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2020 | Book

Introducing Person-Centered Methods Read chapter Read first chapter

Person-Centered Methods

Configural Frequency Analysis (CFA) and Other Methods for the Analysis of Contingency Tables

Author: Prof. Dr. Mark Stemmler

Publisher: Springer International Publishing

Book Series : SpringerBriefs in Statistics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book offers a comprehensible overview of 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. This second edition explores the relationship between two statistical methods: log-linear modeling (LLM) and configural frequency analysis (CFA). Both methods compare expected frequencies with observed frequencies. However, while LLM searches for the underlying dependencies of the involved variables in the data (model-fitting), CFA examines significant residuals in non-fitting models.

New developments in the second edition include: Configural Mediation Models, CFA with covariates, moderator CFA, and CFA modeling branches in tree-based methods. The new developments enable the use of categorical together with continuous variables, which makes CFA a very powerful statistical tool. This new edition continues to utilize R-package confreq (derived from Configural Frequency Analysis), much updated since the first edition and newly adjusted to the new R base program 4.0. An electronic supplement is now available with 18 R-scripts and many datasets.

Table of Contents

Frontmatter
Chapter 1. Introducing Person-Centered Methods
Abstract
This chapter explains the term person-centered methods and how configural frequency analysis (CFA) works. 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 configurations in complex contingency tables while comparing observed cell frequencies with expected frequencies. CFA is a statistical method that looks for over- and under-frequented cells. Over-frequented indicates that the observations in this cell or configuration are observed more often than expected, and under-frequented indicates that this configuration is observed less often than expected. In CFA, a pattern or configuration that contains significantly more observed cases than expected is called a type; similarly, a configuration that contains significantly fewer observed cases than expected is called an antitype. In addition, this chapter includes an explanation of Meehl’s paradox [12], which postulates that it is possible to have a bivariate relationship with a zero association or correlation and, at the same time, a higher order association or correlation. Meehl argued for investigating higher order interactions (beyond bivariate interactions), which can be detected with CFA.
Mark Stemmler
Chapter 2. CFA Software
Abstract
This chapter introduces and explains the CFA software that is available at no cost. The first is freeware written by Alexander von Eye (Michigan State University). The second is the R package confreq, written by Jörg-Henrik Heine (Technical University Munich). Now the confreq version 1.5.5-0 is available on the The Comprehensive R Archive Network (CRAN) server. The use of both software packages is described and demonstrated with data examples. Confreq is used for demonstrations throughout this book.
Mark Stemmler
Chapter 3. Significance Testing in CFA
Abstract
This chapter explains the five significance tests that are available in the von Eye program and/or R package confreq for use in the search for types and antitypes, including the binomial and chi-square tests and their normal approximations. Formulas for each test are provided, and the advantages and disadvantage of each are explained.
Mark Stemmler
Chapter 4. CFA and Log-Linear Modeling
Abstract
This chapter describes the relationship between log-linear modeling and CFA, which may be used as complimentary statistical tools. Log-linear modeling looks for models with an appropriate goodness-of-fit; they can be used to investigate the patterns of association or the structure of dependency among the variables. CFA needs a non-fitting model in order to detect types and/or antitypes. In CFA and log-linear models, the expected frequencies are calculated according to the underlying null model, which is specified in the design matrix using the generalized linear model (GLM). In this chapter, log-linear modeling and hierarchical log-linear modeling are presented. Hi-log modeling is a special form of log-linear modeling. It is the best way to determine the structure of dependency among the variables or to find out which interactions are significant. The main effects and interactions are structured hierarchically, such that if there are significant higher order interactions in the model, all lower order interactions and main effects must be included. In this chapter, I describe a zero-order CFA called configural cluster analysis (CCA) and introduce statistic Q, describing the pregnancy or precision of a cell. Small data examples are presented and analyzed with the R package confreq.
Mark Stemmler
Chapter 5. Longitudinal CFA
Abstract
This chapter explains how to use CFA with longitudinal data. Different ways of arranging the information with the longitudinal data are introduced. First I present the analysis of first differences, in which the research simply looks at increases or decreases between two time points. Second, I explain CFA and visual shape patterning, in which the shapes of the curves are used as configurations or patterns. Third, I provide a test of marginal homogeneity, which tests the null hypothesis of the homogeneity of marginals in a square contingency table. Finally, I describe the discrimination type, a special type that differentiates between two significantly independent samples.
Mark Stemmler
Chapter 6. Other Person-Centered Methods Serving as Complimentary Tools to CFA
Abstract
This chapter explains the use of other person-centered methods as complimentary tools to CFA. Among them are chi-square automatic interaction detection (CHAID) model for contrasting groups; latent class analysis (LCA), which is comparable to a factor analysis using categorical variables; and (multiple) correspondence analysis (CA), which is a technique for dimensional reduction and perceptual mapping. Using small data examples, the essence of each statistical method is explained and its close relationship to CFA is demonstrated. CFA may always be used as a complimentary tool offering additional insight into the data.
Mark Stemmler
Chapter 7. CFA and Its Derivatives
Abstract
This chapter introduces several derivatives of CFA that can be used for different purposes and that extend the CFA tool kit enormously. This is also possible because of advancements in confreq that have added flexibility; all examples are demonstrated using this R-package. First, there is prediction CFA (P-CFA). This version of CFA is comparable to multiple regression. One variable is defined as the dependent variable or criterion, which is usually (but not necessarily) measured with a certain time lag with regard to the other independent variables or predictors. Second, there is interaction structure analysis (ISA). ISA uses an extended definition of interactions, which cannot be analyzed with log-linear modeling (LLM). Instead of searching for singular types or antitypes, one can search for biprediction types by looking for regional instead of local contingency. Third, two-sample CFA is introduced as a very useful statistical tool similar to t-tests for independent samples. This derivative of CFA searches for discrimination types, which differentiate the two samples under investigation. Fourth, the configural mediator models are demonstrated. We use an approach that combines LLM and CFA in a two-step procedure to search for a mediator model that can be interpreted as a causal model. Partial and complete (or fully) mediated models are introduced. Finally, with the new confreq R-package CFA with covariates can be analyzed. We present a data example based on one and two covariates.
Mark Stemmler
Backmatter
Metadata
Title
Person-Centered Methods
Author
Prof. Dr. Mark Stemmler
Copyright Year
2020
Electronic ISBN
978-3-030-49421-6
Print ISBN
978-3-030-49420-9
DOI
https://doi.org/10.1007/978-3-030-49421-6

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