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About this book
About this book
Since the original publication of the bestselling Modelling Binary Data, a number of important methodological and computational developments have emerged, accompanied by the steady growth of statistical computing. Mixed models for binary data analysis and procedures that lead to an exact version of logistic regression form valuable additions to the statistician's toolbox, and author Dave Collett has fully updated his popular treatise to incorporate these important advances.Modelling Binary Data, Second Edition now provides an even more comprehensive and practical guide to statistical methods for analyzing binary data. Along with thorough revisions to the original material-now independent of any particular software package- it includes a new chapter introducing mixed models for binary data analysis and another on exact methods for modelling binary data. The author has also added material on modelling ordered categorical data and provides a summary of the leading software packages.All of the data sets used in the book are available for download from the Internet, and the appendices include additional data sets useful as exercises.
INTRODUCTIONSome ExamplesThe Scope of this BookUse of Statistical SoftwareSTATISTICAL INFERENCE FOR BINARY DATAThe Binomial DistributionInference about the Success ProbabilityComparison of Two ProportionsComparison of Two or More ProportionsMODELS FOR BINARY AND BINOMIAL DATAStatistical ModellingLinear ModelsMethods of EstimationFitting Linear Models to Binomial DataModels for Binomial Response DataThe Linear Logistic ModelFitting the Linear Logistic Model to Binomial DataGoodness of Fit of a Linear Logistic ModelComparing Linear Logistic ModelsLinear Trend in ProportionsComparing Stimulus-Response RelationshipsNon-Convergence and OverfittingSome other Goodness of Fit StatisticsStrategy for Model SelectionPredicting a Binary Response ProbabilityBIOASSAY AND SOME OTHER APPLICATIONSThe Tolerance DistributionEstimating an Effective DoseRelative PotencyNatural ResponseNon-Linear Logistic Regression ModelsApplications of the Complementary Log-Log ModelMODEL CHECKINGDefinition of ResidualsChecking the Form of the Linear PredictorChecking the Adequacy of the Link FunctionIdentification of Outlying ObservationsIdentification of Influential ObservationsChecking the Assumption of a Binomial DistributionModel Checking for Binary DataSummary and RecommendationsOVERDISPERSIONPotential Causes of OverdispersionModelling Variability in Response ProbabilitiesModelling Correlation Between Binary ResponsesModelling Overdispersed DataA Model with a Constant Scale ParameterThe Beta-Binomial ModelDiscussionMODELLING DATA FROM EPIDEMIOLOGICAL STUDIESBasic Designs for Aetiological StudiesMeasures of Association Between Disease and ExposureConfounding and InteractionThe Linear Logistic Model for Data from Cohort StudiesInterpreting the Parameters in a Linear Logistic ModelThe Linear Logistic Model for Data from Case-Control StudiesMatched Case-Control StudiesMIXED MODELS FOR BINARY DATAFixed and Random EffectsMixed Models for Binary DataMultilevel ModellingMixed Models for Longitudinal Data AnalysisMixed Models in Meta-AnalysisModelling Overdispersion Using Mixed ModelsEXACT METHODSComparison of Two Proportions Using an Exact TestExact Logistic Regression for a Single ParameterExact Hypothesis TestsExact Confidence Limits for bkExact Logistic Regression for a Set of ParametersSome ExamplesDiscussionSOME ADDITIONAL TOPICSOrdered Categorical DataAnalysis of Proportions and PercentagesAnalysis of RatesAnalysis of Binary Time SeriesModelling Errors in the Measurement of Explanatory VariablesMultivariate Binary DataAnalysis of Binary Data from Cross-Over TrialsExperimental DesignCOMPUTER SOFTWARE FOR MODELLING BINARY DATAStatistical Packages for Modelling Binary DataInterpretation of Computer OutputUsing Packages to Perform Some