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 ?+ 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
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
Probit模型最终估计结果是
p i = F(y i) = F + x i) 拐点坐标 ,
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
预测正确率结论：线性概率模型RMSE= MAE= MAPE=
Logit模型 RMSE= MAE= MAPE=
Probit模型 RMSE= MAE= MAPE=
由上面结果可知线性概率模型的RMSE、MAE、MAPE 均远远大于Logit模型和Probit模型，说明其误差率比Logit模型和Probit模型大很多，所以正确率远远小于Logit模型和Probit模型。而Logit模型和Probit模型的RMSE、MAE、MAPE相差很小，所以正确率相差不大。综上所诉，此数据可以用Logit模型和Probit模型代替线性概率模型进行分析。