Statistics With SAS

Week 4

Stepwise Selection

/*st104d01.sas*/
  
%let interval=Gr_Liv_Area Basement_Area Garage_Area Deck_Porch_Area Lot_Area Age_Sold Bedroom_AbvGr Total_Bathroom;
/* Define a macro variable 'interval' to contain a list of predictor variables to be used in the analysis */

ods graphics on;
/* Turn on ODS graphics */

proc glmselect data=STAT1.ameshousing3 plots=all;
/* Start PROC GLMSELECT and specify the input data set 'STAT1.ameshousing3' and that all plots should be generated */

    STEPWISE: model SalePrice = &interval / selection=stepwise details=steps select=SL slstay=0.05 slentry=0.05;
    /* Perform stepwise regression using the 'SalePrice' variable as the response variable and the list of predictor variables in 'interval'.
     'selection=stepwise' specifies that stepwise regression is being used.
     'details=steps' requests detailed output of each step of the stepwise regression process.
     'select=SL' specifies that the significance level criterion for variable entry and removal is the SL criterion.
     'slstay=0.05' specifies that a variable must have a p-value less than or equal to 0.05 to remain in the model.
     'slentry=0.05' specifies that a variable must have a p-value less than or equal to 0.05 to be entered into the model. */

    title "Stepwise Model Selection for SalePrice - SL 0.05";
    /* Add a title to the output */

run;
/* End PROC GLMSELECT */

/*
Optional Code that will execute forward and backward selection
Each with slentry and slstay = 0.05.

proc glmselect data=STAT1.ameshousing3 plots=all;
    FORWARD: model SalePrice = &interval / selection=forward details=steps select=SL slentry=0.05;
    title "Forward Model Selection for SalePrice - SL 0.05";
run;

proc glmselect data=STAT1.ameshousing3 plots=all;
    BACKWARD: model SalePrice = &interval / selection=backward details=steps select=SL slstay=0.05;
    title "Backward Model Selection for SalePrice - SL 0.05";
run;
*/
/* This is optional code that performs forward and backward selection using similar options as in the stepwise regression, 
   but it is commented out. The 'forward' and 'backward' keywords indicate which type of selection is being performed. */

Result

/*st104s01.sas*/

/* Part A */
/* Turn on ODS graphics */
ods graphics on;
/* Start PROC GLMSELECT and specify the input data set 'STAT1.bodyfat2' and that all plots should be generated */
proc glmselect data=STAT1.bodyfat2 plots=all;
    /* Perform stepwise regression using the 'PctBodyFat2' variable as the response variable and the list of predictor variables.
     'selection=stepwise' specifies that stepwise regression is being used.
     'select=SL' specifies that the significance level criterion for variable entry and removal is the SL criterion. */
    STEPWISESL: model PctBodyFat2 = Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle Biceps Forearm Wrist / SELECTION=STEPWISE SELECT=SL;
    /* Add a title to the output */
    title 'SL STEPWISE Selection with PctBodyFat2';
/* End PROC GLMSELECT */
run;

/* Part B */
/* Start PROC GLMSELECT and specify the input data set 'STAT1.bodyfat2' and that all plots should be generated */
proc glmselect data=STAT1.bodyfat2 plots=all;
    /* Perform forward selection using the 'PctBodyFat2' variable as the response variable and the list of predictor variables.
     'selection=forward' specifies that forward selection is being used.
     'select=SL' specifies that the significance level criterion for variable entry and removal is the SL criterion. */
    FORWARDSL: model PctBodyFat2 = Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle Biceps Forearm Wrist / SELECTION=FORWARD SELECT=SL;
    /* Add a title to the output */
    title 'SL FORWARD Selection with PctBodyFat2';
/* End PROC GLMSELECT */
run;

/* Part C */
/* Start PROC GLMSELECT and specify the input data set 'STAT1.bodyfat2' and that all plots should be generated */
proc glmselect data=STAT1.bodyfat2 plots=all;
    /* Perform forward selection using the 'PctBodyFat2' variable as the response variable and the list of predictor variables.
     'selection=forward' specifies that forward selection is being used.
     'select=SL' specifies that the significance level criterion for variable entry and removal is the SL criterion.
     'slentry=0.05' specifies that a variable must have a p-value less than or equal to 0.05 to be entered into the model. */
    FORWARDSL: model PctBodyFat2 = Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle Biceps Forearm Wrist / SELECTION=FORWARD SELECT=SL SLENTRY=0.05;
    /* Add a title to the output */
    title 'SL FORWARD (0.05) Selection with PctBodyFat2';
/* End PROC GLMSELECT */
run;

Result

Information Criteria

/*st104s02.sas*/
  
/* Set the list of variables to use in the model */
%let interval=Gr_Liv_Area Basement_Area Garage_Area Deck_Porch_Area Lot_Area Age_Sold Bedroom_AbvGr Total_Bathroom;

/* Turn on ODS graphics */
ods graphics on;

/* Perform stepwise model selection using AIC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    /* Assign a name to this stepwise selection process (optional) */
    STEPWISEAIC: 
    /* Specify the response variable and the list of predictor variables */
    model SalePrice = &interval / selection=stepwise details=steps select=AIC;
    /* Assign a title to the output */
    title "Stepwise Model Selection for SalePrice - AIC";
run;

/* Perform stepwise model selection using BIC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    /* Assign a name to this stepwise selection process (optional) */
    STEPWISEBIC: 
    /* Specify the response variable and the list of predictor variables */
    model SalePrice = &interval / selection=stepwise details=steps select=BIC;
    /* Assign a title to the output */
    title "Stepwise Model Selection for SalePrice - BIC";
run;

/* Perform stepwise model selection using AICC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    /* Assign a name to this stepwise selection process (optional) */
    STEPWISEAICC: 
    /* Specify the response variable and the list of predictor variables */
    model SalePrice = &interval / selection=stepwise details=steps select=AICC;
    /* Assign a title to the output */
    title "Stepwise Model Selection for SalePrice - AICC";
run;

/* Perform stepwise model selection using SBC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    /* Assign a name to this stepwise selection process (optional) */
    STEPWISESBC: 
    /* Specify the response variable and the list of predictor variables */
    model SalePrice = &interval / selection=stepwise details=steps select=SBC;
    /* Assign a title to the output */
    title "Stepwise Model Selection for SalePrice - SBC";
run;

Result

/*st104d02.sas*/

/* Define a macro variable that contains the list of predictor variables */
%let interval=Gr_Liv_Area Basement_Area Garage_Area Deck_Porch_Area 
         Lot_Area Age_Sold Bedroom_AbvGr Total_Bathroom ;

/* Enable ODS graphics */
ods graphics on;

/* Run PROC GLMSELECT with stepwise selection and AIC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    STEPWISEAIC: model SalePrice = &interval / selection=stepwise details=steps select=AIC;
    title "Stepwise Model Selection for SalePrice - AIC";
run;

/* Run PROC GLMSELECT with stepwise selection and BIC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    STEPWISEBIC: model SalePrice = &interval / selection=stepwise details=steps select=BIC;
    title "Stepwise Model Selection for SalePrice - BIC";
run;

/* Run PROC GLMSELECT with stepwise selection and AICC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    STEPWISEAICC: model SalePrice = &interval / selection=stepwise details=steps select=AICC;
    title "Stepwise Model Selection for SalePrice - AICC";
run;

/* Run PROC GLMSELECT with stepwise selection and SBC as the selection criterion */
proc glmselect data=STAT1.ameshousing3 plots=all;
    STEPWISESBC: model SalePrice = &interval / selection=stepwise details=steps select=SBC;
    title "Stepwise Model Selection for SalePrice - SBC";
run;

Result

/* st104s03.sas */
/* Part A: */
/* Turning on imagemap for better visualization */
ods graphics / imagemap=on;

/* Using PROC REG for regression analysis with model selection based on Mallows Cp */
proc reg data=STAT1.BodyFat2 plots(only)=(cp);
   model PctBodyFat2=Age Weight Height
         Neck Chest Abdomen Hip Thigh
         Knee Ankle Biceps Forearm Wrist
         / selection=cp best=60; /* Cp-based model selection with 60 as the maximum number of variables */
   title "Using Mallows Cp for Model Selection"; /* Setting the title for the output */
run;
quit;

Result

Statistics With SAS - Week 4

Hao Sun

Week 4

Stepwise Selection

Information Criteria