Configural Frequency Analysis

Methods, Models, and Applications

Alexander von Eye

• Publisher: Psychology Press
• Year: 2003
• eBook ISBN: 9781135630850
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

Configural Frequency Analysis (CFA) provides an up-to-the-minute comprehensive introduction to its techniques, models, and applications. Written in a formal yet accessible style, actual empirical data examples are used to illustrate key concepts. Step-by-step program sequences are used to show readers how to employ CFA methods using commercial software packages, such as SAS, SPSS, SYSTAT, S-Plus, or those written specifically to perform CFA.

CFA is an important method for analyzing results involved with categorical and longitudinal data. It allows one to answer the question of whether individual cells or groups of cells of cross-classifications differ significantly from expectations. The expectations are calculated using methods employed in log-linear modeling or a priori information. It is the only statistical method that allows one to make statements about empty areas in the data space.

Applied and or person-oriented researchers, statisticians, and advanced students interested in CFA and categorical and longitudinal data will find this book to be a valuable resource. Developed since 1969, this method is now used by a large number of researchers around the world in a variety of disciplines, including psychology, education, medicine, and sociology. Configural Frequency Analysis will serve as an excellent text for courses on configural frequency analysis, categorical variable analysis, or analysis of contingency tables. Prerequisites include an understanding of descriptive statistics, hypothesis testing, statistical model fitting, and some understanding of categorical data analysis and matrix algebra.

Part 1: Concepts and Methods of CFA

“The best methods are capable of uncovering patterns which are unexpected.”

Diggle, Liang, & zeger, 1996, p. 33

1. Introduction: The Goals and Steps of Configural Frequency Analysis

This first chapter consists of three parts. First, it introduces readers to the basic concepts of Configural Frequency Analysis (CFA). It begins by describing the questions that can be answered with CFA. Second, it embeds CFA in the context of Person Orientation, that is, a particular research perspective that emerged in the 1990s. Third, it discusses the five steps involved in the application of CFA. The chapter concludes with a first complete data example of CFA.

1.1 Questions that can be answered with CFA

Configural Frequency Analysis (CFA; Lienert, 1968, 1971a) allows researchers to identify those patterns of categories that were observed more often or less often than expected based on chance. Consider, for example, the contingency table that can be created by crossing the three psychiatric symptoms Narrowed Consciousness (C), Thought Disturbance (T), and Affective Disturbance (A; Lienert, 1964, 1969, 1970; von Eye, 1990). In a sample of 65 students who participated in a study on the effects of LSD 50, each of these symptoms was scaled as 1 = present or 2 = absent. The cross-classification C × T × A, which has been used repeatedly in illustrations of CFA (see, e.g., Heilmann & Schütt, 1985; Lehmacher, 1981; Lindner, 1984; Ludwig, Gottlieb, & Lienert, 1986), appears in Table 1.

Table 1: Cross-classification of the three variables Narrowed Consciousness (C), Thought Disturbance (T), and Affective Disturbance (A); N = 65

Pattern CTA	Observed Frequency
111	20
112	1
121	4
122	12
211	3
212	10
221	15
222	0

In the context of CFA, the patterns denoted by the cell indices 111, 112, …, 222 are termed Configurations. If d variables are under study, each configuration consists of d elements. The configurations differ from each other in at least one and maximally in all d elements. For instance, the first configuration, 111, describes the 20 students who experienced all three disturbances. The second configuration, 112, differs from the first in the last digit. This configuration describes the sole student who experiences narrowed consciousness and thought disturbances, but no affective disturbance. The last configuration, 222, differs from the first in all d = 3 elements. It suggests that no student was found unaffected by LSD 50. A complete CFA of the data in Table 1 follows in Section 3.7.2.2.

The observed frequencies in Table 1 indicate that the eight configurations do not appear at equal rates. Rather, it seems that experiencing no effects is unlikely, experiencing all three effects is most likely, and experiencing only two effects is relatively unlikely. To make these descriptive statements, one needs no further statistical analysis. However, there may be questions beyond the purely descriptive. Given a cross-classification of two or more variables. CFA can be used to answer questions of the following types:

(1) How do the observed frequencies compare with the expected frequencies? As interesting and important as it may be to interpret observed frequencies, one often wonders whether the extremely high or low numbers are still that extreme when we compare them with their expected counterparts. The same applies to the less extreme frequencies. Are they still about average when compared to what could have been expected? To answer these questions, one needs to estimate expected cell frequencies. The expected cell frequencies conform to the specifications made in so-called base models. These are models that reflect the assumptions concerning the relationships among the variables under study. Base models are discussed in Sections 2.1 - 2.3. It goes without saying that different base models can lead to different expected cell frequencies (Mellenbergh, 1996). As a consequence, the answer to this first question depends on the base model selected for frequency comparison, and the interpretation of discrepancies between observed and expected cell frequencies must always consider the characteristics of the base model specified for the estimation of the expected frequencies. The selection of base models is not arbitrary (see Chapter 2 for the definition of a valid CFA base model). The comparison of observed with expected cell frequencies allows one to identify those configurations that were observed as often as expected. It allows one also to identify those configurations that were observed more often than expected and those configurations that were observed less often than expected. Configurations that are observed at different frequencies than expected are of particular interest in CFA applications.

(2) Are the discrepancies between observed and expected cell frequencies statistically significant? It is rarely the case that observed and expected cell frequencies are identical. In most instances, there will be numerical differences. CFA allows one to answer the question whether a numerical difference is random or too large to be considered random. If an observed cell frequency is significantly larger than the expected cell frequency, the respective configuration is said to constitute a CFA type. If an observed frequency is significantly smaller than its expected counterpart, the configuration is said to constitute a CFA antitype. Configurations with observed frequencies that differ from their expectancies only randomly, constitute neither a type nor an antitype. In most CFA applications, researchers will find both, that is, cells that constitute neither a type nor an antitype, and cells that deviate significantly from expectation.

(3) Do two or more groups of respondents differ in their frequency distributions? In the analysis of cross-classifications, this question typically is answered using some form of the χ²-test, some log-linear model, or logistic regression. Variants of χ²-tests can be employed in CFA too (for statistical tests employed in CFA, see Chapter 2). However, CFA focuses on individual configurations rather than on overall goodness-of-fit. CFA indicates the configurations in which groups differ. If the difference is statistically significant, the respective configuration is said to constitute a discrimination type.

(4) Do frequency distributions change over time and what are the characteristics of such changes? There is a large number of CFA methods available for the investigation of change and patterns of change. For example, one can ask whether shifts from one category to some other category occur as often as expected from some chance model. This is of importance, for instance, in investigations of treatment effects, therapy outcome, or voter movements. Part III of this book covers methods of longitudinal CFA.

(5) Do groups differ in their change patterns? In developmental research, in research concerning changes in consumer behavior, in research on changes in voting preferences, or in research on the effects of medicinal or leisure drugs, it is one issue of concern whether groups differ in the changes that occur over time. What are the differences in the processes that lead some customers to purchase holiday presents on the web and others in the stores? CFA allows one to describe these groups, to describe the change processes, and to determine whether differences in change are greater than expected.

(6) Are there predictor-criterion relationships? In educational research, in studies on therapy effects, in investigations on the effects of drugs, and in many other contexts, researchers ask whether events or configurations of events allow one to predict other configurations of events. CFA allows one to identify those configurations for which one can predict that other configurations occur more often than expected, and those configurations for which one can predict that other configurations occur less often than expected based on chance.

This book presents methods of CFA that enable researchers to answer these and more questions.

1.2 CFA and the person perspective¹

William Stern introduced in 1911 the distinction between variability and psychography. Variability is the focus when many individuals are observed in one characteristic with the goal to describe the distribution of this characteristic in the population. Psychographic methods aim at describing one individual in many characteristics. Stern also states that these two methods ...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• List of contents
• Preface
• Part I: Concepts and Methods of CFA
• Part II: Models and Applications of CFA
• Part III: Methods of Longitudinal CFA
• Part IV: The CFA Specialty File and Alternative Approaches to CFA
• Part V: Computational Issues
• Part VI: References, Appendices, and Indices