24986 - All-possible-regressions selection based on PRESS or other statistics

Sample 24986: All-possible-regressions selection based on PRESS or other statistics

All-possible-regressions selection based on PRESS or other statistics

Contents:

Purpose / History / Requirements / Usage / Details / Limitations

PURPOSE:

Provide all-possible-regressions model-selection based on the SELECTION= RSQUARE, ADJRSQ, and CP and display any of the following model statistics: Mallows' C_p (_CP_), predicted residual sum of squares (_PRESS_), root mean square error (_RMSE_), mean square error (_MSE_), R² (_RSQ_), adjusted R² (_ADJRSQ_), Akaike's information criterion (_AIC_), Sawa's Bayesian information criterion (_BIC_), or Schwarz's Bayesian criterion (_SBC_).

HISTORY:

Version 1.1: Merged all code into single macro. Added print= and out= parameters. Fixed data= so that it analyzes last-created data set.

REQUIREMENTS:

SAS 8 or later of Base SAS and SAS/STAT Software.

USAGE:

Follow the instructions in the Downloads tab of this sample to save the %ALLSUBSREG macro definition. Replace the text within quotes in the following statement with the location of the %ALLSUBSREG macro definition file on your system. In your SAS program or in the SAS editor window, specify this statement to define the %ALLSUBSREG macro and make it available for use:

   %inc "<location of your file containing the ALLSUBSREG macro>";

Following this statement, you may call the %ALLSUBSREG macro. See the Results tab for an example.

The following macro parameters are required:

depvar=: The name of the dependent (response) variable.
indepvar=: The names of the independent variables, separated by spaces.

The following macro parameters are optional:

data=

The name of the input data set to be analyzed. If not specified, the last-created data set will be analyzed.

out=

The name of the output data set containing the statistics for all models. If not specified, the data set name is _FINAL.

method=RSQUARE | ADJRSQ | CP

The type of the all-subset model-selection method to be used in the regression analysis. One of the following three methods can be specified: RSQUARE, ADJRSQ, or CP. RSQUARE is the default.

print=yes | no

Indicates if all models and related statistics should be displayed. The default is yes. The results are displayed by model size.

sortvar=

The name of the variable by which the model statistics table should be sorted within each model size. By default, the table is sorted by increasing model size (the number of variables in the model, _IN_). If sortvar= is specified, the table is further sorted within model size by descending value of the specified variable. The sortvar= parameter may be one of these model statistics:

    _P_ _CP_ _PRESS_ _RMSE_ _MSE_ _RSQ_ _ADJRSQ_ 
    _AIC_ _BIC_ _SBC_

printvar=

The names of the model statistics to be displayed in the model statistics table. printvar= is ignored if print=no. If not specified, the final table displays VarsInModel, _IN_, all model statistics, and parameter estimates. The printvar= parameter allows you to select the model statistics displayed in the table. One or more of the following may be specified, separated by spaces:

    _P_ _CP_ _PRESS_ _RMSE_ _MSE_ _RSQ_ _ADJRSQ_ 
    _AIC_ _BIC_ _SBC_

DETAILS:

PROC REG provides all possible regression methods such as SELECTION= RSQUARE, ADJRSQ, CP. The RSQUARE method can efficiently perform all possible subset regressions and display the models in decreasing order of rsquare magnitude within each subset size. Other statistics such as CP, RMSE, MSE, RSQ, ADJRSQ, AIC, BIC, and SBC are available for comparing subsets of different sizes. These statistics, the PRESS statistic, and the estimated regression coefficients can be displayed or output to a SAS data set.

LIMITATIONS:

CLASS variables are not supported. The absolute PRESS statistic is not provided. Note that all possible regression methods can be very resource intensive and should only be used with a relatively small number of potential regressors.

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

EXAMPLE:

The following example requests all possible subset models of six regressors to be sorted by model size and decreasing PRESS statistic value.

data fitness;
      input Age Weight Oxygen RunTime RestPulse RunPulse MaxPulse @@;
      datalines;
   44 89.47 44.609 11.37 62 178 182   40 75.07 45.313 10.07 62 185 185
   44 85.84 54.297  8.65 45 156 168   42 68.15 59.571  8.17 40 166 172
   38 89.02 49.874  9.22 55 178 180   47 77.45 44.811 11.63 58 176 176
   40 75.98 45.681 11.95 70 176 180   43 81.19 49.091 10.85 64 162 170
   44 81.42 39.442 13.08 63 174 176   38 81.87 60.055  8.63 48 170 186
   44 73.03 50.541 10.13 45 168 168   45 87.66 37.388 14.03 56 186 192
   45 66.45 44.754 11.12 51 176 176   47 79.15 47.273 10.60 47 162 164
   54 83.12 51.855 10.33 50 166 170   49 81.42 49.156  8.95 44 180 185
   51 69.63 40.836 10.95 57 168 172   51 77.91 46.672 10.00 48 162 168
   48 91.63 46.774 10.25 48 162 164   49 73.37 50.388 10.08 67 168 168
   57 73.37 39.407 12.63 58 174 176   54 79.38 46.080 11.17 62 156 165
   52 76.32 45.441  9.63 48 164 166   50 70.87 54.625  8.92 48 146 155
   51 67.25 45.118 11.08 48 172 172   54 91.63 39.203 12.88 44 168 172
   51 73.71 45.790 10.47 59 186 188   57 59.08 50.545  9.93 49 148 155
   49 76.32 48.673  9.40 56 186 188   48 61.24 47.920 11.50 52 170 176
   52 82.78 47.467 10.50 53 170 172
   ;

%inc "<location of your file containing the ALLSUBSREG macro>";
%allsubsreg(data=fitness,
            depvar=oxygen,
            indepvar=age weight runtime restpulse runpulse maxpulse,
            sortvar=_press_,
            printvar=_P_ _CP_ _PRESS_ _RMSE_ _MSE_ _RSQ_ _ADJRSQ_ _AIC_ 
                     _BIC_ _SBC_
           );

RESULTS:

Following are partial results from the statements above showing the results for the single-regressor models.

                       All Possible Subset Models Sorted by _press_

---------------------------- Number of regressors in model=1 -----------------------------

     VarsIn
 Obs Model     _IN_ _P_   _CP_  _PRESS_  _RMSE_  _MSE_   _RSQ_  _ADJRSQ_  _AIC_   _BIC_

   1 Weight      1   2  127.395 943.165 5.34606 28.5803 0.02649 -0.00708 105.867 103.392
   2 MaxPulse    1   2  122.707 925.401 5.26427 27.7126 0.05605  0.02350 104.911 102.482
   3 Age         1   2  116.882 906.968 5.16084 26.6343 0.09278  0.06149 103.681 101.312
   4 RestPulse   1   2  106.302 834.260 4.96748 24.6758 0.15949  0.13050 101.313  99.065
   5 RunPulse    1   2  106.477 794.646 4.97073 24.7082 0.15838  0.12936 101.354  99.104
   6 RunTime     1   2   13.699 250.901 2.74478  7.5338 0.74338  0.73453  64.534  65.467

                                                         Rest
 Obs  _SBC_   Intercept     Age     Weight    RunTime    Pulse   RunPulse  MaxPulse

   1 108.735   55.4379     .       -0.10410    .         .         .         .
   2 107.779   71.2907     .         .         .         .         .       -0.13762
   3 106.549   62.2206   -0.31136    .         .         .         .         .
   4 104.181   62.3003     .         .         .       -0.27921    .         .
   5 104.222   82.4582     .         .         .         .       -0.20680    .
   6  67.402   82.4218     .         .       -3.31056    .         .         .

Provide all-possible-regressions model-selection based on the SELECTION= RSQUARE, ADJRSQ, and CP and display any of the following model statistics:

_CP_ _PRESS_ _RMSE_ _MSE_ _RSQ_ _ADJRSQ_ _AIC_ _BIC_ _SBC_

Type:	Sample
Topic:	Analytics ==> Multivariate Analysis SAS Reference ==> Procedures ==> REG Analytics ==> Regression

Date Modified:	2016-06-02 11:18:23
Date Created:	2005-01-13 15:02:49

Operating System and Release Information

Product Family	Product	Host	SAS Release
Product Family	Product	Host	Starting	Ending
SAS System	SAS/STAT	AIX
		ABI+ for Intel Architecture
		64-bit Enabled Solaris
		64-bit Enabled HP-UX
		64-bit Enabled AIX
		Windows Vista for x64
		Windows Vista
		Windows Millennium Edition (Me)
		Windows 7 Ultimate x64
		Windows 7 Ultimate 32 bit
		Windows 7 Professional x64
		Windows 7 Professional 32 bit
		Windows 7 Home Premium x64
		Windows 7 Home Premium 32 bit
		Windows 7 Enterprise x64
		Windows 7 Enterprise 32 bit
		Microsoft Windows XP Professional
		Microsoft Windows Server 2012 Std
		Microsoft Windows Server 2012 R2 Std
		Microsoft Windows Server 2012 R2 Datacenter
		Microsoft Windows Server 2012 Datacenter
		Microsoft Windows Server 2008 for x64
		Microsoft Windows Server 2008 R2
		Microsoft Windows Server 2008
		Microsoft Windows Server 2003 for x64
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows NT Workstation
		Microsoft Windows 2000 Professional
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 95/98
		Microsoft Windows 10
		Microsoft Windows 8.1 Pro x64
		Microsoft Windows 8.1 Pro 32-bit
		Microsoft Windows 8.1 Enterprise x64
		Microsoft Windows 8.1 Enterprise 32-bit
		Microsoft Windows 8 Pro x64
		Microsoft Windows 8 Pro 32-bit
		Microsoft Windows 8 Enterprise x64
		Microsoft Windows 8 Enterprise 32-bit
		OS/2
		Microsoft® Windows® for x64
		Microsoft Windows XP 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		OpenVMS VAX
		z/OS 64-bit
		z/OS
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux for x64
		Linux on Itanium
		OpenVMS Alpha
		OpenVMS on HP Integrity
		Solaris
		Solaris for x64
		Tru64 UNIX

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Sample 24986: All-possible-regressions selection based on PRESS or other statistics

All-possible-regressions selection based on PRESS or other statistics

Operating System and Release Information