Configural frequency trees

Detecting heterogeneity in the causal direction of dependence: A model-based recursive partitioning approach

Methods of causal discovery and direction of dependence to evaluate causal properties of variable relations have experienced rapid development. The majority of causal discovery methods, however, relies on the assumption of causal effect homogeneity, that is, the identified causal structure is expected to hold for the entire population. Because causal mechanisms can vary across subpopulations, we propose combining methods of model-based recursive partitioning and non-Gaussian causal discovery to identify such subpopulations. The resulting algorithm can discover subpopulations with potentially varying magnitude and causal direction of effects under mild parameter inequality assumptions. Feasibility conditions are described and results from synthetic data experiments are presented suggesting that large effects and large sample sizes are beneficial for detecting causally competing subgroups with acceptable statistical performance. In a real-world data example, the extraction of meaningful subgroups that differ in the causal mechanism underlying the development of numerical cognition is illustrated. Potential extensions and recommendations for best practice applications are discussed.

Base Models for Configural Frequency Analysis - Data Generation Processes

In Configural Frequency Analysis (CFA), model-data discrepancies are interpreted with reference to CFA base models. Thus far, CFA base models are defined as probability models that differ in the constraints they place on variable relations. In this article, it is proposed extending the scope of CFA base models. Specifically, it is proposed that the specification of base models is conducted with reference to data generation processes (DGPs). These processes result in uni- or multivariate distributions that reflect variable relations, probability distributions, or processes that result in change in series of observations. The new, DGP-based definition of CFA base models retains the concept of unique interpretability of CFA results, but it opens the doors to many more forms of base models than considered before. Four classes of base models are defined. Data examples illustrate various CFA base models.

Local Effects of Intervention: a Configural 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.