Charting the future of Confi gural Frequency Analysis: The development of a statistical method

1. Configurai Frequency Analysis - the past The first 35 years of the development of Configurai Frequency Analysis (CPA; Lienert, 1969) were characterized by a rapid expansion of possibilities. Full of enthusiasm, researchers developed new designs that allow one to answer increasingly specific questions. The areas of categorical variable analysis, parametric and non-parametric statistics, significance testing, modeling, sampling, [alpha]-protection, frequentist and Bayesian statistics, and many other domains were combed with the goal of identifying methods, models, and techniques that could be adopted for use in CFA. In addition, the advent of CFA triggered the development of new methods, in particular in the areas of significance testing and [alpha] protection. Table 1 presents a non-exhaustive time table of CFA-related innovations. These efforts paid off greatly. CPA now belongs to the arsenal of generally accepted methods of analysis. The method Rnds applications in all areas of the empirical sciences. Empirical articles in which data are analyzed using CFA appear in the best journals. Textbooks on CFA have been published by reputed publishers, computer programs have been published, and CFA as a method is covered by entries in recent and upcoming encyclopedias. In other words, CFA as a method for the exploration of cross-classifications is known to be a useful method (hat is employed widely (for a brief history of CFA sec von Bye & Lautsch, 2000). 2. Configura) Frequency Analysis - the future At least as important as (he recognition and the use of a statistical method is its continuous development. In the history of most methods of statistics, the presentation of a new method is followed by a period of euphoria. During this period, the basics of the method are established, and researchers explore fields of application. The possibilities provided by the new method are charted. Soon, limits become apparent and misuses become known. Researchers leam that there are optimal data characteristics for the application of a method, but that there arc also conditions under which an application is less promising. For example, data bodies may be too small or too large, distributional characteristics may not meet requirements, or the questions asked by researchers cannot be answered using a particular method. In the case of CFA, the bases have been established, as can be seen from the brief time line in Table 1. The method finds widespread application. In addition, methodologists are now in a phase in which the characteristics of elements of CFA are examined under various conditions. Six fields of research on the method of CFA can currently be distinguished: 1. Simulation studies that center on the behavior of statistical tests that are used to make type/ antitype decisions (von Eye, 2002; in press; von Weber, 2000); more studies are under way (see below). 2. Studies concerning the dependency structure of tests performed in CFA. First studies exist (Victor, 1989), in which the authors propose that there be at least 3 or 4 degrees of freedom for each type/antitype in a cross-classification. More studies on this topic are being undertaken (see below). 3. Studies concerning the size of tables that can be meaningfully explored using CFA. Stimulated by a paper by duMouchel (1999), studies arc being undertaken with the goal to determine the maximum and the minimum size of tables for which CFA is a suitable method of analysis (sec below). 4. The statistical bases of CFA arc being expanded. The original approach to CFA is based on methods for the estimation of expected cell frequencies that reside in what is known as [chi]^sup 2^-analysis. These methods have been put in the context of hierarchical log-linear modeling (von Eye, 1988), and in the context of the more general log-linear models of quasi-indepcndencc (Victor, 1989; Kieser & Victor, 1999). In addition, CPA has been reformulated as a method of Bayesian statistics (Wood, Sher, & von Eye. …