
In the preceding statements, NOMISS and MAXITER= are aoptions. (SPLINE and LOG are transforms, and NKNOTS= and PARAMETER= are toptions.) The statements find a spline transformation with 3 knots on y
and a base 2 logarithmic transformation on x1
and x2
. The NOMISS aoption excludes all observations with missing values, and the MAXITER= aoption specifies the maximum number of iterations.
Table 101.4 summarizes the aoptions available in the PROC TRANSREG or MODEL statement.
Table 101.4: Options Available in the PROC TRANSREG or MODEL Statement
Option 
Description 

Input Control 

Restarts iterations 

Specifies input observation type 

Method and Iterations 

Specifies minimum criterion change 

Specifies minimum data change 

Specifies maximum number of iterations 

Specifies iterative algorithm 

Specifies number of canonical variables 

Specifies no restrictions on smoothing models 

Specifies singularity criterion 

Attempts direct solution instead of iteration 

Missing Data Handling 

Fits each model individually (METHOD=MORALS) 

Includes monotone special missing values 

Excludes observations with missing values 

Unties special missing values 

Intercept and CLASS Variables 

Specifies CLASS coded variable name prefix 

Specifies CLASS coded variable label prefix 

Specifies no intercept or centering 

Specifies order of CLASS variable levels 

Controls output of reference levels 

Specifies CLASS coded variable label separators 

Control Displayed Output 

Specifies confidence limits alpha 

Displays parameter estimate confidence limits 

Displays model specification details 

Displays iteration histories 

Suppresses displayed output 

Prints the BoxCox log likelihood table 

Displays the R square 

Suppresses the iteration histories 

Displays regression results 

Displays ANOVA table 

Shortens transformed variable labels 

Displays conjoint partworth utilities 

Standardization 

Fits additive model 

Does not zero constant variables 

Specifies transformation standardization 
The following list provides details about these aoptions. The aoptions are available in the PROC TRANSREG or MODEL statement.