The nature of doing science, be it natural or social, inevitably calls for comparison. Statistical methods are at the heart of such comparison, for they not only help us gain understanding of the world around us but often define how our research is to be carried out. The need to compare between groups is best exemplified by experiments, which have clearly defined statistical methods. However, true experiments are not always possible. What complicates the matter more is a great deal of diversity in factors that are not independent of the outcome.
Statistical Group Comparison brings together a broad range of statistical methods for comparison developed over recent years. The book covers a wide spectrum of topics from the simplest comparison of two means or rates to more recently developed statistics including double generalized linear models and Bayesian as well as hierarchical methods. Coverage includes:
∗ Testing parameter equality in linear regression and other generalized linear models (GLMs), in order of increasing complexity
∗ Likelihood ratio, Wald, and Lagrange multiplier statistics examined where applicable
∗ Group comparisons involving latent variables in structural equation modeling
∗ Models of comparison for categorical latent variables
Examples are drawn from the social, political, economic, and biomedical sciences; many can be implemented using widely available software. Because of the range and the generality of the statistical methods covered, researchers across many disciplines–beyond the social, political, economic, and biomedical sciences–will find the book a convenient reference for many a research situation where comparisons may come naturally.
1.1 Rationale for Statistical Comparison.
1.2 Comparative Research in the Social Sciences.
1.3 Focus of the Book.
1.4 Outline of the Book.
2. Statistical Foundation for Comparison.
2.1 A System for Statistical Comparison.
2.2 Test Statistics.
2.3 What to Compare?
3. Comparison in Linear Models.
3.2 An Example.
3.3 Some Preliminary Considerations.
3.4 The Linear Model.
3.5 Comparing Two Means.
3.7 Multiple Comparison Methods.
3.9 Multiple Linear Regression.
3.10 Regression Decomposition.
3.11 Which Linear Method to Use?
4. Nonparametric Comparison.
4.1 Nonparametric Tests.
4.2 Resampling Methods.
4.3 Relative Distribution Methods.
5. Comparison of Rates.
5.1 The Data.
6. Comparison in Generalized Linear Models.
6.2 Comparing Generalized Linear Models.
6.3 A Logit Model Example.
6.4 A Hazard Rate Model Example.
6.A Data Used in Section 6.4.
7. Additional Topics of Comparison in Generalized Linear Models.
7.2 GLM for Matched Case–Control Studies.
7.3 Dispersion Heterogeneity.
7.4 Bayesian Generalized Linear Models.
7.A The Data for the n : m Design.
8. Comparison in Structural Equation Modeling.
8.2 Statistical Background.
8.3 Mean and Covariance Structures.
8.4 Group Comparison in SEM.
8.5 An Example.
8.A Examples of Computer Program Listings.
9. Comparison with Categorical Latent Variables.
9.2 Latent Class Models.
9.3 Latent Trait Models.
9.4 Latent Variable Models for Continuous Indicators.
9.5 Casual Models with Categorical Latent variables.
9.6 Comparison with Categorical Latent Variables.
9.A Software for Categorical Latent Variables.
9.B Computer Program Listings for the Examples.
10. Comparison in Multilevel Analysis.
10.2 An Introduction to Multilevel Analysis.
10.3 The Basics of the Linear Multilevel Model.
10.4 The Basics of the Generalized Linear Multilevel Model.
10.5 Group as an External Variable in Multilevel Analysis.
10.6 The Relation between Multilevel Analysis and Group Comparison.
10.7 Multiple Membership Models.
10.A Software for Multilevel Analysis.
10.B SAS Program Listings for GLMM Examples.
"...excellent resource book...highly recommended for graduate students, faculty, and researchers." (Choice, Vol. 40, No. 3, November 2002)
"...graduate students and applied researchers may find the book a convenient reference..." (Short Book Reviews, December 2002)
"...brings together a broad range of statistical methods for comparison developed over recent years." (Mathematical Reviews, 2003b)
"...covers a wide variety of statistical methodologies in which group comparisons play a key role...worth reading...to get an overview of...topics covered." (Technometrics, Vol. 45, No. 2, May 2003)