比较线性模型和Probit模型、Logit模型

研究生考试录取相关因素的实验报告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 obsYSCOREobsYSCOREobsYSCORE 11401340332670275 21401350332680273 31392360332690273 41387370331700272 51384380330710267 61379390328720266 71378400328730263 81378410328740261 91376420321750260 101371430321760256 111362440318770252 121362450318780252 131361460316790245 140359470308800243 150358480308810242 161356490304820241 170356500303830239 180355510303840235 190354520299850232 200354530297860228 210353540294870219 220350550293880219 230349560293890214 240349570292900210 250348580291910204 260347590291920198 270347600287930189 280344610286940188 290339620286950182 300338630282960166 310338640282970123 320336650282 330334660278 定义变量 SCORE 考生考试分数 Y 考生录取为 1 未录取为 0 0 0 0 2 0 4 0 6 0 8 1 0 100150200250300350400450 SCORE Y 上图为样本观测值 1 1 线性概率模型线性概率模型 根据上面资料建立模型 iii SCOREBBY 21 用Eviews得到回归结果如图 Dependent Variable Y Method Least Squares Date 12 10 10 Time 20 38 Sample 1 97 Included observations 97 VariableCoefficientStd Errort StatisticProb C 0 0 5 0 0000 SCORE0 0 6 0 0000 R squared0 Mean dependent var0 Adjusted R squared0 S D dependent var0 S E of regression0 Akaike info criterion0 Sum squared resid8 Schwarz criterion0 Log likelihood 19 14890 F statistic40 01790 Durbin Watson stat0 Prob F statistic 0 参数估计结果为 0 0 i Y i SCORE Se 0 0 t 5 6 p 0 0000 0 0000 预测正确率 Forecast YF Actual Y Forecast sample 1 97 Included observations 97 Root Mean Squared Error0 Mean Absolute Error 0 Mean Absolute Percentage Error8 Theil Inequality Coefficient 0 Bias Proportion 0 Variance Proportion 0 Covariance Proportion 0 2 Logit 模型模型 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 derivatives VariableCoefficientStd Errorz StatisticProb C 243 7362125 5564 1 0 0522 SCORE0 0 1 0 0526 Mean dependent var0 S D dependent var0 S E of regression0 Akaike info criterion0 Sum squared resid1 Schwarz criterion0 Log likelihood 3 Hannan Quinn criter 0 Restr log likelihood 40 03639 Avg log likelihood 0 LR statistic 1 df 72 08812 McFadden R squared0 Probability LR stat 0 Obs with Dep 083 Total obs97 Obs with Dep 114 得 Logit 模型估计结果如下 pi F yi 拐点坐标 358 7 0 5 6794 0 7362 243 1 1 i x e 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 Error0 Mean Absolute Error 0 Mean Absolute Percentage Error1 Theil Inequality Coefficient 0 Bias Proportion 0 Variance Proportion 0 Covariance Proportion 0 3 Probit3 Probit 模型模型 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 derivatives VariableCoefficientStd Errorz StatisticProb C 144 456070 19809 2 0 0396 SCORE0 0 2 0 0400 Mean dependent var0 S D dependent var0 S E of regression0 Akaike info criterion0 Sum squared resid1 Schwarz criterion0 Log likelihood 3 Hannan Quinn criter 0 Restr log likelihood 40 03639 Avg log likelihood 0 LR statistic 1 df 72 19938 McFadden R squared0 Probability LR stat 0 Obs with Dep 083 Total obs97 Obs with Dep 114 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 预测正确率 Forecast YF Actual Y Forecast sample 1 97 Included observations 97 Root Mean Squared Error0 Mean Absolute Error 0 Mean Absolute Percentage Error1 Theil Inequality Coefficient 0 Bias Proportion 0 Variance Proportion 0 Covariance Proportion 0 预测正确率结论 线性概率模型 RMSE 0 MAE 0 MAPE 8 Logit 模型 RMSE 0 MAE 0 MAPE 1 Probit 模型 RMSE 0 MAE 0 MAPE 1 由上面结果可知线性概率模型的 R