Statistical Methods for Categorical Data Analysis

by Powers; Xie

• ISBN13: 9780125637367
• ISBN10: 0125637365
• Format: Hardcover
• Copyright: 1999-11-12
• Publisher: Elsevier Science & Technology

Summary

Statistical Methods for Categorical Data Analysislt;/b> is designed as an accessible reference work and textbook about categorical data (that is, data arising from counts instead of measurement. Examples include data about birth, death, marriage, and so forth). It integrates statistical and econometric approaches to the analysis of limited and categorical dependent variables, thereby offering a practical, mathematically uncomplicated approach to the topics of modern data analysis. The volume offers a comprehensive presentation of many different models in a one-volume format (with website). Two features distinguish this book from other analyses of categorical data. First, the authors present both the transformational and latent variable approaches and so synthesize similar methods in statistical and econometric literatures. Second, the book has an applied orientation and features actual examples from social science research. The authors keep discussions of theory to a minimum. Key Features * Exercises and examples utilize popular data already familiar to many social scientists * Examples of the use of various popular software packages * Includes non-standard applications of existing software for estimating models which cannot be handled directly using existing pre-programmed software

Table of Contents

Preface	xiii
Introduction
Why Categorical Data Analysis?	1	(6)
Defining Categorical Variables	2	(1)
Dependent and Independent Variables	3	(1)
Categorical Dependent Variables	4	(1)
Types of Measurement	5	(2)
Two Philosophies of Categorical Data	7	(4)
The Transformational Approach	8	(1)
The Latent Variable Approach	9	(2)
An Historical Note	11	(1)
Approach of This Book	12	(3)
Organization of the Book	13	(2)
Review of Linear Regression Models
Regression Models	15	(9)
Three Conceptualizations of Regression	16	(2)
Anatomy of Linear Regression	18	(2)
Basics of Statistical Inference	20	(2)
Tension between Accuracy and Parsimony	22	(2)
Linear Regression Models Revisited	24	(13)
Least Squares Estimation	24	(1)
Maximum Likelihood Estimation	25	(4)
Assumptions for Least Squares Regression	29	(1)
Comparisons of Conditional Means	30	(2)
Linear Models with Weaker Assumptions	32	(5)
Categorical and Continuous Dependent Variables	37	(4)
A Working Typology	38	(3)
Logit and Probit Models for Binary Data
Introduction to Binary Data	41	(2)
The Transformational Approach	43	(12)
The Linear Probability Model	43	(6)
The Logit Model	49	(3)
The Probit Model	52	(1)
An Application Using Grouped Data	53	(2)
Justification of Logit and Probit Models	55	(20)
The Latent Variable Approach	56	(3)
Extending the Latent Variable Approach	59	(2)
Estimation of Binary Response Models	61	(2)
Goodness-of-Fit and Model Selection	63	(8)
Hypothesis Testing and Statistical Inference	71	(4)
Interpreting Estimates	75	(8)
The Odds-Ratio	75	(1)
Marginal Effects	76	(4)
An Application Using Individual-Level Data	80	(3)
Alternative Probability Models	83	(2)
The Complementary Log--Log Model	83	(2)
Programming Binomial Response Models	85	(1)
Summary	85	(2)
Loglinear Models for Contingency Tables
Contingency Tables	87	(6)
Types of Contingency Tables	88	(1)
An Example and Notation	88	(2)
Independence and the Pearson x2 Statistic	90	(3)
Measures of Association	93	(6)
Homogeneous Proportions	93	(1)
Relative Risks	94	(1)
Odds-Ratios	95	(2)
The Invariance Property of Odds-Ratios	97	(2)
Estimation and Goodness-of-Fit	99	(8)
Simple Models and the Pearson x2 Statistic	100	(2)
Sampling Models and Maximum Likelihood Estimation	102	(2)
The Likelihood-Ratio Chi-Squared Statistic	104	(2)
Bayesian Information Criterion	106	(1)
Models for Two-Way Tables	107	(12)
The General Setup	107	(1)
Normalization	108	(2)
Interpretation of Parameters	110	(1)
Topological Model	111	(3)
Quasi-independence Model	114	(2)
Symmetry and Quasi-symmetry	116	(1)
Crossings Model	117	(2)
Models for Ordinal Variables	119	(10)
Linear-by-Linear Association	119	(1)
Uniform Association	120	(2)
Row-Effect and Column-Effect Models	122	(2)
Goodman's RC Model	124	(5)
Models for Multiway Tables	129	(18)
Three-Way Tables	130	(2)
The Saturated Model for Three-Way Tables	132	(1)
Collapsibility	133	(2)
Classes of Models for Three-Way Tables	135	(5)
Analysis of Variation in Association	140	(5)
Model Selection	145	(2)
Statistical Models for Rates
Introduction	147	(1)
Log-Rate Models	148	(12)
The Role of Exposure	149	(5)
Estimating Log-Rate Models	154	(2)
Illustration	156	(3)
Interpretation	159	(1)
Discrete-Time Hazard Models	160	(8)
Data Structure	161	(1)
Estimation	162	(6)
Semiparametric Rate Models	168	(9)
The Piecewise Constant Exponential Model	169	(5)
The Cox Model	174	(3)
Models for Panel Data	177	(11)
Fixed Effects Models for Binary Data	179	(4)
Random Effects Models for Binary Data	183	(5)
Unobserved Heterogeneity in Event-History Models	188	(11)
The Gamma Mixture Model	190	(9)
Summary	199	(2)
Models for Ordinal Dependent Variables
Introduction	201	(1)
Scoring Methods	202	(4)
Integer Scoring	202	(1)
Midpoint Scoring	203	(1)
Normal Score Transformation	204	(1)
Scaling with Additional Information	205	(1)
Logit Models for Grouped Data	206	(4)
Baseline, Adjacent, and Cumulative Logits	206	(1)
Adjacent Category Logit Model	207	(2)
Adjacent Category Logit Models and Loglinear Models	209	(1)
Ordered Logit and Probit Models	210	(12)
Cumulative Logits and Probits	211	(1)
The Ordered Logit Model	212	(2)
The Ordered Probit Model	214	(1)
The Latent Variable Approach	215	(2)
Estimation	217	(3)
Marginal Effects	220	(2)
Summary	222	(1)
Models for Unordered Dependent Variables
Introduction	223	(1)
Multinomial Logit Models	224	(3)
Review of the Binary Logit Model	224	(1)
General Setup for the Multinomial Logit Model	225	(2)
The Standard Multinomial Logit Model	227	(7)
Estimation	229	(1)
Interpreting Results from Multinomial Logit Models	230	(4)
Loglinear Models for Grouped Data	234	(4)
Two-Way Tables	234	(1)
Three- and Higher-Way Tables	235	(3)
The Latent Variables Approach	238	(1)
The Conditional Logit Model	239	(6)
Interpretation	240	(2)
The Mixed Model	242	(3)
Specification Issues	245	(7)
Independence of Irrelevant Alternatives: The IIA Assumption	245	(4)
Sequential Logit Models	249	(3)
Summary	252	(1)
A The Matrix Approach to Regression
A.1 Introduction	253	(1)
A.2 Matrix Algebra	253	(8)
A.2.1 The Matrix Approach to Regression	254	(1)
A.2.2 Basic Matrix Operations	255	(4)
A.2.3 Numerical Example	259	(2)
B Maximum Likelihood Estimation
B.1 Introduction	261	(1)
B.2 Basic Principles	261	(1)
B.2.1 Example 1: Binomial Proportion	262	(2)
B.2.2 Example 2: Normal Mean and Variance	264	(2)
B.2.3 Example 3: Binary Logit Model	266	(6)
B.2.4 Example 4: Loglinear Model	272	(3)
B.2.5 Iteratively Reweighted Least Squares	275	(2)
B.2.6 Generalized Linear Models	277	(4)
B.2.7 Minimum x2 Estimation	281