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2014 | Buch

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Contingency Table Analysis

Methods and Implementation Using R

verfasst von: Maria Kateri

Verlag: Springer New York

Buchreihe : Statistics for Industry and Technology

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Contingency tables arise in diverse fields, including life sciences, education, social and political sciences, notably market research and opinion surveys. Their analysis plays an essential role in gaining insight into structures of the quantities under consideration and in supporting decision making.

Combining both theory and applications, this book presents models and methods for the analysis of two- and multidimensional-contingency tables. The author uses a threefold approach, presenting fundamental models and related inference, highlighting their interpretational aspects, and demonstrating their practical usefulness. Emphasis is on applications and methods of fitting models using standard statistical tools - such as SPSS, R, and BUGS - and on interpretation of the results.

An excellent reference for advanced undergraduates, graduate students, and practitioners in statistics as well as biosciences, social sciences, education, and economics, the work may also be used as a textbook for a course on categorical data analysis. Prerequisites include basic background on statistical inference and knowledge of statistical software packages.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

Preliminary material on scales, distributions, and inferential procedures for categorical data is briefly presented. Classes of models, usually applied for categorical data analysis, are introduced and discussed. Finally, the outline of the book is presented.

Maria Kateri

Chapter 2. Analysis of Two-way Tables

Abstract

Basic concepts of two-way contingency table analysis are introduced. Descriptive and inferential results on estimation and testing of basic hypotheses are discussed and illustrated in R. In particular the comparison of two independent proportions, the test of independence for 2 × 2 and I × J contingency tables, the linear trend test, and the Fisher’s exact test are presented. Special emphasis is given to the odds ratio for 2 × 2 tables, while the generalized odds ratios for I × J tables are treated in detail. Finally, graphical displays of categorical data (barplot, fourfold plot, sieve diagram, and mosaic plot) are derived using R for examples of this chapter and discussed.

Maria Kateri

Chapter 3. Analysis of Multi-way Tables

Abstract

Issues discussed in Chap.2 for two-way tables are extended to multi-way contingency tables. Emphasis is given to clarifying the concepts of partial and marginal association. Further on, stratified 2 × 2 tables are analyzed by the Mantel–Haenszel and the Breslow–Day–Tarone tests. Types of independence for three-way tables are introduced. Graphs are presented for multi-way contingency tables while fourfold plots are used to visualize stratified 2 × 2 tables. All examples are implemented in R.

Maria Kateri

Chapter 4. Log-Linear Models

Abstract

The classical log-linear models are introduced for two-way and multi-way contingency tables. Estimation theory, goodness-of-fit testing, and model selection procedures are discussed. Characteristic examples are worked out in R and interpreted. Log-linear models for three-dimensional tables are illustrated through mosaic plots. Graphical models are shortly discussed. Finally the collapsibility in multi-way tables, in connection to Simpson’s paradox, is addressed.

Maria Kateri

Chapter 5. Generalized Linear Models and Extensions

Abstract

The generalized linear model (GLM) is reviewed and the log-linear models are integrated in this family. For GLMs, maximum likelihood estimation, model fit, and model selection are discussed. In the GLM framework the analysis of incomplete tables is more straightforward. The quasi-independence model is defined and illustrated in R. Furthermore, the family of generalized log-linear models (GLLMs) is briefly presented and a GLLM is illustrated with a representative example in R.

Maria Kateri

Chapter 6. Association Models

Abstract

The association models, appropriate for the analysis of ordinal contingency tables, are presented for two-way and multi-way contingency tables. Their features, properties, and the associated graphs are discussed. The models of uniform association (U), row effect (R), column effect (C), multiplicative row–column effect (RC), and the more general RC(M) model are illustrated with examples in terms of fit, presentation, and interpretation. They are all worked out in R, through functions provided for their fit and the construction of their scores’ plots.

Maria Kateri

Chapter 7. More on Association Models and Related Methods

Abstract

Advanced issues on association models are discussed in this chapter. These include exploring the rows and/or columns heterogeneity in a contingency table, the issue of merging categories of a classification variable, and the consideration of association models for generalized odds ratios other than the local odds ratios. The uniform association model for the global odds ratios is illustrated with an example in R. Correspondence analysis (CA) is also presented and connected to association models. For comparison purposes, CA is applied in R on one of the examples analyzed in Chap. 6 by association models.

Maria Kateri

Chapter 8. Response Variable Analysis in Contingency Tables

Abstract

Logit models for binary, nominal, and ordinal responses are introduced in Chap. 8. In particular beyond the basic logit model for binary response, the baseline category logit, the cumulative logit, and the proportional odds models are presented. Also logit models for ordinal explanatory variables are considered as well as the logit analysis of stratified 2 × 2 contingency tables. Logit models are connected to association models and illustrated with examples, worked out in R.

Maria Kateri

Chapter 9. Analysis of Square Tables

Abstract

Special models for matched pairs of ordinal responses are presented in Chap. 9. Beyond the classical models of symmetry and quasi symmetry, the models of conditional symmetry, diagonal symmetry, and ordinal quasi symmetry are discussed in detail. The model of marginal homogeneity is tested as a generalized log-linear model and not only conditioning on quasi symmetry, as is usually done. Connections to rater agreement models and mobility table analysis are made.

Maria Kateri

Chapter 10. Further Topics

Abstract

This epilogue chapter refers briefly to alternative methods and approaches in the analysis of contingency tables (latent class models, graphical models, and smoothing), not covered in the book. Furthermore, a bibliography on small sample inference, Bayesian inference, and the analysis of high-dimensional sparse contingency tables is discussed.

Maria Kateri

Backmatter

Titel: Contingency Table Analysis
verfasst von: Maria Kateri
Verlag: Springer New York
Electronic ISBN: 978-0-8176-4811-4
Print ISBN: 978-0-8176-4810-7
DOI: https://doi.org/10.1007/978-0-8176-4811-4