比较线性模型和Probit模型Logit模型

比较线性模型和P r o b i t 模型L o g i t模型

Document serial number【LGGKGB-LGG98YT-LGGT8CB-LGUT-

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

SCORE

R-squared

Mean dependent var

Adjusted R-squared . dependent var . of regression

Akaike info criterion Sum squared resid Schwarz criterion Log likelihood

F-statistic

Durbin-Watson stat

Prob(F-statistic)

参数估计结果为： i

Y ˆ+ i SCORE Se=( t=

p=

预测正确率：

Forecast: YF Actual: Y

Forecast sample: 1 97 Included observations: 97

Root Mean Squared Error

Mean Absolute Error

Mean Absolute Percentage Error Theil Inequality Coefficient Bias Proportion

Variance Proportion Covariance Proportion

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 SCORE

Mean dependent var

. dependent var

. of regression

Akaike info criterion Sum squared resid Schwarz criterion Log likelihood

Hannan-Quinn criter. Restr. log likelihood Avg. log likelihood LR statistic (1 df) McFadden R-squared

Probability(LR stat)

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 ,

其中Y=+

预测正确率

Forecast: YF Actual: Y

Forecast sample: 1 97 Included observations: 97

Root Mean Squared Error

Mean Absolute Error

Mean Absolute Percentage Error Theil Inequality Coefficient Bias Proportion

Variance Proportion Covariance Proportion

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

SCORE