各种回归模型适用条件,logistic回归

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1、LOGISTIC回归线性模型—一般线性模型线性回归方差分析协方差分析响应变量连续，正态连续，正态连续，正态解释变量连续离散连续和离散连接函数恒等式恒等式恒等式SAS实现REG/GLMMIXEDANOVA/MIXEDGLM/GENMODGLM/MIXEDGENMOD线性模型—广义线性模型logistic回归对数线性模型响应变量离散型，B(n,π)事件发生频数解释变量离散型，连续型分类变量联接函数logitln[P/(1-P)]log线性模型的条件LINELLinearIIndependenceNNorma

2、ldistributionEEqualvarianceLOGISTIC模型二值变量（0，1）资料的logit变换设P为事件发生的概率事件发生的优势odds和样本率的关系图1事件发生的优势odds和样本率的关系图2logit函数图图2logit函数图图3logistic曲线例1.饮酒与高血压年龄组25~35~…75~85高血压+—+—+—饮+酒—194265001065164831Dataa;Inputydrinka1a2a3a4a5count@@;Cards;1100000110000000111000

3、0410100005110100025100100021110010042100010034110001019100001036110000151000001801000009000000010601100002600100001640101000290001000138010010027000010013801000101800000108801000010000000131;proclogisticdescending;freqcount;modely=a1a2a3a4a5drink;run;SAS

4、程序1例1SAS结果解释--变量赋值ResponseProfileOrderedTotalValueyFrequency1120020774Probabilitymodeledisy=1.模型中假（哑）变量的定义问题年龄组25~35~45~55~65~75~85Age123456a1010000a2001000a3000100a4000010a5000001模型中假变量的向量表示或参数估计及模型检验最大似然法：使似然函数L达到最大。拟合优度检验：H0:模型拟合观察资料；H1:模型不拟合观察资料。拟合优度

5、检验统计量：-2ln(L)在大样本条件下近似服从ν=N-m-1的χ2分布变量筛选似然比检验（最常用）记分检验:统计量：SCORE（公式略）Wald检验例1模型检验统计量ModelFitStatisticsInterceptInterceptandCriterionOnlyCovariatesAIC991.029802.456SC995.910836.626-2LogL989.029788.456例1模型检验结果TestingGlobalNullHypothesis:BETA=0TestChi-Squar

6、eDFPr>ChiSqLikelihoodRatio200.57316<.0001Score183.55236<.0001Wald125.02286<.0001例1模型吻合情况AssociationofPredictedProbabilitiesandObservedResponsesPercentConcordant75.1Somers'D0.594PercentDiscordant15.7Gamma0.654PercentTied9.1Tau-a0.194Pairs154800c0.797例1结果—

7、参数估计StandardWaldParameterDFEstimateErrorChi-SquarePr>ChiSqIntercept1-5.05341.009425.0637<.0001a111.54261.06592.09440.1478a213.19901.02319.77630.0018a313.71821.018513.32640.0003a413.96671.023015.03370.0001a513.96161.065013.83750.0002drink11.66710.189677.2

8、908<.0001例1结果—优势比OddsRatioEstimatesPoint95%WaldEffectEstimateConfidenceLimitsa14.6770.57937.774a224.5083.299182.048a341.1905.595303.229a452.8107.110392.225a552.5436.516423.683drink5.2973.6537.681参数的意义优势/对数优势优势比常数项与预测和判别的关系