1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 55         
 56         /* MathLogReg4.sas  */
 57         %include '/folders/myfolders/441s16/Lecture/readmath2b.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: PROCEDURE FORMAT used (Total process time):
       real time           0.00 seconds
       cpu time            0.00 seconds
       
 
 166        title2 'Logistic regression with more than 2 resp. categories using
 167        proc catmod';
 168        /*************** Data step continues ************************/
 169        hsutil = hsgpa+hscalc+hsengl;
 170        if hsutil = . then hsmiss=1; else hsmiss=0;
 171        label hsmiss = 'Missing Any High School Data'; format hsmiss ynfmt.;
 172        
 173        if (0<=mark<=49) then outcome = 'Fail';
 174           else if (50<=mark<=100) then outcome = 'Pass';
 175           else outcome = 'Gone';
 176        /*************************************************************/
 177        
 
 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    142 at 169:15   2 at 169:22     
 NOTE: The data set WORK.MATHEX has 579 observations and 37 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.01 seconds
       cpu time            0.02 seconds
       
 178        proc freq;
 
 179             tables outcome*passed / norow nocol nopercent missing;
 180        
 
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.05 seconds
       cpu time            0.06 seconds
       
 181        proc freq;
 
 182             title3 'One at a time cat IVs with proc freq';
 183             tables (course2 sex ethnic tongue hsmiss) * outcome
 184                    / nocol nopercent chisq;
 185        
 
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.22 seconds
       cpu time            0.22 seconds
       
 186        proc logistic descending order=internal;
 
 187             title3 'Simple logistic regression: Reproduce this';
 188             model passed = hsgpa;
 189        
 
 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           0.12 seconds
       cpu time            0.12 seconds
       
 190        proc catmod;
 
 191             title3 'Hsgpa Reproduce b1 = 0.2089, Wald Chisq = 76.5326';
 192             direct hsgpa; /* Direct means no dummy vars please */
 193             model passed = hsgpa  / noprofile;
 194             /* Always suppress the profile when there are quantitative
 195                explanatory variables.  */
 196        
 197        /* The last response category (Y=1) is the reference
 198           (denominator) category so the sign of the regression
 199           coefficient is reversed, but we can live with this. */
 200        
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.06 seconds
       cpu time            0.06 seconds
       
 201        proc catmod;
 
 202             title3 'Hsmiss by outcome';
 203             direct hsmiss; /* It's already a dummy variable. */
 204             model outcome = hsmiss;
 205             contrast 'HS Missing method 1' hsmiss 1;
 206             contrast 'HS Missing method 2'  all_parms 0 0 1 0,
 207                                             all_parms 0 0 0 1;
 208        /*   Model is
 209        
 210             ln(pi1/pi3) = beta01 + beta11 x             Fail vs. Pass
 211             ln(pi1/pi3) = beta02 + beta12 x             Gone vs. Pass
 212        
 213             all_parms reads down the columns
 214                        beta01  beta02  beta11  beta12
 215             all_parms     0       0       1       0,
 216                           0       0       0       1
 217        
 218             Specifying 2 linear combinations of the betas equal
 219             to zero, so there is no relationship with x.
 220        */
 221        
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.10 seconds
       cpu time            0.11 seconds
       
 222        proc iml;
 
 NOTE: IML Ready
 223             title3 'Estimate Probabilities using output from proc catmod';
 224              b01 = -1.3594;
 224      !                      b11 = 0.6663;
 225              b02 = -0.8306;
 225      !                      b12 = 1.2360;
 226              hsmiss = 0;
 227              L1 = b01 + b11*hsmiss;
 228              L2 = b02 + b12*hsmiss;
 229              denom = 1 + exp(L1) + exp(L2);
 230              Fail = exp(L1)/denom;
 230      !                             Gone = exp(L2)/denom;
 230      !                                                   Pass = 1/denom;
 231              print "No  Missing HS Data:" Fail Gone Pass;
 232              hsmiss = 1;
 233              L1 = b01 + b11*hsmiss;
 234              L2 = b02 + b12*hsmiss;
 235              denom = 1 + exp(L1) + exp(L2);
 236              Fail = exp(L1)/denom;
 236      !                             Gone = exp(L2)/denom;
 236      !                                                   Pass = 1/denom;
 237              print "Yes Missing HS Data:" Fail Gone Pass;
 238        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.04 seconds
       cpu time            0.05 seconds
       
 239        proc freq;
 
 240             title3 'Hsmiss by outcome again for comparison';
 241             tables hsmiss * outcome / nocol nopercent;
 242        
 243        /* Now seek a good predictive model */
 244        
 
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.03 seconds
       cpu time            0.03 seconds
       
 245        proc catmod;
 
 246             title3 'HS variables';
 247             direct hsgpa hscalc hsengl;
 248             model outcome = hsgpa hscalc hsengl / noprofile;
 249        
 250        /* Drop HS English */
 251        
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.09 seconds
       cpu time            0.08 seconds
       
 252        proc catmod;
 
 253             title3 'HS gpa and calc + course2 ';
 254             direct hsgpa hscalc;
 255             model outcome = hsgpa hscalc course2 / noprofile;
 256             /* Dummy vars for course2 use effect coding */
 257        
 258        /* Forget course2 */
 259        
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.08 seconds
       cpu time            0.09 seconds
       
 260        proc catmod;
 
 261             title3 'HS gpa and calc + diagnostic test';
 262             direct hsgpa hscalc precalc calc;
 263             model outcome = hsgpa hscalc precalc calc / noprofile;
 264        
 265        /* Drop calc subtest, keep precalc */
 266        
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.09 seconds
       cpu time            0.09 seconds
       
 267        proc catmod;
 
 268             title3 'Try gender, ethnic and mother tongue controlling for good stuff';
 269             direct hsgpa hscalc precalc calc gender mtongue;
 270             model outcome = hsgpa hscalc precalc ethnic gender mtongue / noprofile;
 271             contrast 'Demographics'      ethnic  1 0 0 0 0,
 272                                          ethnic  0 1 0 0 0,
 273                                          ethnic  0 0 1 0 0,
 274                                          ethnic  0 0 0 1 0,
 275                                          ethnic  0 0 0 0 1,
 276                                          gender  1,
 277                                          mtongue 1;
 278             contrast 'Ethnic and Gender' ethnic  1 0 0 0 0,
 279                                          ethnic  0 1 0 0 0,
 280                                          ethnic  0 0 1 0 0,
 281                                          ethnic  0 0 0 1 0,
 282                                          ethnic  0 0 0 0 1,
 283                                          gender  1;
 284        
 285        /* Got this in the log file: "WARNING: The formatted values of one or more
 286        variables are truncated to 16" */
 287        
 288        
 289        /* Mother tongue is significant. Still true when we drop ethnic and gender? */
 290        
 
 WARNING: The formatted values of one or more variables are truncated to 16 characters.
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.12 seconds
       cpu time            0.12 seconds
       
 291        proc catmod;
 
 292             title3 'hsgpa hscalc precalc calc mtongue';
 293             direct hsgpa hscalc precalc calc mtongue;
 294             model outcome = hsgpa hscalc precalc mtongue / noprofile;
 295        
 296        /* Allowing for academic background, students whose first language is English
 297        are more likely to fail the course as opposed to passing, and less likely to
 298        disappear as opposed to passing. If this is replicated, it will be very
 299        interesting. Now explore in more detail.
 300        
 301           Recall the response categories are 1=Fail 2=Gone 3=Pass.
 302        
 303           We want to know whether failing is different from disappearing in terms
 304           of their relationship to the explanatory variables. We are getting
 305           advanced here. What is H0?
 306        
 307        Model (using b instead of beta) is
 308        
 309             ln(pi1/pi3) = b01 + b11 hsgpa + b21 hscalc + b31 precalc + b41 mtongue
 310             ln(pi1/pi3) = b02 + b12 hsgpa + b22 hscalc + b32 precalc + b42 mtongue
 311        
 312             The null hypothesis is b11=b12, b21=b22, b31=b32, b41=b42
 313        
 314             all_parms reads down the columns, so
 315        
 316             beta = b01 b02  b11 b12  b21 b22  b31 b32  b41 b42
 317        
 318             And H0 says that 4 linear combinations of the betas equal zero:
 319        
 320                 b01 b02  b11 b12  b21 b22  b31 b32  b41 b42
 321                   0  0    1  -1    0   0    0   0    0   0
 322                   0  0    0   0    1  -1    0   0    0   0
 323                   0  0    0   0    0   0    1  -1    0   0
 324                   0  0    0   0    0   0    0   0    1  -1
 325        
 326        */
 327        
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.09 seconds
       cpu time            0.09 seconds
       
 328        proc catmod;
 
 329             title3 'Different coefficients for Gone and Fail?';
 330             direct hsgpa hscalc precalc calc mtongue;
 331             model outcome = hsgpa hscalc precalc mtongue / noprofile;
 332             contrast 'Diff Relationships Overall'
 333                      all_parms  0  0  1 -1  0  0  0  0  0  0,
 334                      all_parms  0  0  0  0  1 -1  0  0  0  0,
 335                      all_parms  0  0  0  0  0  0  1 -1  0  0,
 336                      all_parms  0  0  0  0  0  0  0  0  1 -1;
 337             contrast 'Diff Relationships for hsgpa'
 338                      all_parms  0  0  1 -1  0  0  0  0  0  0;
 339             contrast 'Diff Relationships for hscalc'
 340                      all_parms  0  0  0  0  1 -1  0  0  0  0;
 341             contrast 'Diff Relationships for precalc'
 342                      all_parms  0  0  0  0  0  0  1 -1  0  0;
 343             contrast 'Diff Relationships for mtongue'
 344                      all_parms  0  0  0  0  0  0  0  0  1 -1;
 345        
 346        /************************** Replication ***********************
 347        For interpretation, want to replicate 8 findings:
 348        Gone vs. Pass and Fail vs. Pass for each explanatory variable.
 349        ***************************************************************/
 350        
 351        %include '/folders/myfolders/441s16/Lecture/readreplic.sas';
 
 NOTE: The default estimation method for this model is maximum-likelihood.
 NOTE: Maximum likelihood computations converged.
 NOTE: There were 579 observations read from the data set WORK.MATHEX.
 NOTE: PROCEDURE CATMOD used (Total process time):
       real time           0.11 seconds
       cpu time            0.10 seconds
       
 
 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: PROCEDURE FORMAT used (Total process time):
       real time           0.00 seconds
       cpu time            0.00 seconds
       
 
 464        if (0<=mark<=49) then outcome = 'Fail';
 465           else if (50<=mark<=100) then outcome = 'Pass';
 466           else outcome = 'Gone';
 467        
 468        
 
 NOTE: The infile '/folders/myfolders/replicmath2.data.txt' is:
       Filename=/folders/myfolders/replicmath2.data.txt,
       Owner Name=root,Group Name=vboxsf,
       Access Permission=-rwxrwx---,
       Last Modified=30Jan2016:15:16:16,
       File Size (bytes)=38214
 
 NOTE: 579 records were read from the infile '/folders/myfolders/replicmath2.data.txt'.
       The minimum record length was 64.
       The maximum record length was 64.
 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).
       81 at 379:24   81 at 415:18   
 NOTE: The data set WORK.REPLIC has 579 observations and 35 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.03 seconds
       cpu time            0.03 seconds
       
 469        proc catmod data=replic; /* That's the default anyway */
 
 470             title3 'Replicate hsgpa hscalc precalc calc mtongue 0.05/8 = .00625';
 471             direct hsgpa hscalc precalc calc mtongue;
 472             model outcome = hsgpa hscalc precalc mtongue / noprofile;
 473             contrast 'Diff Relationships for mtongue'
 474                      all_parms  0  0  0  0  0  0  0  0  1 -1;
 475        
 476        /* Final conclusions:
 477        
 478             Students with higher High School GPA were more likely to pass as
 479             opposed to failing and more likely to pass as opposed to diappearing.
 480        
 481             Students with higher High School Calculus marks were more likely
 482             to pass as opposed to disappearing.
 483        
 484             Students with higher scores on the pre-calculus portion of the
 485             diagnostic test were more likely to pass as opposed to disappearing.
 486        
 487             There was no convincing evidence of a connection between Mother
 488             Tongue (English vs. Other) and outcome.
 489        
 490         */
 491        
 492        
 493        
 494        
 495        
 496        
 497        
 498        
 499        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 511