基于广义线性模型的多元统计建模 影印版
作者： L.Fahrmeir，G.Tutz 著
出版时间：1998年版
丛编项： Springer Texts in Statistics
内容简介
本书主要讨论广义线性模型在单变量及多变量回归分析中的应用。书中通过生物学、经济学和社会学等方面多达60余个应用实例，对近年来广义线性模型新的科研成果作了系统介绍，内容新颖，实用性强。
目录
Preface
ListofExamples
ListofFigures
ListofTables
1Introduction
1.1Outlineandexamples
1.2Remarksonnotation
1.3Furtherreading
2Modellingandanalysisofcross-sectionaldata:areviewof
univariategeneralizedlinearmodels
2.1Univariategeneralizedlinearmodels
2.1.1Data
Codingofcovariates
Groupedandungroupeddata
2.1.2Definitionofunivariategeneralizedlinearmodels
2.1.3Modelsforcontinuousresponses
Normaldistribution
Gammadistribution
InverseGanssiandistribution
2.1.4Modelsforbinaryandbinomialresponses
Linearprobabilitymodel
Probitmodel
Logitmodel
Complementarylog-logmodel
Binarymodelsasthresholdmodelsoflatentlinear
models
Parameterinterpretation
Overdispersion
2.1.5Modelsforcounteddata
Log-linearPoissonmodel
LinearPoissonmodel
2.2Likelihoodinference
2.2.1Maximumlikelihoodestimation
Log-likelihood,scorefunctionandinformationmatrix
ComputationoftheMLEbyiterativemethods
UniquenessandexistenceofMLE's*
Asymptoticproperties
Discussionofregularityassumptions*
Additionalscaleoroverdispersionparameter
2.2.2Hypothesistestingandgoodness-of-fitstatistics
Goodness-of-fitstatistics
2.3Someextensions
2.3.1Quasi-likelihoodmodels
Basicmodels
Variancefunctionswithunknownparameters
Nonconstantdispersionparameter
2.3.2Bayesmodels
2.3.3Nonlinearandnonexponentialfamilyregression
models*
2.4Furtherdevelopments
Modelsformulticategoricalresponses:
multivariateextensionsofgeneralizedlinearmodels
3.1Multicategoricalresponsemodels
3.1.1Multinomialdistribution
3.1.2Data
3.1.3Themultivariatemodel
3.1.4Multivariategeneralizedlinearmodels
3.2Modelsfornominalresponses
3.2.1Theprincipleofmaximumrandomutility
3.2.2Modellingofexplanatoryvariables:choiceofdesign
matrix
3.3Modelsforordinalresponses
3.3.1Cumulativemodels:thethresholdapproach
Cumulativelogisticmodelorproportionaloddsmodel
GroupedCoxmodelorproportionalhazardsmodel
Extreme-maximal-valuedistributionmodel
3.3.2Extendedversionsofcumulativemodels
3.3.3Linkfunctionsanddesignmatricesforcumulative
models
3.3.4Sequentialmodels
Generalizedsequentialmodels
Linkfunctionsofsequentialmodels
3.3.5Strictstochasticordering*
3.3.6Two-stepmodels
Linkfunctionanddesignmatrixfortwo-stepmodels
3.3.7Alternativeapproaches*
3.4Statisticalinference
3.4.1Maximumlikelihoodestimation
Numericalcomputation
3.4.2Testingandgoodness-of-fit
Testingoflinearhypotheses
Goodness-of-fitstatistics
3.4.3Power-divergencefamily*
Asymptoticpropertiesunderclassical"fixedcells"
assumptions
Sparsenessand"increasing-cells"asymptotics
3.5Multivariatemodelsforcorrelatedresponses
3.5.1Conditionalmodels
Asymmetricmodels
Symmetricmodels
3.5.2Marginalmodels
Statisticalinference
Selectingandcheckingmodels
4.1Variableselection
4.1.1Selectioncriteria
4.1.2Selectionprocedures
All-subsetsselection
Stepwisebackwardandforwardselection
4.2Diagnostics
4.2.1Diagnostictoolsfortheclassicallinearmodel
4.2.2Generalizedhatmatrix
4.2.3Residualsandgoodness-of-fitstatistics
4.2.4Casedeletion
4.3Generaltestsformisspecification*
4.3.1Estimationundermodelmisspecification
4.3.2Hausman-typetests
Hansmantests
Informationmatrixtest
4.3.3Testsfornon-nestedhypotheses
Testsbasedonartificialnesting
GeneralizedWaldandscoretests
5Semi-andnonparametricapproachestoregression
analysis
5.1Smoothingtechniquesforcontinuousresponses
5.1.1Simpleneighbourhoodsmoothers
5.1.2Splinesmoothing
Cubicsmoothingsplines
Regressionsplines
5.1.3Kernelsmoothing
Relationtoothersmoothers
Bias-variancetrade-off
5.1.4Selectionofsmoothingparameters*
5.2Kernelsmoothingwithmulticategoricalresponse
5.2.1Kernelmethodsfortheestimationofdiscrete
distributions
5.2.2Smoothedcategoricalregression
5.2.3Choiceofsmoothingparameters*
5.3Splinesmoothingingeneralizedlinearmodels
5.3.1Cubicsplinesmoothingwithasinglecovariate
Fisherscoringforgeneralizedsplinesmoothing*
Choiceofsmoothingparameter
5.3.2Generalizedadditivemodels
Fisherscoringwithbackfitting*
6Fixedparametermodelsfortimeseriesand
longitudinaldata
6.1Timeseries
6.1.1Conditionalmodels
Generalizedautoregressivemodels
Quasi-likelihoodmodelsandextensions
6.1.2Statisticalinferenceforconditionalmodels
6.1.3Marginalmodels
Estimationofmarginalmodels
6.2Longitudinaldata
6.2.1Conditionalmodels
Generalizedautoregressivemodels,quasi-likelihood
models
Statisticalinference
Transitionmodels
Subject-specificapproachesandconditional
likelihood
6.2.2Marginalmodels
Statisticalinference
Randomeffectsmodels
7.1Linearrandomeffectsmodelsfornormaldata
7.1.1Two-stagerandomeffectsmodels
Randomintercepts
Randomslopes
Multilevelmodels
7.1.2Statisticalinference
Knownvariance-covariancecomponents
Unknownvariance-covariancecomponents
DerivationoftheEM-algorithm*
7.2Randomeffectsingeneralizedlinearmodels
7.3Estimationbasedonposteriormodes
7.3.1Knownvariance-covariancecomponents
7.3.2Unknownvariance-covariancecomponents
7.3.3Algorithmicdetails*
Fisherscoringforgivenvariance-covariance
components
EM-typealgorithm
7.4Estimationbyintegrationtechniques
7.4.1Maximumlikelihoodestimationoffixedparameters
7.4.2Posteriormeanestimationofrandomeffects
7.4.3Algorithmicdetails*
Directmaximization
Indirectmaximization
Posteriormeanestimation
7.5Examples
7.6Marginalestimationapproachtorandomeffectsmodels
7.7Furtherapproaches
Statespacemodels
8.1LinearstatespacemodelsandtheKalmanfilter
8.1.1Linearstatespacemodels
8.1.2Statisticalinference
LinearKalmanfilteringandsmoothing
Kalmanfilteringandsmoothingasposteriormode
estimation*
Unknownhyperparameters
EM-algorithmforestimatinghyperparameters*
8.2Non-normalandnonlinearstatespacemodels
8.2.1Dynamicgeneralizedlinearmodels
Categoricaltimeseries
8.2.2Nonlinearandnonexponentialfamilymodels*
8.3Non-normalfilteringandsmoothing
8.3.1Posteriormodeestimation
GeneralizedextendedKalmanfilterandsmoother*
Gauss-NewtonandFisher.coringfilteringand
smoothing*
Estimationofhyperparameters*
Someapplications
8.3.2Posteriormeanestimation
AGibbssamplingapproach*
Integration-basedapproaches*
8.4Longitudinaldata
8.4.1Statespacemodellingoflongitudinaldata
8.4.2Filteringandsmoothing
GeneralizedKalmanfilterandsmootherfor
longitudinaldata*
9Survivalmodels
9.1Modelsforcontinuoustime
9.1.1Basicmodels
Exponentialdistribution
Weibulldistribution
9.1.2Parametricregressionmodels
Location-scalemodelsforlogT
Proportionalhazardsmodels
Lineartransformationmodelsandbinaryregression
models
9.1.3Censoring
Randomcensoring
TypeIcensoring
9.1.4Estimation
Exponentialmodel
Weibullmodel
9.2Modelsfordiscretetime
9.2.1Lifetableestimates
9.2.2Parametricregressionmodels
Thegroupedproportionalhazardsmodel
Ageneralizedversion:themodelofAranda-Ordaz
Thelogisticmodel
Sequentialmodelandparameterizationofthe
baselinehazard
9.2.3Maximumlikelihoodestimation
9.2.4Time-varyingcovariates
Internalcovariates*
Maximumlikelihoodestimation*
9.3Discretemodelsformultiplemodesoffailure
9.3.1Basicmodels
9.3.2Maximumlikelihoodestimation
9.4Smoothingindiscretesurvivalanalysis
9.4.1Dynamicdiscretetimesurvivalmodels
Posteriormodesmoothing
9.4.2Kernelsmoothing
AppendixA
A.1Exponentialfamiliesandgeneralizedlinearmodels
A.2Basicideasforasymptotics
A.3EM-algorithm
A.4Numericalintegration
A.5MonteCarlomethods
AppendixBSoftwareforfittinggeneralizedlinearmodels
References
AuthorIndex
SubjectIndex
