Categorical Data Analysis by Example

• Record Nr.: UNINA9910823095603321
• Autore: Upton Graham J. G
• Pubbl/distr/stampa: Newark : , : John Wiley & Sons, Incorporated, , 2016; ©2017
• ISBN: 9781119307914; 9781119307860
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (215 pages)
• Disciplina: 519.535
• Soggetti: Multivariate analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- CATEGORICAL DATA ANALYSIS BY EXAMPLE -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 What are Categorical Data? -- 1.2 A Typical Data Set -- 1.3 Visualization and Cross-Tabulation -- 1.4 Samples, Populations, and Random Variation -- 1.5 Proportion, Probability, and Conditional Probability -- 1.6 Probability Distributions -- 1.6.1 The Binomial Distribution -- 1.6.2 The Multinomial Distribution -- 1.6.3 The Poisson Distribution -- 1.6.4 The Normal Distribution -- 1.6.5 The Chi-Squared ( 2) Distribution -- 1.7 *The Likelihood -- 2 Estimation and Inference for Categorical Data -- 2.1 Goodness of Fit -- 2.1.1 Pearson's X2 Goodness-of-Fit Statistic -- 2.1.2 *The Link between X2 and the Poisson and 2-Distributions -- 2.1.3 The Likelihood-Ratio Goodness-of-Fit Statistic, G2 -- 2.1.4 *Why the G2 and X2 Statistics Usually have Similar Values -- 2.2 Hypothesis Tests for a Binomial Proportion (Large Sample) -- 2.2.1 The Normal Score Test -- 2.2.2 *Link to Pearson's X2 Goodness-of-Fit Test -- 2.2.3 G2 for a Binomial Proportion -- 2.3 Hypothesis Tests for a Binomial Proportion (Small Sample) -- 2.3.1 One-Tailed Hypothesis Test -- 2.3.2 Two-Tailed Hypothesis Tests -- 2.4 Interval Estimates for a Binomial Proportion -- 2.4.1 Laplace's Method -- 2.4.2 Wilson's Method -- 2.4.3 The Agresti-Coull Method -- 2.4.4 Small Samples and Exact Calculations -- References -- 3 The 2 × 2 Contingency Table -- 3.1 Introduction -- 3.2 Fisher's Exact Test (for Independence) -- 3.2.1 ; *Derivation of the Exact Test Formula -- 3.3 Testing Independence with Large Cell Frequencies -- 3.3.1 Using Pearson's Goodness-of-Fit Test -- 3.3.2 The Yates Correction -- 3.4 The 2 × 2 Table in a Medical Context -- 3.5 Measuring Lack of Independence (Comparing Proportions) -- 3.5.1 Difference of Proportions -- 3.5.2 Relative Risk -- 3.5.3 Odds-Ratio -- References.; 4 The I × J Contingency Table -- 4.1 Notation -- 4.2 Independence in the I × J Contingency Table -- 4.2.1 Estimation and Degrees of Freedom -- 4.2.2 Odds-Ratios and Independence -- 4.2.3 Goodness of Fit and Lack of Fit of the Independence Model -- 4.3 Partitioning -- 4.3.1 *Additivity of G2 -- 4.3.2 Rules for Partitioning -- 4.4 Graphical Displays -- 4.4.1 Mosaic Plots -- 4.4.2 Cobweb Diagrams -- 4.5 Testing Independence with Ordinal Variables -- References -- 5 The Exponential Family -- 5.1 Introduction -- 5.2 The Exponential Family -- 5.2.1 The Exponential Dispersion Family -- 5.3 Components of a General Linear Model -- 5.4 Estimation -- References -- 6 A Model Taxonomy -- 6.1 Underlying Questions -- 6.1.1 Which Variables are of Interest? -- 6.1.2 What Categories should be Used? -- 6.1.3 What is the Type of Each Variable? -- 6.1.4 What is the Nature of Each Variable? -- 6.2 Identifying the Type of Model -- 7 The 2 × J Contingency Table -- 7.1 A Problem with X2 (and G2) -- 7.2 Using the Logit -- 7.2.1 Estimation of the Logit -- 7.2.2 The Null Model -- 7.3 Individual Data and Grouped Data -- 7.4 Precision, Confidence Intervals, and Prediction Intervals -- 7.4.1 Prediction Intervals -- 7.5 Logistic Regression with a Categorical Explanatory Variable -- 7.5.1 Parameter Estimates with Categorical Variables (J &gt -- 2) -- 7.5.2 The Dummy Variable Representation of a Categorical Variable -- References -- 8 Logistic Regression with Several Explanatory Variables -- 8.1 Degrees of Freedom when there are no Interactions -- 8.2 Getting a Feel for the Data -- 8.3 Models with two-Variable Interactions -- 8.3.1 Link to the Testing of Independence between Two Variables -- 9 Model Selection and Diagnostics -- 9.1 Introduction -- 9.1.1 Ockham's Razor -- 9.2 Notation for Interactions and for Models -- 9.3 Stepwise Methods for Model Selection Using G2.; 9.3.1 Forward Selection -- 9.3.2 Backward Elimination -- 9.3.3 Complete Stepwise -- 9.4 AIC and Related Measures -- 9.5 The Problem Caused by Rare Combinations of Events -- 9.5.1 Tackling the Problem -- 9.6 Simplicity Versus Accuracy -- 9.7 DFBETAS -- References -- 10 Multinomial Logistic Regression -- 10.1 A Single Continuous Explanatory Variable -- 10.2 Nominal Categorical Explanatory Variables -- 10.3 Models for an Ordinal Response Variable -- 10.3.1 Cumulative Logits -- 10.3.2 Proportional Odds Models -- 10.3.3 Adjacent-Category Logit Models -- 10.3.4 Continuation-Ratio Logit Models -- References -- 11 Log-Linear Models for I × J Tables -- 11.1 The Saturated Model -- 11.1.1 Cornered Constraints -- 11.1.2 Centered Constraints -- 11.2 The Independence Model for an I × J Table -- 12 Log-Linear Models for I × J × K Tables -- 12.1 Mutual Independence: A∕B∕C -- 12.2 The Model AB∕C -- 12.3 Conditional Independence and Independence -- 12.4 The Model AB∕AC -- 12.5 The Models AB∕AC∕BC and ABC -- 12.6 Simpson's Paradox -- 12.7 Connection between Log-Linear Models and Logistic Regression -- Reference -- 13 Implications and Uses of Birch's Result -- 13.1 Birch's Result -- 13.2 Iterative Scaling -- 13.3 The Hierarchy Constraint -- 13.4 Inclusion of the All-Factor Interaction -- 13.5 Mostellerizing -- References -- 14 Model Selection for Log-Linear Models -- 14.1 Three Variables -- 14.2 More than Three Variables -- Reference -- 15 Incomplete Tables, Dummy Variables, and Outliers -- 15.1 Incomplete Tables -- 15.1.1 Degrees of Freedom -- 15.2 Quasi-independence -- ; 15.3 Dummy Variables -- 15.4 Detection of Outliers -- 16 Panel Data and Repeated Measures -- 16.1 The Mover-Stayer Model -- 16.2 The Loyalty Model -- 16.3 Symmetry -- 16.4 Quasi-Symmetry -- 16.5 The Loyalty-Distance Model -- References -- Appendix R Code for Cobweb Function -- Index -- Author Index.; Index of Examples -- EULA.