随机效应模型简介.pdf

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1、2012年暑期培训班,长沙随机效应模型简介Introductiontorandomeffectmodels南京医科大学陈峰中国卫生信息学会统计理论与方法专业委员会提纲(outline)1.线性模型简介2.广义线性模型简介3.从几个简单例子介绍随机效应模型4.重复测量资料的随机效应模型GEE多水平模型5.其他非独立数据的随机效应模型6.随机效应模型拟合中的一些问题3.从几个简单例子介绍随机效应模型例3.1(配伍组设计)四种抗癌药物抑瘤效果的配伍组方差分析，测量值越大提示效果越好。配伍组A1A2A3A4B10.800.360.170.28B2

2、0.740.500.420.36B30.310.200.380.25B40.480.180.440.22B50.760.260.280.13区组方差分析结果SourceDFSSMSF_ValuePModel70.523170000.074738574.110.0157a30.410840000.136946677.530.0043b40.112330000.028082501.550.2514Error120.218110000.01817583Total190.74128000例3.1资料的处理效应和区组效应(近似值)配伍组A1A2A3A4

3、MeanEffectB10.800.360.170.280.400.02B20.740.500.420.360.510.13B30.310.200.380.250.29-0.09B40.480.180.440.220.33-0.04B50.760.260.280.130.36-0.02Mean0.620.300.340.250.38Effect0.24-0.07-0.04-0.13根据处理效应、区组效应计算的理论值0.38+0.24+0.02配伍组A1A2A3A4MeanEffectB10.640.330.360.270.400.02B20.

4、750.440.470.380.510.13B30.530.220.250.160.29-0.09B40.580.270.300.210.33-0.04B50.600.290.320.230.36-0.02Mean0.620.300.340.250.38Effect0.24-0.07-0.04-0.13各观察值的残差配伍组A1A2A3A4MeanEffectB10.160.03-0.190.010.400.02B2-0.010.07-0.05-0.020.510.13B3-0.22-0.010.130.090.29-0.09B4-0.09-0

5、.070.150.020.33-0.04B50.16-0.02-0.04-0.100.36-0.02Mean0.620.300.340.250.38Effect0.24-0.07-0.04-0.13固定效应模型Yabeijijij2eN~(0,)ij0随机效应模型Yaeeijiij2eN~(0,)i02eN~(0,)j1•Two-wayANOVA(fixedmodel)•DependentVariable:ySumofSourceDFSquaresMeanSquareFValuePr>FModel70.5231700

6、00.074738574.110.0157Error120.218110000.01817583CorrectedTotal190.74128000R-SquareCoeffVarRootMSEyMean0.70576635.855790.1348180.376000SourceDFAnovaSSMeanSquareFValuePr>Fa30.410840000.136946677.530.0043b40.112330000.028082501.550.2514•TheMixedProcedure•SolutionforFixedEffect

7、s•Standard•EffectEstimateErrorDFtValuePr>

8、t

9、•intercept0.24800.0642743.860.0182•a10.37000.08527124.340.0010•a20.052000.08527120.610.5533•a30.090000.08527121.060.3120•a40....•Type3TestsofFixedEffects•NumDen•EffectDFDFFValuePr>F•a3127.530.0043•CovParmEstimate•b0.002477•Residua

10、l0.01818固定效应模型YabeijijijeN~(0,0.01818)ij随机效应模型Yaeeijijie~N(0,0.01818)ie~