Person-Centered Methods: Configural Frequency Analysis (CFA) and Other Methods for the Analysis of Contingency Tables (SpringerBriefs in Statistics)

This book takes an easy-to-understand look at the statistical approach called the person-centered method. Instead of analyzing means, variances and covariances of scale scores as in the common variable-centered approach, the person-centered approach analyzes persons or objects grouped according to their characteristic patterns or configurations in contingency tables. The main focus of the book will be on Configural Frequency Analysis (CFA; Lienert and Krauth, 1975) which is a statistical method that looks for over and under-frequented cells or patterns. Over frequented means that the observations in this cell or configuration are observed more often than expected, under-frequented means that this cell or configuration is observed less often than expected. In CFA a pattern or configuration that contains more observed cases than expected is called a __type__; similarly, a pattern or configuration that is less observed than expected are called an __antitype__. CFA is similar to log-linear modeling. In log-linear modeling the goal is to come up with a fitting model including all important variables. Instead of fitting a model, CFA looks at the significant residuals of a log-linear model. The book describes the use of an R-package called **confreq (**derived from **Conf**igural **Freq**uency Analysis). The use of the software package is described and demonstrated with data examples. Preface 6 Contents 8 Chapter 1 Introducing Person-Centered Methods 10 1.1 What Is Configural Frequency Analysis (CFA) Good for? 10 1.2 Basics of CFA 12 1.3 Meehl's Paradox 18 References 20 Chapter 2 CFA Software 21 2.1 The Freeware by Alexander von Eye 21 2.2 CFA R-Package 23 References 25 Chapter 3 Significance Testing in CFA 27 3.1 The Binomial Test 27 3.2 Approximation of the Binomial Test Using Stirling's Formula 28 3.3 Chi-Square Test 29 3.4 Chi-Square Approximation to the z-Test 29 3.5 Binomial Approximation to the z-Test 30 3.6 Lehmacher's Asymptotic Test 30 3.7 Küchenhoff's Continuity Correction of Lehmacher's Asymptotic Test 31 References 31 Chapter 4 CFA and Log-Linear Modeling 32 4.1 Log-Linear Modeling: Looking at the Underlying Dependencies 32 4.2 Hierarchical Log-Linear Modeling 42 4.3 Zero-Order CFA or Configural Cluster Analysis (CCA) 46 4.4 The Limits of CFA or Different Base Models, Different Types 52 References 56 Chapter 5 Longitudinal CFA 58 5.1 CFA of First Differences 58 5.2 CFA and Visual Shape Patterns 59 References 63 Chapter 6 Other Person-Centered Methods Serving as Complimentary Tools to CFA 64 6.1 Answer Tree and CFA 64 6.2 Latent Class Analysis and CFA 71 6.3 Correspondence Analysis and CFA 75 References 79 Chapter 7 CFA and Its Derivatives 80 7.1 Prediction-CFA 80 7.2 Interaction Structure Analysis (ISA) 82 7.3 Biprediction-Type 85 7.4 Two-Sample CFA 86 References 89 Glossary 91 Index 93 This book takes an easy-to-understand look at the statistical approach called the person-centered method. Instead of analyzing means, variances and covariances of scale scores as in the common variable-centered approach, the person-centered approach analyzes persons or objects grouped according to their characteristic patterns or configurations in contingency tables. The main focus of the book will be on Configural Frequency Analysis (CFA; Lienert and Krauth, 1975) which is a statistical method that looks for over and under-frequented cells or patterns. Over frequented means that the observations in this cell or configuration are observed more often than expected, under-frequented means that this cell or configuration is observed less often than expected. In CFA a pattern or configuration that contains more observed cases than expected is called a type ; similarly, a pattern or configuration that is less observed than expected are called an antitype . CFA is similar to log-linear modeling. In log-linear modeling the goal is to come up with a fitting model including all important variables. Instead of fitting a model, CFA looks at the significant residuals of a log-linear model. The book describes the use of an R-package called confreq ( derived from Conf igural Freq uency Analysis). The use of the software package is described and demonstrated with data examples. Front Matter....Pages i-viii Introducing Person-Centered Methods....Pages 1-11 CFA Software....Pages 13-18 Significance Testing in CFA....Pages 19-23 CFA and Log-Linear Modeling....Pages 25-50 Longitudinal CFA....Pages 51-56 Other Person-Centered Methods Serving as Complimentary Tools to CFA....Pages 57-72 CFA and Its Derivatives....Pages 73-83 Errata: Person-Centered Methods....Pages E1-E3 Back Matter....Pages 85-88