Multigroup Comparisons with Configural Frequency Analysis.

In standard statistical data analysis, the effects of intervention or prevention efforts are evaluated in terms of variable relations. Results from application of regression-type methods suggest whether, overall, intervention is successful. In this article, we propose using configural frequency analysis (CFA) either in tandem with regression-type methods or by itself. CFA allows one to adopt a person-oriented perspective in which individuals are targeted that can be characterized by particular profiles. The questions asked in CFA concern these individuals instead of variables. In prevention research, one can ask whether, for particular profiles, the preventive measures are successful. In three real-world data examples, CFA is applied and compared to standard log-linear modeling. Examples consider non-randomized (observational) and randomized intervention settings. The results of these analyses suggest that person-oriented CFA and standard variable-oriented methods of analysis respond to different questions. We show that integrating person- and variable-oriented perspectives can help researchers obtain a fuller picture of intervention effectiveness. Extensions of the CFA approach are discussed.

Configural frequency analysis (CFA) is a widely used method of explorative data analysis. It tries to detect patterns in the data that occur significantly more or significantly less often than expected by chance. Patterns which occur more often than expected by chance are called CFA types, while those which occur less often than expected by chance are called CFA antitypes. The patterns detected are used to generate knowledge about the mechanisms underlying the data. We investigate the ability of CFA to detect adequate types and antitypes in a number of simulation studies. The basic idea of these studies is to predefine sets of types and antitypes and a mechanism which uses them to create a simulated data set. This simulated data set is then analysed with CFA and the detected types and antitypes are compared to the predefined ones. The predefined types and antitypes together with the method to generate the data are called a data generation model. The results of the simulation studies show that CFA can be used in quite different research contexts to detect structural dependencies in observed data. In addition, we can learn from these simulation studies how much data is necessary to enable CFA to reconstruct the predefined types and antitypes with sufficient accuracy. For one of the data generation models investigated, implicitly underlying knowledge space theory, it was shown that zero-order CFA can be used to reconstruct the predefined types (which can be interpreted in this context as knowledge states) with sufficient accuracy. Theoretical considerations show that first-order CFA cannot be used for this data generation model. Thus, it is wrong to consider first-order CFA, as is done in many publications, as the standard or even only method of CFA.

The article introduces Parametric Configural Frequency Analysis (CFA). It is argued that there are two types of parameters that can be of importance in CFA models. The first is effect parameters that are estimated from the data. This type of parameter is involved in almost all models of Classical, nonparametric CFA. The second type involves a priori or distributional parameters that can be used for estimation of expected frequencies. These parameters are specified a priori rather than estimated from data. A combination of models from Classical CFA and Parametric CFA is introduced as Semi‐Parametric CFA. Data examples illustrate the new CFA models in comparison with the Classical CFA. Interpretational issues are discussed.

Configural frequency analysis and log-linear modeling are presented as person-centered analytic approaches for the analysis of categorical or categorized data in multi-way contingency tables. Person-centered developmental psychology, based on the holistic interactionistic perspective of the Stockholm working group around David Magnusson and Lars Bergman, is briefly revisited. According to person-centered theory, systems or individuals are seen as a whole and as inseparable units; individuals are embedded and strongly interconnected with their context; the individual and the environment influence each other, and the individual is seen as an active agent or producer of his or her own development. Four models of configural frequency analysis are presented: (1) First-order configural frequency analysis, which is basically the analysis of a main effects log-linear model; (2) prediction configural frequency analysis, which defines one or more dependent variables; (3) two-group configural frequency analysis, which proposes that there is no association between discrimination variables and group membership; and (4) functional configural frequency analysis, which allows us to blank out certain outlier cells in order to test for the quasi-independence of the rest of the cross-table. The use of the open source R-package confreq for computational analysis is demonstrated. The advantages, as well as the limitations, of configural frequency analysis are discussed.

The person-centered approach in categorical data analysis is introduced as a complementary approach to the variable-centered approach. The former uses persons, animals, or objects on the basis of their combination of characteristics which can be displayed in multiway contingency tables. Configural Frequency Analysis (CFA) and log-linear modeling (LLM) are the two most prominent (and related) statistical methods. Both compare observed frequencies (foi…k) with expected frequencies (fei…k). While LLM uses primarily a model-fitting approach, CFA analyzes residuals of non-fitting models. Residuals with significantly more observed than expected frequencies (foi…k>fei…k) are called types, while residuals with significantly less observed than expected frequencies (foi…k<fei…k) are called antitypes. The R package confreq is presented and its use is demonstrated with several data examples. Results of contingency table analyses can be displayed in tables but also in graphics representing the size and type of residual. The expected frequencies represent the null hypothesis and different null hypotheses result in different expected frequencies. Different kinds of CFAs are presented: the first-order CFA based on the null hypothesis of independence, CFA with covariates, and the two-sample CFA. The calculation of the expected frequencies can be controlled through the design matrix which can be easily handled in confreq.

This article reviews the premises of configural frequency analysis (CFA), including methods of choosing significance tests and base models, as well as protecting alpha, and discusses why CFA is a useful approach when conducting longitudinal person-oriented research. CFA operates at the manifest variable level. Longitudinal CFA seeks to identify those temporal patterns that stand out as more frequent (CFA types) or less frequent (CFA antitypes) than expected with reference to a base model. A base model that has been used frequently in CFA applications, prediction CFA, and a new base model, auto-association CFA, are discussed for analysis of cross-classifications of longitudinal data. The former base model takes the associations among predictors and among criteria into account. The latter takes the auto-associations among repeatedly observed variables into account. Application examples of each are given using data from a longitudinal study of domestic violence. It is demonstrated that CFA results are not redundant with results from log-linear modeling or multinomial regression and that, of these approaches, CFA shows particular utility when conducting person-oriented research.

Most statements in the empirical social and behavioral sciences are based on analyses of aggregate‐level data. In such analyses, researchers relate variables to each other, create factor spaces of variables, or regress latent variables onto each other. This is done although it is known that aggregate‐level statements rarely, if ever, describe data at the level of individuals (Molenaar, 2004; von Eye & Bergman, 2003). Configural frequency analysis (CFA) allows researchers to analyze profiles of individuals instead of relations among variables. By using CFA, researchers can test very detailed hypotheses, specifically those that apply only to individuals with particular profiles. CFA uses cross‐classifications of categorical variables. It allows researchers to specify hypotheses either cross sectionally or longitudinally. It also allows researchers to identify typical as well as atypical trajectories of development. This is of importance when the multitude of developmental pathways is to be depicted but also in developmental psychopathology, where unusual developmental patterns are of interest, and where treatment options can be tailored to the individual pattern of development. In this chapter, we introduce readers to CFA and present data examples for each of the CFA models.

Configural Frequency Analysis (CFA) is a useful statistical method for the analysis of multiway contingency tables and an appropriate tool for person-oriented or person-centered methods. In complex contingency tables, patterns or configurations are analyzed by comparing observed cell frequencies with expected frequencies. Significant differences between observed and expected frequencies lead to the emergence of Types and Antitypes. Types are patterns or configurations which are significantly more often observed than the expected frequencies; Antitypes represent configurations which are observed less frequently than expected. The R-package confreq is an easy-to-use software for conducting CFAs; another useful shareware to run CFAs was developed by Alexander von Eye. Here, CFA is presented based on the log-linear modeling approach. CFA may be used together with interval level variables which can be added as covariates into the design matrix. In this article, a real data example and the use of confreq are presented. In sum, the use of a covariate may bring the estimated cell frequencies closer to the observed cell frequencies. In those cases, the number of Types or Antitypes may decrease. However, in rare cases, the Type-Antitype pattern can change with new emerging Types or Antitypes.

Standard Configural Frequency Analysis (CFA) is a one-step procedure that determines which cells of a cross-classification contradict a base model. The results are possible types/antitypes depending on whether the observed cell frequencies are significantly lower/higher with respect to the base model. Selecting these cells out does not guarantee that the base model fits. Therefore, the role played by these cells for the base model is unclear, and interpretation of types and antitypes can be problematic. In this paper, functional CFA is proposed. This model of CFA pursues two goals simultaneously. First, cells are selected out that constitute types and antitypes. Second, the base model is fit to the data. This is done using an iterative procedure that blanks out individual cells one at a time, until the base model fits or until there are no more cells that can be blanked out. In comparison to standard CFA, functional CFA is shown to be more parsimonious, that is, fewer types and antitypes need to be selected out. The methods are illustrated and compared using data examples from the literature.

Longitudinal Configural Frequency Analysis (CFA) seeks to identify, at the manifest variable level, those temporal patterns that are observed more frequently (CFA types) or less frequently (CFA antitypes) than expected with reference to a base model. This article discusses, compares, and extends two base models of interest in longitudinal data analysis. The first of these, Prediction CFA (P-CFA), is a base model that can be used in the configural analysis of both cross-sectional and longitudinal data. This model takes the associations among predictors and among criteria into account. The second base model, Auto-Association CFA (A-CFA), was specifically designed for longitudinal data. This model takes the auto-associations among repeatedly observed variables into account. Both models are extended to accommodate covariates, for example, stratification variables. Application examples are given using data from a longitudinal study of domestic violence. It is illustrated that CFA is able to yield results that are not redundant with results from log-linear modeling or multinomial regression. It is concluded that CFA is particularly useful in the context of person-oriented research.

Although variable-oriented analyses are dominant in developmental psychopathology, researchers have championed a person-oriented approach that focuses on the individual as a totality. This view has methodological implications and various person-oriented methods have been developed to test person-oriented hypotheses. Configural frequency analysis (CFA) has been identified as a prime method for a person-oriented analysis of categorical data. CFA searches for configurations in cross-classifications and asks whether the number of observed cases is larger (CFA type) or smaller (CFA antitype) than expected under a probability model. The present study introduces a combination of CFA and model-based recursive partitioning (MOB) to test for type/antitype heterogeneity in the population. MOB CFA is well suited to detect complex moderation processes and can distinguish between subpopulation and population types/antitypes. Model specifications are discussed for first-order CFA and prediction CFA. Results from two simulation studies suggest that MOB CFA is able to detect moderation processes with high accuracy. Two empirical examples are given from school mental health research for illustrative purposes. The first example evaluates heterogeneity in student behavior types/antitypes, the second example focuses on the effect of a teacher classroom management intervention on student behavior. An implementation of the approach is provided in R.

Oscillating series of scores can be approximated with locally optimized smoothing functions. In this article, we describe how such series can be approximated with locally estimated (loess) smoothing, and how Configural Frequency Analysis (CFA) can be used to evaluate and interpret results. Loess functions are often hard to describe because they cannot be represented by just one function that has interpretable parameters. In this article, we suggest that specification of the CFA base model be based on the width of the window that is used for local curve optimization, the weight given to data points in the neighborhood of the approximated one, and by the function that is used to locally approximate observed data. CFA types indicate that more cases were found than expected from the local optimization model. CFA antitypes indicate that fewer cases were found. In a real-world data example, the development of Covid-19 diagnoses in France is analyzed for the beginning period of the pandemic.

Configural Frequency Analysis (CFA) is a method for cell‐wise inspection of cross‐classifications. CFA searches for types, that is, patterns of variable categories that occur more often than expected from some chance model, and for antitypes, that is, patterns observed less often than expected. Thus far, CFA has been plagued by the difficulties involved when looking for patterns of types and antitypes. This article introduces Bayesian CFA. Using Bayesian CFA one can (1) search for types and antitypes as before with the advantage that adjustment of the experiment‐wise significance level α is not necessary; and (2) test whether groups of types and antitypes form composite types or composite antitypes. This option is crucial when patterns of types or antitypes must exist for a concept to be retained. Empirical examples use data from alcohol research and from sleep research to illustrate both new options. Characteristics of Bayesian CFA and extensions are discussed.

Configural frequency analysis (CFA) tests whether certain individual patterns in different variables are observed more frequently in a sample than expected by chance. In normative CFA, these patterns are derived from the subject's specific position in relation to sample characteristics such as the median or the mean. In ipsative CFA, patterns are defined within an individual reference system, e.g. relative to the subject's median of different variable scores. Normative CFA examines dimensionality of scales and is comparable to factor analysis in this respect. Ipsative CFA rather yields information about location of scores in different variables, in a similar way to ANOVA or Friedman testing. However, both normative and ipsative CFA may supply information not obtainable by means of the aforementioned methods. This is illustrated in a reanalysis of data in four scales of an anxiety inventory. © 1997 John Wiley & Sons, Ltd.

Configural frequency analysis (CFA) is a widely used method for the identification of types and syndromes in contingency tables. However, the type model of CFA shows some major deficiencies. In this paper, we propose an alternative modeling of types eliminating the shortcomings of CFA. Basically, a type is modeled as a combination of traits or symptoms that deviates from the pattern of association holding true for the complementary configurations of the contingency table. The new approach is formulated in terms of a log-linear model. It is shown that parameter estimation can be performed with methods known from the analysis of incomplete contingency tables. Test procedures for confirmatory analysis and methods for exploratory search for type configurations are developed. We illustrate the methodology with two practical examples.