Detecting Heterogeneity of Intervention Effects in Comparative Judgments

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.

The Bradley-Terry Regression Trunk approach for Modeling Preference Data with Small Trees

This paper introduces the Bradley-Terry regression trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the preferences expressed by individuals depend on their characteristics. Within the framework of tree-based partitioning, we specify a tree-based model estimating the joint effects of subject-specific covariates over and above their main effects. We, therefore, combine a tree-based model and the log-linear Bradley-Terry model using the outcome of the comparisons as response variable. The proposed model provides a solution to discover interaction effects when no a-priori hypotheses are available. It produces a small tree, called trunk, that represents a fair compromise between a simple interpretation of the interaction effects and an easy to read partition of judges based on their characteristics and the preferences they have expressed. We present an application on a real dataset following two different approaches, and a simulation study to test the model's performance. Simulations showed that the quality of the model performance increases when the number of rankings and objects increases. In addition, the performance is considerably amplified when the judges' characteristics have a high impact on their choices.

New Frontiers in Prevention Research Models: Commentary on the Special Issue

Models considered in the current special issue represent valuable additions to the statistical toolbox of prevention researchers for many types of research questions and designs. Their appropriate use, however, depends on critical evaluation relative to previously existing techniques. This evaluation includes (a.) model choice involving "right-sizing" of the model relative to the amount and quality of data at hand, (b.) examination of the external validity of identified associations relative to observed or latent subgroups, (c.) confirmation of the reasonableness of the functional form assumed by the model, and (d.) identification of influential or outlying observations which unduly affect model fit or parameter estimates. Models in this issue allow for testing of new types of hypotheses in prevention research, and can constitute counterarguments to existing statistical practice. These models may, however, in turn be the object of critical examination of counterarguments a reasonable skeptic may offer.

Advanced Categorical Data Analysis in Prevention Science

A variety of health and social problems are routinely measured in the form of categorical outcome data (such as presence/absence of a problem behavior or stages of disease progression). Therefore, proper quantitative analysis of categorical data lies at the heart of the empirical work conducted in prevention science. Categorical data analysis constitutes a broad dynamic field of methods research and data analysts in prevention science can benefit from incorporating recent advances and developments in the statistical evaluation of categorical outcomes in their methodological repertoire. The present Special Issue, Advanced Categorical Data Analysis in Prevention Science, highlights recent methods developments and illustrates their application in the context of prevention science. Contributions of the Special Issue cover a wide variety of areas ranging from statistical models for binary as well as multi-categorical data, advances in the statistical evaluation of moderation and mediation effects for categorical data, developments in model evaluation and measurement, as well as methods that integrate variable- and person-oriented categorical data analysis. The articles of this Special issue make methodological advances in these areas accessible to the audience of prevention scientists to maintain rigorous statistical practice and decision making. The current paper provides background and rationale for this Special Issue, an overview of the articles, and a brief discussion of some potential future directions for prevention research involving categorical data analysis.

Assessing Heterogeneity in Students' Visual Judgment: Model-Based Partitioning of Image Rankings

Differences in the ability of students to judge images can be assessed by analyzing the individual preference order (ranking) of images. To gain insights into potential heterogeneity in judgement of visual abstraction among students, we combine Bradley-Terry preference modeling and model-based recursive partitioning. In an experiment a sample of 1,020 high-school students ranked five sets of images, three of which with respect to their level of visual abstraction. Additionally, 24 art experts and 25 novices were given the same task, while their eye movements were recorded. Results show that time spent on the task, the students' age, and self-reported interest in visual puzzles had significant influence on rankings. Fixation time of experts and novices revealed that both groups paid more attention to ambiguous images. The presented approach makes the underlying latent scale of visual judgments quantifiable.