The TRANSREG Procedure

## Output Data Set

The OUT= output data set can contain a great deal of information; however, in most cases, the output data set contains a small portion of the entire range of available information and is organized for direct input into the %PLOTIT macro or graphical or analysis procedures. For information on the %PLOTIT macro, see Appendix B, "Using the %PLOTIT Macro."

### Output Data Set Examples

The next section provides a complete list of the contents of the OUT= data set. However, before presenting complete details, this section provides three brief examples, illustrating some typical output data sets.

The first example shows the output data set from a two-way ANOVA model. The following statements produce Figure 65.12:

```   title 'ANOVA Output Data Set Example';

data ReferenceCell;
input Y X1 \$ X2 \$;
datalines;
11  a  a
12  a  a
10  a  a
4  a  b
5  a  b
3  a  b
5  b  a
6  b  a
4  b  a
2  b  b
3  b  b
1  b  b
;

*---Fit Reference Cell Two-Way ANOVA Model---;
proc transreg data=ReferenceCell;
model identity(Y) = class(X1 | X2);
output coefficients replace predicted residuals;
run;

*---Print the Results---;
proc print;
run;

proc contents position;
ods select position;
run;
```

 ANOVA Output Data Set Example

 Obs _TYPE_ _NAME_ Y PY RY Intercept X1a X2a X1aX2a X1 X2 1 SCORE ROW1 11 11 0 1 1.0 1 1 a a 2 SCORE ROW2 12 11 1 1 1.0 1 1 a a 3 SCORE ROW3 10 11 -1 1 1.0 1 1 a a 4 SCORE ROW4 4 4 0 1 1.0 0 0 a b 5 SCORE ROW5 5 4 1 1 1.0 0 0 a b 6 SCORE ROW6 3 4 -1 1 1.0 0 0 a b 7 SCORE ROW7 5 5 0 1 0.0 1 0 b a 8 SCORE ROW8 6 5 1 1 0.0 1 0 b a 9 SCORE ROW9 4 5 -1 1 0.0 1 0 b a 10 SCORE ROW10 2 2 0 1 0.0 0 0 b b 11 SCORE ROW11 3 2 1 1 0.0 0 0 b b 12 SCORE ROW12 1 2 -1 1 0.0 0 0 b b 13 M COEFFI Y . . . 2 2.0 3 4 14 MEAN Y . . . . 7.5 8 11

 ANOVA Output Data Set Example

 The CONTENTS Procedure

 -----Variables Ordered by Position----- # Variable Type Len Pos Label 1 _TYPE_ Char 8 56 2 _NAME_ Char 32 64 3 Y Num 8 0 4 PY Num 8 8 Y Predicted Values 5 RY Num 8 16 Y Residuals 6 Intercept Num 8 24 Intercept 7 X1a Num 8 32 X1 a 8 X2a Num 8 40 X2 a 9 X1aX2a Num 8 48 X1 a * X2 a 10 X1 Char 8 96 11 X2 Char 8 104

Figure 65.12: ANOVA Example Output Data Set Contents

The _TYPE_ variable indicates observation type: score, multiple regression coefficient (parameter estimates), and marginal means. The _NAME_ variable contains the default observation labels, "ROW1", "ROW2", and so on, and contains the dependent variable name (Y) for the remaining observations. If you specify an ID statement, _NAME_ contains the values of the first ID variable for score observations. The Y variable is the dependent variable, PY contains the predicted values, RY contains the residuals, and the variables Intercept through X1aX2a contain the design matrix. The X1 and X2 variables are the original CLASS variables.

The next example shows the contents of the output data set from fitting a curve through a scatter plot.

```   title 'Output Data Set for Curve Fitting Example';

data A;
do X = 1 to 100;
Y = log(x) + sin(x / 10) + normal(7);
output;
end;
run;

proc transreg;
model identity(Y) = spline(X / nknots=9);
output predicted out=B;
run;

proc contents position;
ods select position;
run;
```

These statements produce Figure 65.13.

 Output Data Set for Curve Fitting Example

 The CONTENTS Procedure

 -----Variables Ordered by Position----- # Variable Type Len Pos Label 1 _TYPE_ Char 8 56 2 _NAME_ Char 32 64 3 Y Num 8 0 4 TY Num 8 8 Y Transformation 5 PY Num 8 16 Y Predicted Values 6 Intercept Num 8 24 Intercept 7 X Num 8 32 8 TIntercept Num 8 40 Intercept Transformation 9 TX Num 8 48 X Transformation

Figure 65.13: Predicted Values Example Output Data Set Contents

The OUT= data set contains _TYPE_ and _NAME_ variables. Since no coefficients or coordinates are requested, all observations are _TYPE_='SCORE'. The Y variable is the original dependent variable, TY is the transformed dependent variable, PY contains the predicted values, X is the original independent variable, and TX is the transformed independent variable. The data set also contains an Intercept and transformed intercept TIntercept variable. (In this case, the transformed intercept is the same as the intercept. However, if you specify the TSTANDARD= and ADDITIVE options, these are not always the same.)

The next example shows the results from specifying METHOD=MORALS when there is more than one dependent variable.

```   title 'METHOD=MORALS Output Data Set Example';

data x;
input Y1 Y2 X1 \$ X2 \$;
datalines;
11 1 a a
10 4 b a
5 2 a b
5 9 b b
4 3 c c
3 6 b a
1 8 a b
;

*---Fit Reference Cell Two-Way ANOVA Model---;
proc transreg data=x noprint dummy;
model spline(Y1 Y2) = opscore(X1 X2 / name=(N1 N2));
output coefficients predicted residuals;
id x1 x2;
run;

*---Print the Results---;
proc print;
run;

proc contents position;
ods select position;
run;
```

These statements produce Figure 65.14.

 METHOD=MORALS Output Data Set Example

 Obs _DEPVAR_ _TYPE_ _NAME_ _DEPEND_ T_DEPEND_ P_DEPEND_ R_DEPEND_ Intercept N1 N2 TIntercept TN1 TN2 X1 X2 1 Spline(Y1) SCORE a 11 13.1600 11.1554 2.00464 1 0 0 1.0000 0.06711 -0.09384 a a 2 Spline(Y1) SCORE b 10 6.1931 6.8835 -0.69041 1 1 0 1.0000 1.51978 -0.09384 b a 3 Spline(Y1) SCORE a 5 2.4467 4.7140 -2.26724 1 0 1 1.0000 0.06711 1.32038 a b 4 Spline(Y1) SCORE b 5 2.4467 0.4421 2.00464 1 1 1 1.0000 1.51978 1.32038 b b 5 Spline(Y1) SCORE c 4 4.2076 4.2076 -0.00000 1 2 2 1.0000 0.23932 1.32038 c c 6 Spline(Y1) SCORE b 3 5.5693 6.8835 -1.31422 1 1 0 1.0000 1.51978 -0.09384 b a 7 Spline(Y1) SCORE a 1 4.9766 4.7140 0.26261 1 0 1 1.0000 0.06711 1.32038 a b 8 Spline(Y1) M COEFFI Y1 . . . . . . . 10.9253 -2.94071 -4.55475 Y1 Y1 9 Spline(Y2) SCORE a 1 -0.5303 -0.5199 -0.01043 1 0 0 1.0000 0.03739 -0.09384 a a 10 Spline(Y2) SCORE b 4 5.5487 4.5689 0.97988 1 1 0 1.0000 1.51395 -0.09384 b a 11 Spline(Y2) SCORE a 2 3.8940 4.5575 -0.66347 1 0 1 1.0000 0.03739 1.32038 a b 12 Spline(Y2) SCORE b 9 9.6358 9.6462 -0.01043 1 1 1 1.0000 1.51395 1.32038 b b 13 Spline(Y2) SCORE c 3 5.6210 5.6210 0.00000 1 2 2 1.0000 0.34598 1.32038 c c 14 Spline(Y2) SCORE b 6 3.5994 4.5689 -0.96945 1 1 0 1.0000 1.51395 -0.09384 b a 15 Spline(Y2) SCORE a 8 5.2314 4.5575 0.67390 1 0 1 1.0000 0.03739 1.32038 a b 16 Spline(Y2) M COEFFI Y2 . . . . . . . -0.3119 3.44636 3.59024 Y2 Y2

 METHOD=MORALS Output Data Set Example

 The CONTENTS Procedure

 -----Variables Ordered by Position----- # Variable Type Len Pos Label 1 _DEPVAR_ Char 42 80 Dependent Variable Transformation(Name) 2 _TYPE_ Char 8 122 3 _NAME_ Char 32 130 4 _DEPEND_ Num 8 0 Dependent Variable 5 T_DEPEND_ Num 8 8 Dependent Variable Transformation 6 P_DEPEND_ Num 8 16 Dependent Variable Predicted Values 7 R_DEPEND_ Num 8 24 Dependent Variable Residuals 8 Intercept Num 8 32 Intercept 9 N1 Num 8 40 10 N2 Num 8 48 11 TIntercept Num 8 56 Intercept Transformation 12 TN1 Num 8 64 N1 Transformation 13 TN2 Num 8 72 N2 Transformation 14 X1 Char 8 162 15 X2 Char 8 170

Figure 65.14: METHOD=MORALS Rolled Output Data Set

If you specify METHOD=MORALS with multiple dependent variables, PROC TRANSREG performs separate univariate analyses and stacks the results in the OUT= data set. For this example, the results of the first analysis are in the partition designated by _DEPVAR_='Spline(Y1)' and the results of the first analysis are in the partition designated by _DEPVAR_='Spline(Y2)', which are the transformation and dependent variable names. Each partition has _TYPE_='SCORE' observations for the variables and a _TYPE_='M COEFFI' observation for the coefficients. In this example, an ID variable is specified, so the _NAME_ variable contains the formatted values of the first ID variable. Since both dependent variables have to go into the same column, the dependent variable is given a new name, _DEPEND_. The dependent variable transformation is named T_DEPEND_, the predicted values variable is named P_DEPEND_, and the residuals variable is named R_DEPEND_.

The independent variables are character OPSCORE variables. By default, PROC TRANSREG replaces character OPSCORE variables with category numbers and discards the original character variables. To avoid this, the input variables are renamed from X1 and X2 to N1 and N2 and the original X1 and X2 are added to the data set as ID variables. The N1 and N2 variables contain the initial values for the OPSCORE transformations, and the TN1 and TN2 variables contain optimal scores. The data set also contains an Intercept and transformed intercept TIntercept variable. The regression coefficients are in the transformation columns, which also contain the variables to which they apply.

### Output Data Set Contents

This section presents the various matrices that can result from PROC TRANSREG processing and that appear in the OUT= data set. The exact contents of an OUT= data set depends on many options.

Table 65.6: PROC TRANSREG OUT= Data Set Contents
 _TYPE_ Contents Options, Default Prefix SCORE dependent variables DREPLACE not specified SCORE independent variables IREPLACE not specified SCORE transformed dependent variables default, TDPREFIX=T SCORE transformed independent variables default, TIPREFIX=T SCORE predicted values PREDICTED, PPREFIX=P SCORE residuals RESIDUALS, RDPREFIX=R SCORE leverage LEVERAGE, LEVERAGE=Leverage SCORE lower individual confidence limits CLI, LILPREFIX=LIL, CILPREFIX=CIL SCORE upper individual confidence limits CLI, LIUPREFIX=LIU, CIUPREFIX=CIU SCORE lower mean confidence limits CLM, LMLPREFIX=LML, CMLPREFIX=CML SCORE upper mean confidence limits CLM, LMUPREFIX=LMU, CMUPREFIX=CMU SCORE dependent canonical variables CANONICAL, CDPREFIX=Cand SCORE independent canonical variables CANONICAL, CIPREFIX=Cani SCORE redundancy variables REDUNDANCY, RPREFIX=Red SCORE ID, CLASS, BSPLINE variables ID, CLASS, BSPLINE, SCORE independent variables approximations IAPPROXIMATIONS, IAPREFIX=A M COEFFI multiple regression coefficients COEFFICIENTS, MRC C COEFFI canonical coefficients COEFFICIENTS, CCC MEAN marginal means COEFFICIENTS, MEANS M REDUND multiple redundancy coefficients MREDUNDANCY R REDUND multiple redundancy coefficients MREDUNDANCY M POINT point coordinates COORDINATES or MPC, POINT M EPOINT elliptical point coordinates COORDINATES or MEC, EPOINT M QPOINT quadratic point coordinates COORDINATES or MQC, QPOINT C POINT canonical point coordinates COORDINATES or CPC, POINT C EPOINT canonical elliptical point coordinates COORDINATES or CEC, EPOINT C QPOINT canonical quadratic point coordinates COORDINATES or CQC, QPOINT

The independent and dependent variables are created from the original input data. Several potential differences exist between these variables and the actual input data. An intercept variable can be added, new variables can be added for POINT, EPOINT, QPOINT, CLASS, IDENTITY, PSPLINE, and BSPLINE variables, and category numbers are substituted for character OPSCORE variables. These matrices are not always what is input to the first iteration. After the expanded data set is stored for inclusion in the output data set, several things happen to the data before they are input to the first iteration: column means are substituted for missing values; zero degree SPLINE and MSPLINE variables are transformed so that the iterative algorithms get step function data as input, which conform to the zero degree transformation family restrictions; and the nonoptimal transformations are performed.

#### Details for the UNIVARIATE Method

When you specify METHOD=UNIVARIATE (in the MODEL or PROC TRANSREG statement), PROC TRANSREG can perform several analyses, one for each dependent variable. While each dependent variable can be transformed, their independent variables are not transformed. The OUT= data set optionally contains all of the _TYPE_='SCORE' observations, optionally followed by coefficients or coordinates.

#### Details for the MORALS Method

When you specify METHOD=MORALS (in the MODEL or PROC TRANSREG statement), successive analyses are performed, one for each dependent variable. Each analysis transforms one dependent variable and the entire set of the independent variables. All information for the first dependent variable (scores then, optionally, coefficients) appear first. Then all information for the second dependent variable (scores then, optionally, coefficients) appear next. This arrangement is repeated for all dependent variables.

#### Details for the CANALS and REDUNDANCY Methods

For METHOD=CANALS and METHOD=REDUNDANCY (specified in either the MODEL or PROC TRANSREG statement), one analysis is performed that simultaneously transforms all dependent and independent variables. The OUT= data set optionally contains all of the _TYPE_='SCORE' observations, optionally followed by coefficients or coordinates.

### Variable Names

As shown in the preceding examples, some variables in the output data set directly correspond to input variables and some are created. All original optimal and nonoptimal transformation variable names are unchanged.

The names of the POINT, QPOINT, and EPOINT expansion variables are also left unchanged, but new variables are created. When independent POINT variables are present, the sum-of-squares variable _ISSQ_ is added to the output data set. For each EPOINT and QPOINT variable, a new squared variable is created by appending "_2". For example, Dim1 and Dim2 are expanded into Dim1, Dim2, Dim1_2, and Dim2_2. In addition, for each pair of QPOINT variables, a new crossproduct variable is created by combining the two names, for example, Dim1Dim2.

The names of the CLASS variables are constructed from original variable names and levels. Lengths are controlled by the CPREFIX= a-option. For example, when X1 and X2 both have values of 'a' and 'b', CLASS(X1 | X2 / ZERO=NONE) creates X1 main effect variable names X1a X1b, X2 main effect variable names X2a X2b, and interaction variable names X1aX2a X1aX2b X1bX2a X1bX2b.

PROC TRANSREG then uses these variable names when creating the transformed, predicted, and residual variable names by affixing the relevant prefix and possibly dropping extra characters.

#### METHOD=MORALS Variable Names

When you specify METHOD=MORALS and only one dependent variable is present, the output data set is structured exactly as if METHOD=REDUNDANCY (see the section "Details for the CANALS and REDUNDANCY Methods"). When more than one dependent variable is present, the dependent variables are output in the variable _DEPEND_, transformed dependent variables are output in the variable T_DEPEND_, predicted values are output in the variable P_DEPEND_, and residuals are output in the variable R_DEPEND_. You can partition the data set into BY groups, one per dependent variable, by referring to the character variable _DEPVAR_, which contains the original dependent variable names and transformations.

#### Duplicate Variable Names

When the same name is generated from multiple variables in the OUT= data set, new names are created by appending "2", "3", or "4", and so on, until a unique name is created. For 32-character names, the last character is replaced with a numeric suffix until a unique name is created. For example, if there are two output variables that otherwise would be named X, then X and X2 are created instead. If there are two output variables that otherwise would be named ThisIsAThirtyTwoCharacterVarName, then ThisIsAThirtyTwoCharacterVarName and ThisIsAThirtyTwoCharacterVarNam2 are created instead.