This unique book provides a comprehensive and detailed coverage of configural frequency analysis (CFA), the most useful method of analysis of categorical data in person-oriented research. It presents the foundations, methods, and models of CFA and features numerous empirical data examples from a range of disciplines that can be reproduced by the readers. It also addresses computer applications, including relevant R packages and modules.
Configural frequency analysis is a statistical method that allows the processing of important and interesting questions in categorical data. The perspective of CFA differs from the usual perspective of relations among variables; its focus is on patterns of variable categories that stand out with respect to specific hypotheses, and as such, CFA allows for testing numerous substantive hypotheses.
The book describes the origins of CFA and their relation to chi-square analysis as well as the developments that are based on log-linear modeling. The models covered range from simple models of variable independence to complex models that are needed when causal hypotheses are tested. Empirical data examples are provided for each model. New models are introduced for person-oriented mediation analysis and locally optimized time series analysis, and new results concerning the characteristics of CFA methods are bolstered using Monte Carlo simulations.
Primarily intended for researchers and students in the social and behavioral sciences, the book will also appeal to anyone who deals with categorical data from a person-centered perspective.
Author(s): Alexander von Eye, Wolfgang Wiedermann
Series: Statistics for Social and Behavioral Sciences
Publisher: Springer
Year: 2022
Language: English
Pages: 403
City: Cham
Preface
Contents
Chapter 1: Questions that Can Be Answered with CFA
References
Chapter 2: Elements of CFA
2.1 Lienert´s Version of CFA
2.2 Log-Linear Models for the Estimation of Expected Cell Frequencies in CFA
2.3 CFA Base Models and Their Design Matrices
2.4 Base Models of CFA
2.4.1 A Classification of Base Models for CFA
2.4.2 Global CFA Base Models
2.4.3 Regional Models of CFA
2.4.4 Multi-Step CFA Models
2.5 CFA of Transformed Data
2.6 CFA Under Consideration of Special Variables
2.7 Testing Hypotheses in CFA
2.7.1 CFA Significance Tests
2.7.2 The Exact Binomial Test
2.7.3 Approximative Tests
2.7.4 Tests for Groups of Configurations
2.7.5 Protecting the Significance Level α
2.7.6 Methods for the Protection of α
2.8 The Four Steps of CFA
References
Chapter 3: Models of CFA
3.1 Global CFA Models
3.1.1 Zero Order CFA
3.1.2 First Order CFA
3.1.3 Second and Higher Order CFA
3.1.4 Global CFA After Removal of a Group of Effects
3.2 Regional Models of CFA
3.2.1 Finding Groups of Variables for CFA
3.2.2 Prediction CFA
3.2.3 Bi-Prediction CFA
3.2.4 Comparing Groups of Data Carriers
3.2.4.1 Two-Group CFA
3.2.4.2 Descriptive Measures for Two-Group CFA
Gonzles-Debén´s Effect Strength π*
Rosenthal and Rubin´s Binomial Effect Strength (BES)
3.2.4.3 Three Ways to Deviate from Independence
3.2.4.4 CFA for the Comparison of Multiple Groups
References
Chapter 4: Models of Longitudinal CFA
4.1 CFA of Differences
4.1.1 Difference Scores
4.1.2 CFA of Differences
4.1.3 Expected Frequencies in the Analysis of Difference Variables
4.2 Level, Variability, and Shape of Series of Measures
4.2.1 CFA of Change in Level of Series of Measures
4.2.2 CFA of Variability of Series of Measures
4.2.3 CFA of Polynomial Parameters
4.2.4 Series of Scores that Differ in Length
4.3 CFA in Quasi-Experimental and in Experimental Designs
4.3.1 CFA and Designs with no Control Group
4.3.2 CFA of Data from Control Group Designs
4.4 Confirmatory CFA of Longitudinal Data
4.5 CFA of Longitudinal Correlations or Distances
4.6 Prediction in Longitudinal Data
4.6.1 Predicting the End Point of a Series of Scores
4.6.2 Predicting a Trajectory with CFA
4.6.3 Predicting One Trajectory from another
4.7 Auto-Association CFA
4.8 Predicting the Shape of a Curve: The Case of Multiple Predictors
4.9 CFA of Lags: Intra-Individual Series of Scores
4.10 Functions as CFA Base Models
References
Chapter 5: Designs for CFA
5.1 Fractional Factorial Designs for CFA
5.1.1 Fractional Factorial Designs: An Introduction
5.1.2 Creating Fractional Factorial Designs
5.1.3 Fractional Factorial Designs in CFA
5.2 Structural Zeros in CFA
5.2.1 Incomplete Tables and Separability
5.2.2 Design-Specific Structural Zeros
References
Chapter 6: Special Variables in CFA
6.1 Covariates in CFA
6.2 CFA with Ordinal Variables
6.2.1 Iterative Proportional Fitting
6.2.2 The Linear-by-Linear Association Model
6.3 Moderator Variables in CFA
6.4 Mediator CFA
6.4.1 Significance Testing of the Indirect Effect
6.4.2 Evaluating Mediator Hypotheses
6.4.3 Causal Mediator Analysis
6.4.4 Mediator Models for Categorical Variables
6.4.5 Configural Mediation Analysis
6.4.5.1 Pattern-Specific Mediation Models
6.4.5.2 von Eye et al.´s (2009) Method of Mediation Analysis
6.4.5.3 Smyth and MacKinnon´s (2020) Modifications
6.4.5.4 Wiedermann and von Eye´s (2020) Method
References
Chapter 7: The Treasure Chest of CFA
7.1 Alternative Approaches to CFA
7.1.1 Victor´s Alternative Exploratory CFA
7.1.2 von Eye and Mair´s Alternative Sequential CFA
7.2 Functional CFA
7.2.1 Functional CFA I: The Ascending, Inclusive Strategy
7.2.2 Functional CFA II: The Descending Excluding Strategy
7.3 CFA and Tree Structures
7.4 Rater Agreement
7.5 CFA of Large Sparse Tables
7.6 CFA as Test of Multivariate Normality
7.7 Latent Class Analysis and CFA
7.8 CFA and Causality
7.8.1 Forms of Causal Relations
7.8.2 CFA and Granger Causality
7.9 CFA of Intensive Longitudinal Data
7.10 Bayes CFA
7.10.1 Bayes Definition of Types and Antitypes
7.10.2 Patterns of Types and Antitypes
7.11 Limits of CFA: Issues and Countermeasures
References
Chapter 8: Software for CFA
8.1 CFA Fortran Program
8.2 R Packages and Modules
8.2.1 Global CFA Base Models
8.2.2 Prediction CFA
8.2.3 Two-Group CFA
8.2.4 Bayes CFA
References
References
Index
