Applied categorical and count data analysis

"Preface This book focuses on statistical analysis of discrete data, including categorical and count outcomes. Discrete variables are abundant in practice, and knowledge about and ability to analyze such data is important for professionals and practitioners in a wide range of biomedical and psy...

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Detalles Bibliográficos
Autor principal: Tang, Wan
Otros Autores: He, Hua, Tu, Xin M.
Formato: Libro
Lenguaje:English
Publicado: Boca Raton : CRC Press, 2012.
Colección:Texts in statistical science.
Materias:
Análisis de regresión
Categorías (Matemáticas)
Tabla de Contenidos:
  • 1.1. Discrete Outcomes
  • 1.2. Data Source
  • 1.3. Outline of the Book
  • 1.3.1. Distribution of Random Variables
  • 1.3.2. Association between Two Random Variables
  • 1.3.3. Regression Analysis
  • 1.3.4. Log-Linear Methods for Contingency Tables
  • 1.3.5. Discrete Survival Data Analysis
  • 1.3.6. Longitudinal Data Analysis
  • 1.3.7. Validity and Reliability Data Analysis
  • 1.3.8. Incomplete Data Analysis
  • 1.4. Review of Key Statistical Results
  • 1.4.1. Central Limit Theorem and Law of Large Numbers
  • 1.4.2. Delta Method and Slutsky's Theorem
  • 1.4.3. Maximum Likelihood Estimate
  • 1.4.4. Estimating Equations
  • 1.4.5. U-Statistics
  • 1.5. Software
  • Exercises
  • 2.1. Inference for One-Way Frequency Table
  • 2.1.1. Binary Case
  • 2.1.2. Inference for Multinomial Variable
  • 2.1.3. Inference for Count Variable
  • 2.2. Inference for 2 x 2 Table
  • 2.2.1. Testing Association
  • 2.2.2. Measures of Association
  • 2.2.3. Test for Marginal Homogeneity
  • 2.2.4. Agreement
  • 2.3. Inference for 2 x r Tables
  • 2.3.1. Cochran-Armitage Trend Test
  • 2.3.2. Mann-Whitney-Wilcoxon Test
  • 2.4. Inference for s x r Table
  • 2.4.1. Tests of Association
  • 2.4.2. Marginal Homogeneity and Symmetry
  • 2.4.3. Agreement
  • 2.5. Measures of Association
  • 2.5.1. Measures of Association for Ordinal Outcome
  • 2.5.2. Measures of Association for Nominal Outcome
  • Exercises
  • 3.1. Confounding Effects
  • 3.2. Sets of 2 x 2 Tables
  • 3.2.1. Cochran-Mantel-Haenszel Test for Independence
  • 3.2.2. Estimates and Tests of Common Odds Ratios
  • 3.3. Sets of s x r Tables
  • 3.3.1. Tests of General Association
  • 3.3.2. Mean Score Statistic
  • 3.3.3. Correlation Statistic
  • 3.3.4. Kappa Coefficients for Stratified Tables
  • Exercises
  • 4.1. Logistic Regression for Binary Response
  • 4.1.1. Motivation of Logistic Regression
  • 4.1.2. Definition of Logistic Models
  • 4.1.3. Parameter Interpretation
  • 4.1.4. Invariance to Study Designs
  • 4.1.5. Simpson's Paradox Revisited
  • 4.1.6. Breslow-Day Test and Moderation Analysis
  • 4.2. Inference About Model Parameters
  • 4.2.1. Maximum Likelihood Estimate
  • 4.2.2. General Linear Hypotheses
  • 4.2.3. Exact Inference for Logistic Regression
  • 4.2.4. Bias Reduced Logistic Regression
  • 4.3. Goodness of Fit
  • 4.3.1. Pearson Chi-Square Statistic
  • 4.3.2. Deviance Test
  • 4.3.3. Hosmer-Lemeshow Test
  • 4.3.4. Lack of Fit
  • 4.4. Generalized Linear Models
  • 4.4.1. Introduction
  • 4.4.2. Regression Models for Binary Response
  • 4.4.3. Inference
  • 4.5. Regression Models for Polytomous Response
  • 4.5.1. Model for Nominal Response
  • 4.5.2. Models for Ordinal Response
  • 4.5.3. Inference
  • Exercises
  • 5.1. Poisson Regression Model for Count Response
  • 5.1.1. Parameter Interpretation
  • 5.1.2. Inference About Model Parameters
  • 5.1.3. Offsets in Log-Linear Model
  • 5.2. Goodness of Fit
  • 5.2.1. Pearson's Chi-Square Statistic
  • 5.2.2. Scaled Deviance Statistic
  • 5.3. Overdispersion
  • 5.3.1. Detection of Overdispersion
  • 5.3.2. Correction for Overdispersion
  • 5.4. Parametric Models for Clustered Count Response
  • 5.4.1. Negative Binomial Model
  • 5.4.2. Zero-Modified Poisson and Negative Binomial Models
  • 5.4.3. Zero-Truncated Poisson and NB Regression Models
  • 5.4.4. Hurdle Models
  • Exercises
  • 6.1. Analysis of Log-Linear Models
  • 6.1.1. Motivation
  • 6.1.2. Log-Linear Models for Contingency Tables
  • 6.1.3. Parameter Interpretation
  • 6.1.4. Inference
  • 6.2. Two-Way Contingency Tables
  • 6.2.1. Independence
  • 6.2.2. Symmetry and Marginal Homogeneity
  • 6.3. Three-Way Contingency Tables
  • 6.3.1. Independence
  • 6.3.2. Association Homogeneity
  • 6.4. Irregular Tables
  • 6.4.1. Structure Zeros in Contingency Tables
  • 6.4.2. Models for Irregular Tables
  • 6.4.3. Bradley-Terry Model
  • 6.5. Model Selection
  • 6.5.1. Model Evaluation
  • 6.5.2. Stepwise Selection
  • 6.5.3. Graphical Models
  • Exercises
  • 7.1. Special Features of Survival Data
  • 7.1.1. Censoring
  • 7.1.2. Truncation
  • 7.1.3. Discrete Survival Time
  • 7.1.4. Survival and Hazard Functions
  • 7.2. Life Table Methods
  • 7.2.1. Life Tables
  • 7.2.2. Mantel-Cox Test
  • 7.3. Regression Models
  • 7.3.1. Complementary Log-Log Regression
  • 7.3.2. Discrete Proportional Odds Model
  • Exercises
  • 8.1. Data Preparation and Exploration
  • 8.1.1. Longitudinal Data Formats
  • 8.1.2. Exploratory Analysis
  • 8.2. Marginal Models
  • 8.2.1. Models for Longitudinal Data
  • 8.2.2. Generalized Estimation Equations
  • 8.2.3. Extensions to Categorical Responses
  • 8.3. Generalized Linear Mixed-Effects Model
  • 8.3.1. Linear Mixed-Effects Models
  • 8.3.2. Generalized Linear Mixed-Effects Models
  • 8.3.3. Comparison of GLMM with Marginal Models
  • 8.3.4. Maximum Likelihood Inference
  • 8.4. Model Diagnostics
  • 8.4.1. Marginal Models
  • 8.4.2. Generalized Linear Mixed-Effect Models
  • Exercises
  • 9.1. Diagnostic-Ability
  • 9.1.1. Receiver Operating Characteristic Curves
  • 9.1.2. Inference
  • 9.1.3. Areas under ROC Curves
  • 9.2. Criterion Validity
  • 9.2.1. Concordance Correlation Coefficient
  • 9.3. Internal Reliability
  • 9.3.1. Spearman--Brown Rho
  • 9.3.2. Cronbach Coefficient Alpha
  • 9.3.3. Intraclass Correlation Coefficient
  • 9.4. Test-Retest Reliability
  • Exercises
  • 10.1. Incomplete Data and Associated Impact
  • 10.1.1. Observational Missing
  • 10.1.2. Missing by Design
  • 10.1.3. Counterfactual Missing
  • 10.1.4. Impact of Missing Values
  • 10.2. Missing Data Mechanism
  • 10.2.1. Missing Completely at Random
  • 10.2.2. Missing at Random
  • 10.2.3. Missing Not at Random
  • 10.3. Methods for Incomplete Data
  • 10.3.1. Maximum Likelihood Method
  • 10.3.2. Imputation Methods
  • 10.3.3. Inverse Probability Weighting
  • 10.3.4. Sensitivity Analysis
  • 10.4. Applications
  • 10.4.1. Verification Bias of Diagnostic Studies
  • 10.4.2. Causal Inference of Treatment Effects
  • 10.4.3. Longitudinal Data with Missing Values
  • 10.4.4. Survey Studies
  • Exercises.

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