/* This is a replication of the example in the Chapter 4 of Franses and Paap textbook. The total number of observations is 2798. We put the last purchase of each household into a test data set. So we have 2498 observations for model building and 300 observations for out of sample forecasting.*/ /* Load the in-sample data set (2498 observations) for model building. */ data brands_in; input ID HOUSEHOLDID LASTPURCHASE HEINZ HUNTS PRICEHEINZ PRICEHUNTS DISPLHEINZ DISPLHUNTS FEATHEINZ FEATHUNTS FEATDISPLHEINZ FEATDISPLHUNTS ; datalines; 1 1 0 1 0 0.052000001 0.034000002 0 0 0 0 0 0 2 1 0 1 0 0.052000001 0.044 0 0 0 0 0 0 3 1 0 1 0 0.046 0.048 0 0 1 0 0 0 4 1 0 1 0 0.052000001 0.034000002 0 0 0 0 0 0 5 1 0 1 0 0.046 0.048 0 0 1 0 0 0 6 1 0 1 0 0.046999998 0.029999999 0 0 0 0 0 0 7 1 0 1 0 0.046 0.041000001 0 0 0 0 0 1 8 1 0 1 0 0.046 0.030999999 0 0 0 0 0 0 9 1 0 1 0 0.046999998 0.030999999 0 0 0 0 0 0 10 1 0 1 0 0.050000001 0.028000001 0 1 0 0 0 0 11 1 0 1 0 0.050000001 0.041000001 0 0 0 0 0 0 12 1 0 1 0 0.050000001 0.034000002 0 0 0 0 0 0 13 1 0 1 0 0.052999999 0.037 0 0 0 0 0 0 15 2 0 1 0 0.052000001 0.037 0 0 0 0 0 0 16 2 0 1 0 0.030999999 0.034000002 0 0 0 0 0 0 17 2 0 1 0 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0 0 0 0 0 0 2318 248 1 1 0 0.016000001 0.028000001 0 0 0 0 0 0 2337 249 1 1 0 0.030999999 0.037 1 0 0 0 0 0 2345 250 1 1 0 0.045000002 0.039999999 0 0 0 0 0 0 2357 251 1 1 0 0.030999999 0.037 1 0 0 0 0 0 2364 252 1 1 0 0.043000001 0.034000002 0 0 0 0 0 0 2369 253 1 1 0 0.052999999 0.037 0 0 0 0 0 0 2376 254 1 1 0 0.037999999 0.041999999 0 0 0 0 0 0 2383 255 1 1 0 0.021 0.034000002 0 0 1 0 0 0 2388 256 1 1 0 0.052999999 0.037 1 0 0 0 0 0 2416 257 1 1 0 0.022 0.034000002 0 0 0 0 0 0 2421 258 1 0 1 0.041333334 0.028000001 0 0 0 0 0 0 2426 259 1 1 0 0.030999999 0.034000002 1 0 0 0 0 0 2432 260 1 1 0 0.015 0.041000001 0 0 1 0 0 0 2439 261 1 1 0 0.032000002 0.037 0 0 1 0 0 0 2447 262 1 0 1 0.045333333 0.025 0 1 0 0 0 0 2463 263 1 1 0 0.034000002 0.030999999 0 0 0 0 0 0 2469 264 1 1 0 0.017999999 0.041999999 0 0 0 0 0 0 2474 265 1 1 0 0.050000001 0.041000001 0 0 1 0 0 0 2481 266 1 1 0 0.046 0.043000001 0 0 0 0 0 0 2488 267 1 0 1 0.041333334 0.028000001 0 0 0 0 0 0 2494 268 1 1 0 0.022 0.034000002 0 0 0 0 0 0 2511 269 1 1 0 0.030999999 0.030999999 1 0 0 0 0 0 2525 270 1 1 0 0.039000001 0.035 0 0 1 0 0 0 2530 271 1 1 0 0.037 0.034000002 0 0 0 0 0 0 2539 272 1 1 0 0.039000001 0.037 0 0 0 0 0 0 2545 273 1 1 0 0.039000001 0.037 0 0 0 0 0 0 2554 274 1 0 1 0.041333334 0.028000001 0 0 0 0 0 0 2561 275 1 1 0 0.021 0.034000002 0 0 0 0 0 0 2566 276 1 0 1 0.037666667 0.034000002 0 0 0 0 0 0 2606 277 1 1 0 0.037 0.035999998 0 0 0 0 0 0 2611 278 1 1 0 0.037 0.033 0 0 0 0 0 0 2621 279 1 1 0 0.044 0.034000002 0 0 0 0 0 0 2626 280 1 1 0 0.052999999 0.037 0 0 0 0 0 0 2631 281 1 1 0 0.030999999 0.035 0 0 0 0 0 0 2638 282 1 0 1 0.045333333 0.028000001 0 0 0 0 0 0 2643 283 1 1 0 0.039000001 0.037 1 0 0 0 0 0 2648 284 1 0 1 0.041666668 0.028000001 0 0 0 0 0 0 2653 285 1 1 0 0.035 0.028000001 0 0 0 1 0 0 2658 286 1 1 0 0.044 0.034000002 0 0 0 0 0 0 2665 287 1 1 0 0.044 0.041000001 0 0 1 0 0 0 2672 288 1 1 0 0.030999999 0.037 0 0 0 0 0 0 2677 289 1 1 0 0.035 0.028000001 0 0 0 0 0 0 2684 290 1 1 0 0.032000002 0.037 1 0 0 0 0 0 2691 291 1 1 0 0.022 0.034000002 0 0 0 0 0 0 2706 292 1 1 0 0.037 0.037 1 0 0 0 0 0 2716 293 1 1 0 0.021 0.034000002 0 0 0 0 0 0 2740 294 1 1 0 0.037 0.034000002 0 0 0 0 0 0 2752 295 1 1 0 0.023 0.037 1 0 0 0 0 0 2758 296 1 1 0 0.035 0.037 0 0 0 0 1 0 2766 297 1 1 0 0.039000001 0.037 0 0 0 0 0 0 2781 298 1 1 0 0.022 0.033 0 0 0 0 0 0 2791 299 1 1 0 0.043000001 0.034000002 0 0 0 0 0 0 2798 300 1 1 0 0.035 0.034000002 0 0 1 0 0 0 ; /* Generate the variable of the log of the ratio of prices. */ data brands_in; set brands_in; log_pheinzvsphunts=log(PRICEHEINZ/PRICEHUNTS); run; data brands_out; set brands_out; log_pheinzvsphunts=log(PRICEHEINZ/PRICEHUNTS); run; /* Here we are replicating the results in Table 4.1 in Franses and Paap */ /* To replicate the prediction-relization table, we need to set the cut-off point to be 0.891 using pprob=0.891. The option ctable provides the classification table. The option plots=roc will generate the ROC curve. The option outroc=brands_in_roc in the model statement stores the data for generating ROC curve of the model in the brands_in_roc dataset. The option outroc=brands_out_roc in the score statement stores the data for generating ROC curve of the out-of-sample in the brands_out_roc dataset.*/ proc logistic data=brands_in descending plots=roc; title "Logistic analysis of Heinz vs Hunt brand choice"; model heinz = displheinz featheinz featdisplheinz displhunts feathunts featdisplhunts log_pheinzvsphunts/rsquare ctable pprob=0.891 outroc=brands_in_roc; score out=score_in; score data=brands_out out=score_out outroc=brands_out_roc; run; title 'ROC curve sensitivity vs. 1 - specificity'; proc print data = brands_out_roc; run; /* Although SAS Proc Logistic uses the default cutoff probability to be the proportion of 1's in the training data set, prob = 0.891, as it turns out the accuracy (hit) rate is maximized using the cutoff probability of 0.72527. As we see below that cutoff probability produces a maximum accuracy rate of 0.92 in the training data set. */ data acc; set brands_out_roc; num = _pos_ + _neg_ ; den = _pos_ + _neg_ + _falpos_ + _falneg_ ; acc = num/den; keep _prob_ acc; run; title 'Accuracy Rate vs Cutoff Probability'; proc print data = acc; run; proc gplot data=acc; plot acc*_prob_; run; /* Here we are just verifying the results for probit estimation that appear in the Franses and Paap book. */ proc probit data=brands_in order=data; title "Probit analysis of Heinz vs Hunt brand choice"; class heinz; model heinz = displheinz featheinz featdisplheinz displhunts feathunts featdisplhunts log_pheinzvsphunts/lackfit; run; /* Using the options of ctable and pprob=0.891 give the results that are slightly different from the table on page 68 of the textbook. The following code can generate the exactly same prediction-realization table (within sample dataset) as in the textbook. */ data score_in; set score_in; if (HEINZ=1 & P_1>=0.891) then n11=1; if (HEINZ=1 & P_1<0.891) then n10=1; if (HEINZ=0 & P_1>=0.891) then n01=1; if (HEINZ=0 & P_1<0.891) then n00=1; run; proc sql; title 'Prediction-Realization Table for Within Sample Data'; select 0.891 as Cut_off_Prob, sum(n11) as Correct_Event, sum(n10) as Incorrect_Non_Event, sum(n01) as Incorrect_Event, sum(n00) as Correct_Non_Event, sum(n11)/2498 as Obs_Heinz_Pre_Heinz, /*Note: 2498 is the total number of observations in the within sample dataset */ sum(n10)/2498 as Obs_Heinz_Pre_Hunts, sum(n01)/2498 as Obs_Hunts_Pre_Heinz, sum(n00)/2498 as Obs_Hunts_Pre_Hunts from score_in; quit; /* Similarly, we can get the prediction-realization table for the out-of-sample forecast. */ data score_out; set score_out; if (HEINZ=1 & P_1>=0.891) then n11=1; if (HEINZ=1 & P_1<0.891) then n10=1; if (HEINZ=0 & P_1>=0.891) then n01=1; if (HEINZ=0 & P_1<0.891) then n00=1; run; proc sql; title 'Prediction-Realization Table for Out-of-Sample Data'; select 0.891 as Cut_off_Prob, sum(n11) as Correct_Event, sum(n10) as Incorrect_Non_Event, sum(n01) as Incorrect_Event, sum(n00) as Correct_Non_Event, sum(n11)/300 as Obs_Heinz_Pre_Heinz, /*Note: 300 is the total number of observations in the out-of-sample dataset */ sum(n10)/300 as Obs_Heinz_Pre_Hunts, sum(n01)/300 as Obs_Hunts_Pre_Heinz, sum(n00)/300 as Obs_Hunts_Pre_Hunts from score_out; quit;