1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 NOTE: ODS statements in the SAS Studio environment may disable some output features.
 73         
 74         /* mathlogreg1.sas */
 75         title2 'Logistic Regression on the Exploratory Math data';
 76         %include '/home/u1407221/441s24/SAS08/ReadLabelMath2.sas';
 NOTE: Format YNFMT is already on the library WORK.FORMATS.
 NOTE: Format YNFMT has been output.
 NOTE: Format CRSFMT is already on the library WORK.FORMATS.
 NOTE: Format CRSFMT has been output.
 NOTE: Format NFMT is already on the library WORK.FORMATS.
 NOTE: Format NFMT has been output.
 NOTE: Format NCFMT is already on the library WORK.FORMATS.
 NOTE: Format NCFMT has been output.
 
 NOTE: PROCEDURE FORMAT used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              257.46k
       OS Memory           28580.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        111  Switch Count  0
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       Page Reclaims                     19
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       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           32
       
 
 
 NOTE: The infile '/home/u1407221/441s24/data/math.data.txt' is:
       Filename=/home/u1407221/441s24/data/math.data.txt,
       Owner Name=u1407221,Group Name=oda,
       Access Permission=-rw-r--r--,
       Last Modified=10Feb2024:16:04:10,
       File Size (bytes)=90324
 
 NOTE: 1158 records were read from the infile '/home/u1407221/441s24/data/math.data.txt'.
       The minimum record length was 76.
       The maximum record length was 76.
 NOTE: Missing values were generated as a result of performing an operation on missing values.
       Each place is given by: (Number of times) at (Line):(Column).
       180 at 122:24   
 NOTE: The data set WORK.MATH has 1158 observations and 37 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              1193.96k
       OS Memory           29352.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        112  Switch Count  2
       Page Faults                       0
       Page Reclaims                     156
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       Voluntary Context Switches        19
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           776
       
 
 
 NOTE: There were 1158 observations read from the data set WORK.MATH.
 NOTE: The data set WORK.REPLIC has 579 observations and 37 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              1411.37k
       OS Memory           29740.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        113  Switch Count  2
       Page Faults                       0
       Page Reclaims                     140
       Page Swaps                        0
       Voluntary Context Switches        9
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           520
       
 
 
 NOTE: There were 1158 observations read from the data set WORK.MATH.
 NOTE: The data set WORK.EXPLORE has 579 observations and 28 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              1409.06k
       OS Memory           29740.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        114  Switch Count  2
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       Page Reclaims                     134
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       Involuntary Context Switches      0
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       Block Output Operations           520
       
 
 237        
 238        proc freq data=explore;
 239             title3 'Course by passed with proc freq';
 240             tables course2 * passed / nocol nopercent chisq;
 241        
 
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.05 seconds
       user cpu time       0.04 seconds
       system cpu time     0.01 seconds
       memory              3862.40k
       OS Memory           30896.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        115  Switch Count  5
       Page Faults                       0
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       Voluntary Context Switches        29
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           536
       
 
 242        proc logistic data=explore;
 243             title3 'Course by passed with dummy vars: Compare LR Chisq = 34.4171';
 244             model passed (event='Yes') = c1 c3; /* Omit c2 so Mainstream is reference category */
 245             /* Without proc format, (event='1') would work. */
 246             /* Wald chi-squared tests */
 247             course:       test c1=c3=0;
 248             Course1_vs_2: test c1=0;
 249             Course1_vs_3: test c1=c3;
 250             Course2_vs_3: test c3=0;
 251        
 252        /*
 253        Question: The estimated odds of passing the course are ___ times as great for a
 254                  student in the elite course, compared to a student in the mainstream course.
 255        
 256        Question: With 95% confidence, the chances of a student passing the catch-up
 257                  course are between ___% and ___% as great as the chances of passing the
 258                  mainstream course.
 259        
 260                  Note the deliberately vague but useful word "chances."
 261        
 262        > exp(-1.4838)
 263        [1] 0.2267743
 264        > A = -1.4838 - 1.96*0.3171; B = -1.4838 + 1.96*0.3171
 265        > exp(c(A,B))
 266        [1] 0.1218072 0.4221967
 267        
 268        
 269        A few details about the output :
 270        
 271             The higher the minus 2 Log Likelihood, the lower the (estimated) maximum
 272             probability of observing these responses. It is a meaure of lack of
 273             model fit. The Akaike information criterion and Schwarz's Bayesian
 274             criterion both impose a further penalty for number of explanatory
 275             variables. Small is good.
 276        
 277             "Association of Predicted Probabilities and Observed Responses":
 278                  * Every case has Y=0 or Y=1.
 279                  * Every case has a p-hat.
 280                  * Pick a case with Y=0, and another case with Y=1. That's a pair.
 281                  * If the case with Y=0 has a lower p-hat than the case with Y=1,
 282                    the pair is concordant.
 283        */
 284        
 
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.07 seconds
       user cpu time       0.07 seconds
       system cpu time     0.00 seconds
       memory              2649.12k
       OS Memory           32184.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        116  Switch Count  1
       Page Faults                       0
       Page Reclaims                     364
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       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           64
       
 
 285        proc iml;
 NOTE: IML Ready
 286             title3 'Estimate prob. of passing for for course=3: Compare 31/39 = 0.7949';
 287             b0 = 0.4077;
 287      !                   b1 = -1.4838;
 287      !                                 b2 = 0.9468;
 288             c1 = 0;
 288      !              c3=1;
 289             lcombo = b0 + b1*c1 + b2*c3;
 290             probpass = exp(lcombo) / (1+exp(lcombo));
 291             print "Estimated probability of passing course 3 (Elite) is " probpass;
 292        
 293        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              558.21k
       OS Memory           31140.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        117  Switch Count  1
       Page Faults                       0
       Page Reclaims                     97
       Page Swaps                        0
       Voluntary Context Switches        9
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           24
       
 
 294        proc logistic data=explore;
 295             title3 'Use the class and contrast statements';
 296             class course2 / param=ref;  /* This param option makes the ALPHABETICALLY
 297                                            last category (Mainstream) the reference
 298                                            category. Default is effect coding. */
 299             model passed (event='Yes') = course2;
 300             contrast 'Catch-up vs Mainstream' course2  1  0;
 301             contrast 'Elite vs Mainstream'    course2  0  1;
 302             contrast 'Catch-up vs Elite'      course2  1 -1;
 303        
 304        /* Contrast is a little tricky in proc logistic compared to proc glm.
 305           It lets you specify a set of linear combinations of regression
 306           coefficients to test against zero. It is essential to know exactly
 307           what the dummy variable coding scheme is. This can still be more
 308           convenient than defining your own dummy variables in the data step. */
 309        
 
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.07 seconds
       user cpu time       0.08 seconds
       system cpu time     0.00 seconds
       memory              2480.21k
       OS Memory           32440.00k
       Timestamp           02/29/2024 05:56:40 PM
       Step Count                        118  Switch Count  1
       Page Faults                       0
       Page Reclaims                     236
       Page Swaps                        0
       Voluntary Context Switches        11
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           64
       
 
 310        proc logistic data=explore;
 311             title3 'Course controlling for score on diagnostic test';
 312             class course2 / param=ref;
 313             model passed (event='Yes') = course2 totscore;
 314             contrast 'Course controlling for totscore' course2 1  0,
 315                                                        course2 0  1;
 316             contrast 'Catch-up vs. Elite controlling for totscore'
 317                                                        course2 1 -1;
 318        run;
 
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.09 seconds
       user cpu time       0.08 seconds
       system cpu time     0.00 seconds
       memory              2452.18k
       OS Memory           32440.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        119  Switch Count  1
       Page Faults                       0
       Page Reclaims                     198
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      3
       Block Input Operations            0
       Block Output Operations           88
       
 
 319        
 320        /* Estimate a probability of passing without typing in the
 321         * estimated regression coefficients: Use the Output Delivery
 322         * System (ODS). All the tables in a SAS results file have names.
 323         * You can find out what they are with a web search on
 324         * "proc logistic ods table names" , which will take you to the
 325         * manual. Easier is to do a preliminary run with ods trace on,
 326         * which writes the table names on the log file as they are produced.
 327         */
 328        
 329        ods trace on;
 330        proc logistic data=explore;
 331             title3 'What are the ods table names?';
 332             model passed (event='Yes') = c1 c3 totscore;
 333        run;
 
 
 Output Added:
 -------------
 Name:       ModelInfo
 Label:      Model Information
 Template:   Stat.Logistic.ModelInfo
 Path:       Logistic.ModelInfo
 -------------
 
 Output Added:
 -------------
 Name:       NObs
 Label:      Observations Summary
 Template:   Stat.Logistic.NObs
 Path:       Logistic.NObs
 -------------
 
 Output Added:
 -------------
 Name:       ResponseProfile
 Label:      Response Profile
 Template:   Stat.Logistic.ResponseProfile
 Path:       Logistic.ResponseProfile
 -------------
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 
 Output Added:
 -------------
 Name:       ConvergenceStatus
 Label:      Convergence Status
 Template:   Stat.Logistic.MConvergenceStatus
 Path:       Logistic.ConvergenceStatus
 -------------
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 
 Output Added:
 -------------
 Name:       FitStatistics
 Label:      Fit Statistics
 Template:   Stat.Logistic.FitStatistics
 Path:       Logistic.FitStatistics
 -------------
 
 Output Added:
 -------------
 Name:       GlobalTests
 Label:      Global Tests
 Template:   Stat.Logistic.GlobalTests
 Path:       Logistic.GlobalTests
 -------------
 
 Output Added:
 -------------
 Name:       ParameterEstimates
 Label:      Parameter Estimates
 Template:   Stat.Logistic.ParameterEstimates
 Path:       Logistic.ParameterEstimates
 -------------
 
 Output Added:
 -------------
 Name:       OddsRatios
 Label:      Odds Ratios
 Template:   Stat.Logistic.OddsRatios
 Path:       Logistic.OddsRatios
 -------------
 
 Output Added:
 -------------
 Name:       Association
 Label:      Association Statistics
 Template:   Stat.Logistic.Association
 Path:       Logistic.Association
 -------------
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.06 seconds
       user cpu time       0.07 seconds
       system cpu time     0.00 seconds
       memory              2344.28k
       OS Memory           32440.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        120  Switch Count  1
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       Voluntary Context Switches        9
       Involuntary Context Switches      0
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       Block Output Operations           64
       
 
 333      !      /* Need run with ods trace */
 334        ods trace off;
 335        
 336        ods output ParameterEstimates = estimout;
 337        /* The ParameterEstimates table will be written to a SAS data
 338           set called estimout. */
 339        proc logistic data=explore;
 340             title3 'Save parameter estimates in data set estimout using ods';
 341             model passed (event='Yes') = c1 c3 totscore;
 342        
 
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 NOTE: The data set WORK.ESTIMOUT has 4 observations and 7 variables.
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.06 seconds
       user cpu time       0.06 seconds
       system cpu time     0.01 seconds
       memory              2720.78k
       OS Memory           32700.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        121  Switch Count  3
       Page Faults                       0
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       Page Swaps                        0
       Voluntary Context Switches        27
       Involuntary Context Switches      1
       Block Input Operations            0
       Block Output Operations           320
       
 
 343        proc print data=estimout;
 344        
 
 NOTE: There were 4 observations read from the data set WORK.ESTIMOUT.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              687.93k
       OS Memory           31400.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        122  Switch Count  0
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       Page Reclaims                     65
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       Voluntary Context Switches        1
       Involuntary Context Switches      0
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       Block Output Operations           8
       
 
 345        proc iml;
 NOTE: IML Ready
 346             title3 'Estimated Probabilty of Passing';
 347             use estimout;
 348             read all var {Estimate} into b;
 349             print "Estimated regression coefficients";
 350             print b;
 351             /* Student in the catch-up class who got 10 right out of 20 */
 352             x1 = {1, 1, 0, 10};
 352      !                          /* Rows are separated by commas */
 353             pihat1 = exp(x1`*b)/(1+exp(x1`*b));
 354             print "Student in the catch-up class who got 10 right out of 20" pihat1;
 355             /* Student in the elite class who got all 20 right */
 356             x2 = {1, 0, 1, 20};
 356      !                          /* Rows are separated by commas */
 357             Pihat2 = exp(x2`*b)/(1+exp(x2`*b));
 358             print "Student in the elite class who got 20 right out of 20" pihat2;
 359        
 360        
 361        /********************** Output not shown ****************************/
 362        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              873.81k
       OS Memory           31656.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        123  Switch Count  1
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       Page Reclaims                     98
       Page Swaps                        0
       Voluntary Context Switches        12
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           16
       
 
 363        proc logistic data=explore noprint;
 364             title3 'Course controlling for score on diagnostic test';
 365             class course2 / param=ref;
 366             model passed (event='Yes') = course2 totscore;
 367             contrast 'Course controlling for totscore' course2     1  0,
 368                                                        course2     0  1 / e;
 369        /* The e option gives the "effect" matrix L in H0: L beta = 0 */
 370        
 
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              1808.21k
       OS Memory           32696.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        124  Switch Count  1
       Page Faults                       0
       Page Reclaims                     187
       Page Swaps                        0
       Voluntary Context Switches        9
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           32
       
 
 371        proc logistic data=explore noprint;
 372             title3 'Course controlling for score on diagnostic test';
 373             class course2 / param=ref;
 374             model passed (event='Yes') = course2 totscore;
 375             contrast 'Course controlling for totscore' course2 -19.7  0,
 376                                                        course2     0  9 / e;
 377        
 378        
 379        
 380        quit;
 
 NOTE: PROC LOGISTIC is modeling the probability that passed='Yes'.
 NOTE: Convergence criterion (GCONV=1E-8) satisfied.
 NOTE: There were 579 observations read from the data set WORK.EXPLORE.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              1808.00k
       OS Memory           32696.00k
       Timestamp           02/29/2024 05:56:41 PM
       Step Count                        125  Switch Count  1
       Page Faults                       0
       Page Reclaims                     189
       Page Swaps                        0
       Voluntary Context Switches        10
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           32
       
 
 381        
 382        
 383        /********************************************************************/
 384        
 385        
 386        
 387        
 388        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 400