定性数据研究方法chap6

第六章用于多项式分布Logit模型

MulticategoryLogitModels6.1名义因变量logit模型6.2有序因变量的累积logit模型6.3配对分类有序logit模型6.4检验条件独立性设,()是因变量的J个类别的结果发生的概率J个类别分布是多项分布

6.1名义因变量logit模型

LOGITMODELSFORNOMINALRESPONSESBaseline-CategoryLogitsModel当把第J类j结果作为Baseline(基线),Logits模型有J-1个方程利用软件可同时给出这J-1个方程的参数估计，和其它统计量对结果落在a类和b类的概率的比也是线性形式,与基线的选取无关其中例Y三种基本食物：F,I,O,x:长度

F=fishI=InvertebratesO=otherAnalysisofMaximumLikelihoodEstimatesFunctionStandardChi-ParameterNumberEstimateErrorSquarePr>ChiSq-------------------------------------------------------------------Intercept11.61771.30731.530.215925.69741.793710.090.0015length1-0.11010.51710.050.83142-2.46540.89967.510.0061

即结论：1.检验：食物的选择与鳄鱼长度无关假设检验表6.2,p值0.0002，拒绝零假设.2.在鱼和无脊椎动物之间,大鳄鱼易选前者.X增加1单位,胜算比为：exp(2.355)=10.5EstimatingResponseProbabilities计算各类概率它满足例中其中，1可以看为：对每个给定x，如最长鳄而，即此鳄吃鱼的可能性最大0.76，吃无脊椎动物的可能性是0.005,吃其它的可能性为0.23

dataAlligator;inputsizetype$@@;cards;1.24I1.30I1.30I1.32F1.32F1.40F1.42I1.42F1.45I1.45O1.47I1.47F1.50I1.52I1.55I1.60I1.63I1.65O1.65I1.65F1.65F1.68F1.70I1.73O1.78I1.78I1.78O1.80I1.80F1.85F1.88I1.93I1.98I2.03F2.03F2.16F2.26F2.31F2.31F2.36F2.36F2.39F2.41F2.44F2.46F2.56O2.67F2.72I2.79F2.84F3.25O3.28O3.33F3.56F3.58F3.66F3.68O3.71F3.89F;proclogistic;modeltype(ref='O')=size/link=glogitexpb;run;SAS程序TheLOGISTICProcedureType3AnalysisofEffectsWaldEffectDFChi-SquarePr>ChiSqsize28.93600.0115AnalysisofMaximumLikelihoodEstimatesStandardWaldParametertypeDFEstimateErrorChi-SquarePr>ChiSqExp(Est)InterceptF11.61771.30731.53140.21595.042InterceptI15.69741.793810.08810.0015298.104sizeF1-0.11010.51710.04530.83140.896sizeI1-2.46540.89977.51010.00610.085OddsRatioEstimatesPoint95%WaldEffecttypeEstimateConfidenceLimitssizeF0.8960.3252.468sizeI0.0850.0150.496

点击gator.sav选Analyze–regression–MultinomialLogisticRegression将food放到dependent，选定referencecategory(last),把length放到CovariateSPSS程序例2：Y信仰(是、不确定、否);X1性别;X2种族具体模型为（最终模型与前面相同）：你有可能得到下面的SPSS输出具体模型为：模型检验：

如去掉genderDeviance:8.0-0.8=7.2（df=2）

P值0.03检验：如果去掉raceDeviance:

2.8-0.8=2（df=2）

P值0.368各类人beliefinafterlife的概率datacatbelief;inputrace$gender$belief$count@@;cards;WhiteFY371WhiteFU49WhiteFN74WhiteMY250WhiteMU45WhiteMN71BlackFY64BlackFU9BlackFN15BlackMY25BlackMU5BlackMN13;proc

logistic;freqcount;classgender(ref='M')race(ref='Black')/param=ref;modelbelief(ref='N')=genderrace/link=glogitexpb;run;SAS程序TestingGlobalNullHypothesis:BETA=0TestChi-SquareDFPr>ChiSqLikelihoodRatio8.743740.0678Score8.849840.0650Wald8.781840.0668Type3AnalysisofEffectsWaldEffectDFChi-SquarePr>ChiSqgender27.20740.0272race22.08240.3530AnalysisofMaximumLikelihoodEstimates

StandardWaldParameterbeliefDFEstimateErrorChi-SquarePr>ChiSqExp(Est)InterceptU1-0.75820.36144.40310.03590.468InterceptY10.88280.242613.23900.00032.418genderFU10.10510.24650.18170.66991.111genderFY10.41860.17135.97370.01451.520raceWhiteU10.27120.35410.58630.44381.311raceWhiteY10.34200.23702.08140.14911.408OddsRatioEstimatesPoint95%WaldEffectbeliefEstimateConfidenceLimitsgenderFvsMU1.1110.6851.801genderFvsMY1.5201.0862.126raceWhitevsBlackU1.3110.6552.6256.2有序因变量的累积logit模型CUMULATIVELOGITMODELSFORORDINALRESPONSES模型：

X轴是否出错了？概率：

对所有j上述似然比的log值

log似然比为例1：

x=1是demo模型统计推断的95%置信区间即:=模型拟合Noevidenceoflackoffit拟合不充分时,可把原模型中用代替datapoliti;inputgenderpartybeliefcount@@;cards;00144002470031180042300532011180122801386014390154810136102341035310418105231111211218113621144511551;proclogistic;freqcount;classparty(param=refref='1');modelbelief=party;run;SAS程序TheLOGISTICProcedureModelFitStatisticsInterceptInterceptandCriterionOnlyCovariatesAIC2541.6302484.985SC2560.5402508.622-2LogL2533.6302474.985TestingGlobalNullHypothesis:BETA=0TestChi-SquareDFPr>ChiSqLikelihoodRatio58.64511<.0001Score57.24481<.0001Wald57.01821<.0001

Type3AnalysisofEffectsWaldEffectDFChi-SquarePr>ChiSqparty157.0182<.0001AnalysisofMaximumLikelihoodEstimatesStandardWaldParameterDFEstimateErrorChi-SquarePr>ChiSqIntercept11-2.46900.1318350.8122<.0001Intercept21-1.47450.1091182.7151<.0001Intercept310.23710.09486.24970.0124Intercept411.06950.1046104.6082<.0001

party010.97450.129157.0182<.0001OddsRatioEstimatesPoint95%WaldEffectEstimateConfidenceLimitsparty0vs12.6502.0583.412

SPSS输出例2：SES:(1high,0low);lifeevents:过去三年Birthofchild,newjob,divorce,deathoffamily模型：给定lifeevents值，对高SES水平的人得轻一级别精神损伤的胜算是e(1.111）=3对给定SES,Lifeevents的数目多的人易得更严重的精神病

用更复杂的模型：发现交叉项不显著AnalysisofMaximumLikelihoodEstimatesStandardWaldParameterDFEstimateErrorChi-SquarePr>ChiSqIntercept110.09810.81100.01460.9037Intercept211.59250.83723.61860.0571Intercept312.60660.90978.21110.0042life1-0.42040.19034.88110.0272SES10.37091.13020.10770.7428life*SES10.18130.23610.58960.4426datamental;inputnummentalSESlife@@;cards;11112121921192220331142321341132421151022530061102631471012730381132830991132931610117303041110131303121023241813215334121420634417152133540516201364041721837404182123841819205394082021540409;proclogistic;modelmental=lifeses;run;proclogistic;modelmental=lifeseslife*ses;run;SAS程序TheLOGISTICProcedureTestingGlobalNullHypothesis:BETA=0TestChi-SquareDFPr>ChiSqLikelihoodRatio9.944220.0069Score9.143120.0103Wald8.501820.0143AnalysisofMaximumLikelihoodEstimatesStandardWaldParameterDFEstimateErrorChi-SquarePr>ChiSqIntercept11-0.28180.6231