Configural Frequency Analysis: Foundations, Models, and Applications (Statistics for Social and Behavioral Sciences)

"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."--Page [4] of cover Preface 6 Contents 8 Chapter 1: Questions that Can Be Answered with CFA 12 References 19 Chapter 2: Elements of CFA 21 2.1 Lienert ́s Version of CFA 21 2.2 Log-Linear Models for the Estimation of Expected Cell Frequencies in CFA 24 2.3 CFA Base Models and Their Design Matrices 26 2.4 Base Models of CFA 29 2.4.1 A Classification of Base Models for CFA 32 2.4.2 Global CFA Base Models 32 2.4.3 Regional Models of CFA 36 2.4.4 Multi-Step CFA Models 38 2.5 CFA of Transformed Data 39 2.6 CFA Under Consideration of Special Variables 40 2.7 Testing Hypotheses in CFA 42 2.7.1 CFA Significance Tests 42 2.7.2 The Exact Binomial Test 43 2.7.3 Approximative Tests 44 2.7.4 Tests for Groups of Configurations 52 2.7.5 Protecting the Significance Level α 54 2.7.6 Methods for the Protection of α 56 2.8 The Four Steps of CFA 61 References 65 Chapter 3: Models of CFA 70 3.1 Global CFA Models 70 3.1.1 Zero Order CFA 71 3.1.2 First Order CFA 73 3.1.3 Second and Higher Order CFA 76 3.1.4 Global CFA After Removal of a Group of Effects 82 3.2 Regional Models of CFA 84 3.2.1 Finding Groups of Variables for CFA 85 3.2.2 Prediction CFA 89 3.2.3 Bi-Prediction CFA 95 3.2.4 Comparing Groups of Data Carriers 98 3.2.4.1 Two-Group CFA 99 3.2.4.2 Descriptive Measures for Two-Group CFA 104 Gonzles-Debén ́s Effect Strength π* 104 Rosenthal and Rubin ́s Binomial Effect Strength (BES) 105 3.2.4.3 Three Ways to Deviate from Independence 106 3.2.4.4 CFA for the Comparison of Multiple Groups 110 References 116 Chapter 4: Models of Longitudinal CFA 120 4.1 CFA of Differences 121 4.1.1 Difference Scores 121 4.1.2 CFA of Differences 124 4.1.3 Expected Frequencies in the Analysis of Difference Variables 128 4.2 Level, Variability, and Shape of Series of Measures 130 4.2.1 CFA of Change in Level of Series of Measures 131 4.2.2 CFA of Variability of Series of Measures 134 4.2.3 CFA of Polynomial Parameters 139 4.2.4 Series of Scores that Differ in Length 147 4.3 CFA in Quasi-Experimental and in Experimental Designs 152 4.3.1 CFA and Designs with no Control Group 152 4.3.2 CFA of Data from Control Group Designs 158 4.4 Confirmatory CFA of Longitudinal Data 159 4.5 CFA of Longitudinal Correlations or Distances 164 4.6 Prediction in Longitudinal Data 167 4.6.1 Predicting the End Point of a Series of Scores 167 4.6.2 Predicting a Trajectory with CFA 170 4.6.3 Predicting One Trajectory from another 173 4.7 Auto-Association CFA 175 4.8 Predicting the Shape of a Curve: The Case of Multiple Predictors 182 4.9 CFA of Lags: Intra-Individual Series of Scores 185 4.10 Functions as CFA Base Models 191 References 197 Chapter 5: Designs for CFA 200 5.1 Fractional Factorial Designs for CFA 201 5.1.1 Fractional Factorial Designs: An Introduction 203 5.1.2 Creating Fractional Factorial Designs 207 5.1.3 Fractional Factorial Designs in CFA 211 5.2 Structural Zeros in CFA 215 5.2.1 Incomplete Tables and Separability 219 5.2.2 Design-Specific Structural Zeros 224 References 228 Chapter 6: Special Variables in CFA 230 6.1 Covariates in CFA 230 6.2 CFA with Ordinal Variables 239 6.2.1 Iterative Proportional Fitting 240 6.2.2 The Linear-by-Linear Association Model 242 6.3 Moderator Variables in CFA 245 6.4 Mediator CFA 253 6.4.1 Significance Testing of the Indirect Effect 254 6.4.2 Evaluating Mediator Hypotheses 255 6.4.3 Causal Mediator Analysis 256 6.4.4 Mediator Models for Categorical Variables 258 6.4.5 Configural Mediation Analysis 261 6.4.5.1 Pattern-Specific Mediation Models 261 6.4.5.2 von Eye et al. ́s (2009) Method of Mediation Analysis 262 6.4.5.3 Smyth and MacKinnon ́s (2020) Modifications 265 6.4.5.4 Wiedermann and von Eye ́s (2020) Method 266 References 275 Chapter 7: The Treasure Chest of CFA 278 7.1 Alternative Approaches to CFA 278 7.1.1 Victor ́s Alternative Exploratory CFA 278 7.1.2 von Eye and Mair ́s Alternative Sequential CFA 282 7.2 Functional CFA 289 7.2.1 Functional CFA I: The Ascending, Inclusive Strategy 289 7.2.2 Functional CFA II: The Descending Excluding Strategy 295 7.3 CFA and Tree Structures 298 7.4 Rater Agreement 305 7.5 CFA of Large Sparse Tables 310 7.6 CFA as Test of Multivariate Normality 312 7.7 Latent Class Analysis and CFA 317 7.8 CFA and Causality 324 7.8.1 Forms of Causal Relations 325 7.8.2 CFA and Granger Causality 331 7.9 CFA of Intensive Longitudinal Data 336 7.10 Bayes CFA 339 7.10.1 Bayes Definition of Types and Antitypes 340 7.10.2 Patterns of Types and Antitypes 341 7.11 Limits of CFA: Issues and Countermeasures 344 References 347 Chapter 8: Software for CFA 353 8.1 CFA Fortran Program 353 8.2 R Packages and Modules 360 8.2.1 Global CFA Base Models 360 8.2.2 Prediction CFA 367 8.2.3 Two-Group CFA 370 8.2.4 Bayes CFA 371 References 374 References 375 Index 391