1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 55         
 56         /* MathLogReg1.sas  */
 57         %include '/folders/myfolders/441s16/Lecture/readmath2b.sas';
 NOTE: Format YNFMT has been output.
 NOTE: Format CRSFMT has been output.
 NOTE: Format NFMT has been output.
 
 NOTE: PROCEDURE FORMAT used (Total process time):
       real time           0.03 seconds
       cpu time            0.01 seconds
       
 
 166        title2 'Logistic Regression with dummy variables on the Math data';
 167        
 168        /* Recall definition of passed
 169             if (50<=mark<=100) then passed=1; else passed=0;
 170        
 171         And
 172        
 173        if course=4 then course2=.; else course2=course;
 174        
 175        if course2=. then c1=.; else if course2=1 then c1=1; else c1=0;
 176        if course2=. then c2=.; else if course2=2 then c2=1; else c2=0;
 177        if course2=. then c3=.; else if course2=3 then c3=1; else c3=0;
 178        label c1 = 'Catch-up' c2 = 'Mainstream' c3 = 'Elite';
 179         */
 180        
 181        
 
 NOTE: The infile '/folders/myfolders/exploremath.data.txt' is:
       Filename=/folders/myfolders/exploremath.data.txt,
       Owner Name=root,Group Name=vboxsf,
       Access Permission=-rwxrwx---,
       Last Modified=18Jan2016:17:34:49,
       File Size (bytes)=44583
 
 NOTE: 579 records were read from the infile '/folders/myfolders/exploremath.data.txt'.
       The minimum record length was 75.
       The maximum record length was 75.
 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).
       99 at 80:24    99 at 117:13   
 NOTE: The data set WORK.MATHEX has 579 observations and 34 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.05 seconds
       cpu time            0.05 seconds
       
 182        proc freq;
 
 183             title3 'Check course2 and dummy vars -- and why so many no course?';
 184             tables (course c1-c3) * course2
 185                    / norow nocol nopercent missing;
 186        
 
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.25 seconds
       cpu time            0.24 seconds
       
 187        proc freq;
 
 188             title3 'A few simple Chi-squared tests to predict passed';
 189             tables (course2 sex ethnic tongue) * passed / nocol nopercent chisq;
 190        
 
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.34 seconds
       cpu time            0.33 seconds
       
 191        proc logistic descending order=internal; /* To model Y=1 */
 
 192             title3 'Course2 by passed with dummy vars: Compare LR Chisq = 34.4171';
 193             model passed = c1 c3; /* Mainstream is reference category */
 194             Course1_vs_2: test c1=0;
 195             Course1_vs_3: test c1=c3;
 196             Course2_vs_3: test c3=0;
 197        
 198        /*
 199        A few details:
 200        
 201             The higher the minus 2 Log Likelihood, the lower the (estimated) maximum
 202             probability of observing these responses. It is a meaure of lack of
 203             model fit. The Akaike information criterion and Schwarz's Bayesian
 204             criterion both impose a further penalty for number of explanatory
 205             variables. Small is good.
 206        
 207             Association of Predicted Probabilities and Observed Responses:
 208                  * Every case has Y=0 or Y=1.
 209                  * Every case has a p-hat.
 210                  * Pick a case with Y=0, and another case with Y=1. That's a pair.
 211                  * If the case with Y=0 has a lower p-hat than the case with Y=1,
 212                    the pair is concordant.
 213        */
 214        
 215        
 
 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.MATHEX.
 NOTE: PROCEDURE LOGISTIC used (Total process time):
       real time           0.28 seconds
       cpu time            0.25 seconds
       
 216        proc iml;
 
 NOTE: IML Ready
 217             title3 'Estimate prob. of passing for for course=3: Compare 31/39 = 0.7949';
 218             b0 = 0.4077;
 218      !                   b1 = -1.4838;
 218      !                                 b2 = 0.9468;
 219             c1 = 0;
 219      !              c3=1;
 220             lcombo = b0 + b1*c1 + b2*c3;
 221             probpass = exp(lcombo) / (1+exp(lcombo));
 222             print "Estimated probability of passing course 3 is " probpass;
 223        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.03 seconds
       cpu time            0.03 seconds
       
 224        proc logistic descending order=internal;
 
 225             title3 'Use the Class statement';
 226             class course2 / param=ref;  /* This param option makes the ALPHABETICALLY
 227                                            last category (Mainstream) the reference
 228                                            category */
 229             model passed = course2;
 230             contrast 'Catch-up vs Mainstream' course2  1 0;
 231             contrast 'Elite vs Mainstream' course2  0 1;
 232             contrast 'Catch-up vs Elite' course2  1 -1;
 233        
 234        /* Contrast is a little tricky in proc logistic. It lets you specify a
 235           set of linear combinations (not necessarily contrasts) to test on the
 236           regression coefficients. It is essential to know exactly what the dummy
 237           variable coding scheme is. This can still be more convenient than
 238           defining your own dummy variables in the data step. */
 239        
 240        
 241        
 242        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 254