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

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

定义变量SCORE ：考生考试分数；Y ：考生录取为1，未录取为0。 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

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

Variable Coefficient Std. 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 0.288983 ????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： i

Y ˆ-0.847407+0.003297 i SCORE Se=(0.159663)( 0.000521) 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 ?????Variance 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 derivatives

Variable Coefficient Std. 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 likelihood -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

p i = F (y i ) =

)

6794.07362.243(11

i x e +--+ 拐点坐标 (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? 0.025338

?????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 derivatives

Variable Coefficient Std. 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 ????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