比较线性模型和Probit模型、Logit模型

1、研究生考试录取相关因素的实验报告一，研究目的通过对南开大学国际经济研究所1999 级研究生考试分数及录取情况的研究，引入录取与未录取这一虚拟变量，比较线性概率模型与probit模型，logit 模型，预测正确率。二，模型设定表 1，南开大学国际经济研究所1999 级研究生考试分数及录取情况见数据表obs y score obs y score obs y score 1 1 401 34 0 332 67 0 275 2 1 401 35 0 332 68 0 273 3 1 392 36 0 332 69 0 273 4 1 387 37 0 331 70 0 272 5 1 384 38

2、0 330 71 0 267 6 1 379 39 0 328 72 0 266 7 1 378 40 0 328 73 0 263 8 1 378 41 0 328 74 0 261 9 1 376 42 0 321 75 0 260 10 1 371 43 0 321 76 0 256 11 1 362 44 0 318 77 0 252 12 1 362 45 0 318 78 0 252 13 1 361 46 0 316 79 0 245 14 0 359 47 0 308 80 0 243 15 0 358 48 0 308 81 0 242 16 1 356 49 0 304 8

3、2 0 241 17 0 356 50 0 303 83 0 239 18 0 355 51 0 303 84 0 235 19 0 354 52 0 299 85 0 232 20 0 354 53 0 297 86 0 228 21 0 353 54 0 294 87 0 219 22 0 350 55 0 293 88 0 219 23 0 349 56 0 293 89 0 214 24 0 349 57 0 292 90 0 210 25 0 348 58 0 291 91 0 204 26 0 347 59 0 291 92 0 198 27 0 347 60 0 287 93 0

4、 189 28 0 344 61 0 286 94 0 188 29 0 339 62 0 286 95 0 182 30 0 338 63 0 282 96 0 166 31 0 338 64 0 282 97 0 123 32 0 336 65 0 282 33 0 334 66 0 278 定义变量 score ：考生考试分数； y ：考生录取为 1，未录取为 0。0.00.81.0100150200250300350400450scorey上图为样本观测值。1 线性概率模型根据上面资料建立模型iiiscorebby*21用eviews 得到回归结果如图：depende

5、nt variable: y method: least squaresdate: 12/10/10 time: 20:38 sample: 1 97 included observations: 97 variable coefficientstd. error t-statistic prob. c -0.847407 0.159663 -5.307476 0.0000 score 0.003297 0.000521 6.325970 0.0000 r-squared 0.296390 mean dependent var 0.144330 adjusted r-squared 0.288

6、983 s.d. dependent var 0.353250 s.e. of regression 0.297866 akaike info criterion 0.436060 sum squared resid 8.428818 schwarz criterion 0.489147 log likelihood -19.14890 f-statistic 40.01790 durbin-watson stat 0.359992 prob(f-statistic) 0.000000 参数估计结果为：iy?-0.847407+0.003297 iscore se=(0.159663)( 0.

7、000521) t=(-5.307476) (6.325970) p=(0.0000) (0.0000) 预测正确率：forecast: yf actual: y forecast sample: 1 97 included observations: 97 root mean squared error 0.294780 mean absolute error 0.233437 mean absolute percentage error 8.689503 theil inequality coefficient 0.475786 bias proportion 0.000000 varia

8、nce proportion 0.294987 covariance proportion 0.705013 2.logit 模型dependent variable: y method: ml - binary logit (quadratic hill climbing) date: 12/10/10 time: 21:38 sample: 1 97 included observations: 97 convergence achieved after 11 iterations covariance matrix computed using second derivativesvar

9、iable coefficientstd. error z-statistic prob. c -243.7362 125.5564 -1.941248 0.0522 score 0.679441 0.350492 1.938536 0.0526 mean dependent var 0.144330 s.d. dependent var 0.353250 s.e. of regression 0.115440 akaike info criterion 0.123553 sum squared resid 1.266017 schwarz criterion 0.176640 log lik

10、elihood -3.992330 hannan-quinn criter. 0.145019 restr. log likelihood -40.03639 avg. log likelihood -0.041158 lr statistic (1 df) 72.08812 mcfadden r-squared 0.900282 probability(lr stat) 0.000000 obs with dep=0 83 total obs 97 obs with dep=1 14 得 logit 模型估计结果如下pi = f(yi) = )6794.07362.243(11ixe拐点坐标

11、(358.7, 0.5) 其中y=-243.7362+0.6794x 预测正确率forecast: yf actual: y forecast sample: 1 97 included observations: 97 root mean squared error 0.114244 mean absolute error 0.025502 mean absolute percentage error 1.275122 theil inequality coefficient 0.153748 bias proportion 0.000000 variance proportion 0.02

12、5338 covariance proportion 0.974662 3.probit模型dependent variable: y method: ml - binary probit (quadratic hill climbing) date: 12/10/10 time: 21:40 sample: 1 97 included observations: 97 convergence achieved after 11 iterations covariance matrix computed using second derivativesvariable coefficients

13、td. error z-statistic prob. c -144.4560 70.19809 -2.057833 0.0396 score 0.402868 0.196186 2.053504 0.0400 mean dependent var 0.144330 s.d. dependent var 0.353250 s.e. of regression 0.116277 akaike info criterion 0.122406 sum squared resid 1.284441 schwarz criterion 0.175493 log likelihood -3.936702

14、hannan-quinn criter.0.143872 restr. log likelihood -40.03639 avg. log likelihood -0.040585 lr statistic (1 df) 72.19938 mcfadden r-squared 0.901672 probability(lr stat) 0.000000 obs with dep=0 83 total obs 97 obs with dep=1 14 probit模型最终估计结果是pi = f(yi) = f (-144.456 + 0.4029 xi) 拐点坐标(358.5, 0.5) 预测正

15、确率forecast: yf actual: y forecast sample: 1 97 included observations: 97 root mean squared error 0.115072 mean absolute error 0.025387 mean absolute percentage error 1.216791 theil inequality coefficient 0.154476 bias proportion 0.000084 variance proportion 0.020837 covariance proportion 0.979080 预测正确率结论：线性概率模型rmse=0.294780 mae=0.233437 mape=8.689503 logit模型 rmse=0.114244 mae=0.025502 mape=1.275122 probit模型 rm