比较线性模型和Probit模型、Logit模型

1、精选优质文档-倾情为你奉上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obsYSCOREobsYSCOREobsYSCORE11401340332670275214013503326802733139236033269027341387370331700272513843803307102676137939032872026671378400328

2、730263813784103287402619137642032175026010137143032176025611136244031877025212136245031878025213136146031679024514035947030880024315035848030881024216135649030482024117035650030383023918035551030384023519035452029985023220035453029786022821035354029487021922035055029388021923034956029389021424034957

3、0292900210250348580291910204260347590291920198270347600287930189280344610286940188290339620286950182300338630282960166310338640282970123320336650282330334660278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: YMethod: Least SquaresDate: 12/10/10 Time:

4、 20:38Sample: 1 97Included observations: 97VariableCoefficientStd. Errort-StatisticProb.C-0.0.-5.0.0000SCORE.0000R-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-19.14890F-sta

5、tistic40.01790Durbin-Watson stat0.Prob(F-statistic)0.参数估计结果为：-0.+0. Se=(0.)( 0.) t=(-5.) (6.) p=(0.0000) (0.0000) 预测正确率：Forecast: YFActual: YForecast sample: 1 97Included observations: 97Root Mean Squared Error0.Mean Absolute Error0.Mean Absolute Percentage Error8.Theil Inequality Coefficient0.Bias

6、Proportion0.Variance Proportion0.Covariance Proportion0.2.Logit模型Dependent Variable: YMethod: ML - Binary Logit (Quadratic hill climbing)Date: 12/10/10 Time: 21:38Sample: 1 97Included observations: 97Convergence achieved after 11 iterationsCovariance matrix computed using second derivativesVariableC

7、oefficientStd. Errorz-StatisticProb.C-243.7362125.5564-1.0.0522SCORE.0526Mean 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-40.03639Avg. log likelihood-0.LR stati

8、stic (1 df)72.08812McFadden R-squared0.Probability(LR stat)0.Obs with Dep=083Total obs97Obs with Dep=114得Logit模型估计结果如下 pi = F(yi) = 拐点坐标 (358.7, 0.5)其中Y=-243.7362+0.6794X预测正确率Forecast: YFActual: YForecast sample: 1 97Included observations: 97Root Mean Squared Error0.Mean Absolute Error0.Mean Absolut

9、e Percentage Error1.Theil Inequality Coefficient0.Bias Proportion0.Variance Proportion0.Covariance Proportion0.3.Probit模型Dependent Variable: YMethod: ML - Binary Probit (Quadratic hill climbing)Date: 12/10/10 Time: 21:40Sample: 1 97Included observations: 97Convergence achieved after 11 iterationsCov

10、ariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb.C-144.456070.19809-2.0.0396SCORE.0400Mean 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.Res

11、tr. log likelihood-40.03639Avg. log likelihood-0.LR statistic (1 df)72.19938McFadden R-squared0.Probability(LR stat)0.Obs with Dep=083Total obs97Obs with Dep=114Probit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: YFActual: YForecast sample: 1 97Included observations: 97Root Mean Squared Error0.Mean Absolute Error0.Mean Absolute Percentage Error1.Theil Inequality Coefficient0.Bias Proportion0.Variance Proportion0.Covariance Proportion0.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