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Viser: An Introduction to Categorical Data Analysis

An Introduction to Categorical Data Analysis, 2. udgave

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Alan Agresti
(2007)
John Wiley & Sons
562,00 kr.
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An Introduction to Categorical Data Analysis, 2. udgave

An Introduction to Categorical Data Analysis Vital Source e-bog

Alan Agresti
(2007)
John Wiley & Sons
449,00 kr.
Leveres umiddelbart efter køb
An Introduction to Categorical Data Analysis

An Introduction to Categorical Data Analysis

Alan Agresti
(2007)
Sprog: Engelsk
John Wiley & Sons, Limited
640,00 kr. 149,00 kr.
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Detaljer Om Varen

  • 2. Udgave
  • Vital Source E-book
  • Udgiver: John Wiley & Sons (Marts 2007)
  • ISBN: 9780470114742
An Introduction to Categorical Data Analysis, Second Edition presents an introduction to the most important methods for analyzing categorical data. It summarizes methods that have long played a prominent role such as chi-squared tests and measures of association. It provides special emphasis, however, to logistic regression and loglinear modeling techniques for univariate and correlated multivariate categorical responses. This Second Edition presents new methods for clustered data, which are increasingly common in longitudinal studies, for example. Two new chapters discuss these methods along with improvements in major software. Chapter 10 deals with marginal models, including the generalized estimating equations (GEE) approach. Chapter 11 deals with random effects models through generalized linear models. Earlier chapters and appendices are updated.
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Detaljer Om Varen

  • 2. Udgave
  • Vital Source leje e-bog 365 dage
  • Udgiver: John Wiley & Sons (Marts 2007)
  • ISBN: 9780470114742R365
An Introduction to Categorical Data Analysis, Second Edition presents an introduction to the most important methods for analyzing categorical data. It summarizes methods that have long played a prominent role such as chi-squared tests and measures of association. It provides special emphasis, however, to logistic regression and loglinear modeling techniques for univariate and correlated multivariate categorical responses. This Second Edition presents new methods for clustered data, which are increasingly common in longitudinal studies, for example. Two new chapters discuss these methods along with improvements in major software. Chapter 10 deals with marginal models, including the generalized estimating equations (GEE) approach. Chapter 11 deals with random effects models through generalized linear models. Earlier chapters and appendices are updated.
Licens varighed:
Online udgaven er tilgængelig: 365 dage fra købsdato.
Offline udgaven er tilgængelig: 365 dage fra købsdato.

Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 10 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)

Detaljer Om Varen

  • Hardback: 400 sider
  • Udgiver: John Wiley & Sons, Limited (April 2007)
  • ISBN: 9780471226185
The first edition of this text has sold over 19,600 copies.However, the use of statistical methods for categorical data hasincreased dramatically in recent years, particularly forapplications in the biomedical and social sciences. A secondedition of the introductory version of the book will suit itnicely. Wiley also published a second editionof Categorical Data Analysis, which is an advanced,more technical text, in 2003.

 

Preface
to the Second Edition xv
1. Introduction
1
1.
1 Categorical Response Data, 1
1.
1.
1 Response / Explanatory Variable Distinction, 2
1.
1.
2 Nominal / Ordinal Scale Distinction, 2
1.
1.
3 Organization of this Book, 3
1.
2 Probability Distributions for Categorical Data, 3
1.
2.
1 Binomial Distribution, 4
1.
2.
2 Multinomial Distribution, 5
1.
3 Statistical Inference for a Proportion, 6
1.
3.
1 Likelihood Function and Maximum Likelihood Estimation, 6
1.
3.
2 Significance Test About a Binomial Proportion, 8
1.
3.
3 Example: Survey Results on Legalizing Abortion, 8
1.
3.
4 Confidence Intervals for a Binomial Proportion, 9
1.
4 More on Statistical Inference for Discrete Data, 11
1.
4.
1 Wald, Likelihood-Ratio, and Score Inference, 11
1.
4.
2 Wald, Score, and Likelihood-Ratio Inference for Binomial Parameter, 12
1.
4.
3 Small-Sample Binomial Inference, 13
1.
4.
4 Small-Sample Discrete Inference is Conservative, 14
1.
4.
5 Inference Based on the Mid P -value, 15
1.
4.
6 Summary, 16 Problems, 16
2. Contingency Tables 21
2.
1 Probability Structure for Contingency Tables, 21
2.
1.
1 Joint, Marginal, and Conditional Probabilities, 22
2.
1.
2 Example: Belief in Afterlife, 22
2.
1.
3 Sensitivity and Specificity in Diagnostic Tests, 23
2.
1.
4 Independence, 24
2.
1.
5 Binomial and Multinomial Sampling, 25
2.
2 Comparing Proportions in Two-by-Two Tables, 25
2.
2.
1 Difference of Proportions, 26
2.
2.
2 Example: Aspirin and Heart Attacks, 26
2.
2.
3 Relative Risk, 27
2.
3 The Odds Ratio, 28
2.
3.
1 Properties of the Odds Ratio, 29
2.
3.
2 Example: Odds Ratio for Aspirin Use and Heart Attacks, 30
2.
3.
3 Inference for Odds Ratios and Log Odds Ratios, 30
2.
3.
4 Relationship Between Odds Ratio and Relative Risk, 32
2.
3.
5 The Odds Ratio Applies in Case-Control Studies, 32
2.
3.
6 Types of Observational Studies, 34
2.
4 Chi-Squared Tests of Independence, 34
2.
4.
1 Pearson Statistic and the Chi-Squared Distribution, 35
2.
4.
2 Likelihood-Ratio Statistic, 36
2.
4.
3 Tests of Independence, 36
2.
4.
4 Example: Gender Gap in Political Affiliation, 37
2.
4.
5 Residuals for Cells in a Contingency Table, 38
2.
4.
6 Partitioning Chi-Squared, 39
2.
4.
7 Comments About Chi-Squared Tests, 40
2.
5 Testing Independence for Ordinal Data, 41
2.
5.
1 Linear Trend Alternative to Independence, 41
2.
5.
2 Example: Alcohol Use and Infant Malformation, 42
2.
5.
3 Extra Power with Ordinal Tests, 43
2.
5.
4 Choice of Scores, 43
2.
5.
5 Trend Tests for I ? 2 and 2 ? J Tables, 44
2.
5.
6 Nominal-Ordinal Tables, 45
2.
6 Exact Inference for Small Samples, 45
2.
6.
1 Fisher''s Exact Test for 2 ? 2 Tables, 45
2.
6.
2 Example: Fisher''s Tea Taster, 46
2.
6.
3 P -values and Conservatism for Actual P (Type I Error), 47
2.
6.
4 Small-Sample Confidence Interval for Odds Ratio, 48
2.
7 Association in Three-Way Tables, 49
2.
7.
1 Partial Tables, 49
2.
7.
2 Conditional Versus Marginal Associations: Death Penalty Example, 49
2.
7.
3 Simpson''s Paradox, 51
2.
7.
4 Conditional and Marginal Odds Ratios, 52
2.
7.
5 Conditional Independence Versus Marginal Independence, 53
2.
7.
6 Homogeneous Association, 54 Problems, 55
3. Generalized Linear Models 65
3.
1 Components of a Generalized Linear Model, 66
3.
1.
1 Random Component, 66
3.
1.
2 Systematic Component, 66
3.
1.
3 Link Function, 66
3.
1.
4 Normal GLM, 67
3.
2 Generalized Linear Models for Binary Data, 68
3.
2.
1 Linear Probability Model, 68
3.
2.
2 Example: Snoring and Heart Disease, 69
3.
2.
3 Logistic Regression Model, 70
3.
2.
4 Probit Regression Model, 72
3.
2.
5 Binary Regression and Cumulative Distribution Functions, 72
3.
3 Generalized Linear Models for Count Data, 74
3.
3.
1 Poisson Regression, 75
3.
3.
2 Example: Female Horseshoe Crabs and their Satellites, 75
3.
3.
3 Overdispersion: Greater Variability than Expected, 80
3.
3.
4 Negative Binomial Regression, 81
3.
3.
5 Count Regression for Rate Data, 82
3.
3.
6 Example: British Train Accidents over Time, 83
3.
4 Statistical Inference and Model Checking, 84
3.
4.
1 Inference about Model Parameters, 84
3.
4.
2 Example: Snoring and Heart Disease Revisited, 85
3.
4.
3 The Deviance, 85
3.
4.
4 Model Comparison Using the Deviance, 86
3.
4.
5 Residuals Comparing Observations to the Model Fit, 87
3.
5 Fitting Generalized Linear Models, 88
3.
5.
1 The Newton-Raphson Algorithm Fits GLMs, 88
3.
5.
2 Wald, Likelihood-Ratio, and Score Inference Use the Likelihood Function, 89
3.
5.
3 Advantages of GLMs, 90 Problems, 90
4. Logistic Regression 99
4.
1 Interpreting the Logistic Regression Model, 99
4.
1.
1 Linear Approximation Interpretations, 100
4.
1.
2 Horseshoe Crabs: Viewing and Smoothing a Binary Outcome, 101
4.
1.
3 Horseshoe Crabs: Interpreting the Logistic Regression Fit, 101
4.
1.
4 Odds Ratio Interpretation, 104
4.
1.
5 Logistic Regression with Retrospective Studies, 105
4.
1.
6 Normally Distributed X Implies Logistic Regression for Y , 105
4.
2 Inference for Logistic Regression, 106
4.
2.
1 Binary Data can be Grouped or Ungrouped, 106
4.
2.
2 Confidence Intervals for Effects, 106
4.
2.
3 Significance Testing, 107
4.
2.
4 Confidence Intervals for Probabilities, 108
4.
2.
5 Why Use a Model to Estimate Probabilities?, 108
4.
2.
6 Confidence Intervals for Probabilities: Details, 108
4.
2.
7 Standard Errors of Model Parameter Estimates, 109
4.
3 Logistic Regression with Categorical Predictors, 110
4.
3.
1 Indicator Variables Represent Categories of Predictors, 110
4.
3.
2 Example: AZT Use and AIDS, 111
4.
3.
3 ANOVA-Type Model Representation of Factors, 113
4.
3.
4 The Cochran-Mantel-Haenszel Test for 2 ? 2 ? K Contingency Tables, 114
4.
3.
5 Testing the Homogeneity of Odds Ratios, 115
4.
4 Multiple Logistic Regression, 115
4.
4.
1 Example: Horseshoe Crabs with Color andWidth Predictors, 116
4.
4.
2 Model Comparison to Check Whether a Term is Needed, 118
4.
4.
3 Quantitative Treatment of Ordinal Predictor, 118
4.
4.
4 Allowing Interaction, 119
4.
5 Summarizing Effects in Logistic Regression, 120
4.
5.
1 Probability-Based Interpretations, 120
4.
5.
2 Standardized Interpretations, 121 Problems, 121
5. Building and Applying Logistic Regression Models 137
5.
1 Strategies in Model Selection, 137
5.
1.
1 How Many Predictors CanYou Use?, 138
5.
1.
2 Example: Horseshoe Crabs Revisited, 138
5.
1.
3 Stepwise Variable Selection Algorithms, 139
5.
1.
4 Example: Backward Elimination for Horseshoe Crabs, 140
5.
1.
5 AIC, Model Selection, and the "Correct" Model, 141
5.
1.
6 Summarizing Predictive Power: Classification Tables, 142
5.
1.
7 Summarizing Predictive Power: ROC Curves, 143
5.
1.
8 Summarizing Predictive Power: A Correlation, 144
5.
2 Model Checking, 144
5.
2.
1 Likelihood-Ratio Model Comparison Tests, 144
5.
2.
2 Goodness of Fit and the Deviance, 145
5.
2.
3 Checking Fit: Grouped Data, Ungrouped Data, and Continuous Predictors, 146
5.
2.
4 Residuals for Logit Models, 147
5.
2.
5 Example: Graduate Admissions at University of Florida, 149
5.
2.
6 Influence Diagnostics for Logistic Regression, 150
5.
2.
7 Example: Heart Disease and Blood Pressure, 151
5.
3 Effects of Sparse Data, 152
5.
3.
1 Infinite Effect Estimate: Quantitative Predictor, 152
5.
3.
2 Infinite Effect Estimate: Categorical Predictors, 153
5.
3.
3 Example: Clinical Trial with Sparse Data, 154
5.
3.
4 Effect of Small Samples on X 2 and G 2 Tests, 156
5.
4 Conditional Logistic Regression and Exact Inference, 157
5.
4.
1 Conditional Maximum Likelihood Inference, 157
5.
4.
2 Small-Sample Tests for Contingency Tables, 158
5.
4.
3 Example: Promotion Discrimination, 159
5.
4.
4 Small-Sample Confidence Intervals for Logistic Parameters and Odds Ratios, 159
5.
4.
5 Limitations of Small-Sample Exact Methods, 160
5.
5 Sample Size and Power for Logistic Regression, 160
5.
5.
1 Sample Size for Comparing Two Proportions, 161
5.
5.
2 Sample Size in Logistic Regression, 161
5.
5.
3 Sample Size in Multiple Logistic Regression, 162 Problems, 163
6. Multicategory Logit Models 173
6.
1 Logit Models for Nominal Responses, 173
6.
1.
1 Baseline-Category Logits, 173
6.
1.
2 Example: Alligator Food Choice, 174
6.
1.
3 Estimating Response Probabilities, 176
6.
1.
4 Example: Belief in Afterlife, 178
6.
1.
5 Discrete Choice Models, 179
6.
2 Cumulative Logit Models for Ordinal Responses, 180
6.
2.
1 Cumulative Logit Models with Proportional Odds Property, 180
6.
2.
2 Example: Political Ideology and Party Affiliation, 182
6.
2.
3 Inference about Model Parameters, 184
6.
2.
4 Checking Model Fit, 184
6.
2.
5 Example: Modeling Mental Health, 185
6.
2.
6 Interpretations Comparing Cumulative Probabilities, 187
6.
2.
7 Latent Variable Motivation, 187
6.
2.
8 Invariance to Choice of Response Categories, 189
6.
3 Paired-Category Ordinal Logits, 189
6.
3.
1 Adjacent-Categories Logits, 190
6.
3.
2 Example: Political Ideology Revisited, 190
6.
3.
3 Continuation-Ratio Logits, 191
6.
3.
4 Example: A Developmental Toxicity Study, 191
6.
3.
5 Overdispersion in Clustered
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