多变量方差分析

多元统计分析方法TheMethodsofMultivariateStatisticalAnalysis第四章多变量方差分析什么是多变量方差分析？多变量方差分析在医学中的应用方差分析的分类单反应变量(y)多反应变量(y1,y2…yk)单效应因子(A)双效应因子(A,B)多效应因子(A,B,C)无交互效应有交互效应2）根据效应因子的随机性：固定模型(fixedmodel)：效应因子是专门指定的。随机模型(randommodel)：效应因子是从很多的因子中随机抽取出来的。混合模型(mixedmodel)：效应因子包含两种类型因子。1）根据变量的个数：什么是多变量方差分析？MANOVA分析一个或多个效应因子是如何影响一组反应变量的。身高：y1体重：y2胸围：y3=父母SES舒张压：y1收缩压：y2=职务生活方式+反应变量效应因子多变量方差分析在医学中的应用实例1、单组设计资料的MANOVA2、配对设计资料的MANOVA3、成组设计资料的MANOVA4、多因子的MANOVA5、重复设计资料的MANOVA6、有协变量的MANOVA【例4-1】单组设计资料的MANOVA实例为了了解某地在不同时期的儿童生长发育情况，调查了20名8岁男童身高(x1)、体重(x2)、胸围(x3)，数据列在表4-6中。10年前该地大量调查获得身高、体重、胸围的均值分别为：121.57cm、21.54kg、57.98cm。试问：本次调查结果与10年前结果是否相同？表4-6儿童生长发育情况调查数据【SAS程序】dataeg4_1；inputidx1x2x3@@；y1=x1-121.57；y2=x2-21.54；y3=x3-57.98；cards；1141.231.863.6……20121.419.156.5run；procmeans；vary1-y3；run；procglm；modely1y2y3=/ss3nouni；manovah=intercept/printeprinth；run；【SAS输出的结果】①TheMEANSProcedureVariableNMeanStdDevMinimumMaximum------------------------------------------------------------------------y1207.1700004.7157519-0.17000019.63000y2202.5250003.1504845-2.74000010.26000y3202.3650003.8276659-6.7800007.82000------------------------------------------------------------------------②TheGLMProcedureNumberofobservations20MultivariateAnalysisofVarianceMANOVATestCriteriaandExactFStatisticsfortheHypothesisofNoOverallInterceptEffectStatisticValueFValueNumDFDenDFPrFWilks'Lambda0.2065624621.77317.0001Pillai'sTrace0.7934375421.77317.0001Hotelling-LawleyTrace3.8411507321.77317.0001Roy'sGreatestRoot3.8411507321.77317.0001结论：因为P0.0001，说明该地本次对8岁男童以身高、体重、胸围三个指标为代表的儿童生长发育情况与10年前调查结果的差异存在极显著性。本次该地8岁男童的身高、体重与胸围都比10年前有所增加。【例4-2】配对设计资料的MANOVA实例对9名乳腺癌患者进行大剂量化疗。表4-7列出的是化疗前、后测量其血液中尿素氮BUN(mg%)与血清肌酐Gr(mg%)水平的结果。试问：该化疗对患者的肾功能有无影响？表4-7乳腺癌患者化疗前后BUN和Gr检测数据【SAS程序】dataeg4_2；inputidx0x1y0y1@@；d1=x1-x0；d2=y1-y0；cards；111.710.61.30.8……914.613.80.90.8run；procmeans；vard1d2；run；procglm；modeld1d2=/ss3nouni；manovah=intercept；run；【SAS主要输出结果】：①TheMEANSProcedureVariableNMeanStdDevMinimumMaximum---------------------------------------------------------------------d19-0.16666671.9924859-3.20000003.6000000d29-0.16666670.2598076-0.60000000.3000000---------------------------------------------------------------------②TheGLMProcedureMANOVATestCriteriaandExactFStatisticsfortheHypothesisofNoOverallInterceptEffectStatisticValueFValueNumDFDenDFPrFWilks'Lambda0.610268282.24270.1776Pillai'sTrace0.389731722.24270.1776Hotelling-LawleyTrace0.638623582.24270.1776Roy'sGreatestRoot0.638623582.24270.1776【例4-3】成组设计资料的MANOVA实例为了研究某种疾病的治疗，观察了24个病人使用三种不同药品后的两个指标，每种药品观察了4个男性和4个女性，数据列在表4-8中。试比较药品对两个指标所起的作用。表4-8三种不同药品用药后的观察数据【SAS程序】dataeg4_3；inputsex$drug$@；inputy1y2@；output；inputy1y2@；output；inputy1y2@；output；inputy1y2@；output；cards；MA56549976……FC14131212121087run;procglmmanova；classesdrug；modely1y2=drug/nouni；contrast'DrugAvsB'drug1-10；contrast'DrugAvsC'drug10-1；contrast'DrugBvsC'drug01-1；manovah=drug；meansdrug；run；【SAS部分输出结果】GeneralLinearModelsProcedureClassLevelInformationClassLevelsValuesSEX2FemaleMaleDRUG3ABCNumberofobservationsindataset=24MultivariateAnalysisofVariance①ManovaTestCriteriaandFApproximationsfortheHypothesisofnoOverallDRUGEffectStatisticValueFNumDFDenDFPrFWilks'Lambda0.2176311511.43584400.0001Pillai'sTrace0.883664128.31154420.0001Hotelling-LawleyTrace3.1294858314.86514380.0001Roy'sGreatestRoot2.9729246131.21572210.0001②ManovaTestCriteriaandExactFStatisticsfortheHypothesisofnoOverallDrugAvsBEffectStatisticValueFNumDFDenDFPrFWilks'Lambda0.864461831.56792200.2331Pillai'sTrace0.135538171.56792200.2331Hotelling-LawleyTrace0.156789081.56792200.2331Roy'sGreatestRoot0.156789081.56792200.2331③ManovaTestCriteriaandExactFStatisticsfortheHypothesisofnoOverallDrugAvsCEffectStatisticValueFNumDFDenDFPrFWilks'Lambda0.3038906622.90662200.0001Pillai'sTrace0.6961093422.90662200.0001Hotelling-LawleyTrace2.2906572922.90662200.0001Roy'sGreatestRoot2.2906572922.90662200.0001④ManovaTestCriteriaandExactFStatisticsfortheHypothesisofnoOverallDrugBvsCEffectStatisticValueFNumDFDenDFPrFWilks'Lambda0.3079972422.46782200.0001Pillai'sTrace0.6920027622.46782200.0001Hotelling-LawleyTrace2.2467823822.46782200.0001Roy'sGreatestRoot2.2467823822.46782200.0001⑤Levelof--------------Y1---------------------------Y2-------------DRUGNMeanSDMeanSDA85.62500001.846811925.62500001.76776695B86.12500001.552647517.12500002.29518129C813.25000002.9640705611.37500002.38671921【例4-4】析因设计资料的MANOVA实例为了研究某种疾病的治疗，观察了24个病人使用三种不同药品后的两个指标，每种药品观察了4个男性和4个女性，数据列在表4-8中。试分析性别和药品对两个指标所起的作用。表4-8三种不同药品用药后的观察数据【SAS程序】procglmdata=eg4_3manova；classessexdrug；modely1y2=sexdrugsex*drug/nouni；contrast'DrugAvsB'drug1-10；contrast'DrugAvsC'drug10-1；contrast'DrugBvsC'drug01-1；contrast'DrugAvsB/sex=m'drug1-10sex*drug1-10000；contrast'DrugAvsB/sex=f'drug1-10sex*drug0001-10；contrast'DrugAvsC/sex=m'drug10-1sex*drug10-1000；contrast'DrugAvsC/sex=f'drug10-1sex*drug00010-1；contrast'DrugBvsC/sex=m'drug01-1sex*drug01-1000；contrast'DrugBvsC/sex=f'drug01-1sex*drug00001-1；manovah=sexdrugsex*drug；meanssexdrug；run；【SAS主要输出结果】GeneralLinearModelsProcedureMultivariateAnalysisofVariance①M