On Causal Identification under Markov Equivalence

In this work, we investigate the problem of computing an experimental distribution from a combination of the observational distribution and a partial qualitative description of the causal structure of the domain under investigation. This description is given by a partial ancestral graph (PAG) that represents a Markov equivalence class of causal diagrams, i.e., diagrams that entail the same conditional independence model over observed variables, and is learnable from the observational data. Accordingly, we develop a complete algorithm to compute the causal effect of an arbitrary set of intervention variables on an arbitrary outcome set.

A log-linear analysis of efficiency in elite basketball applied to observational methodology

Although the full potential of observational methodology is realized through diachronic analyses, synchronic analyses can be used to investigate associations between categorical variables. Log-linear modeling is an appropriate method for investigating associations between three or more dimensions using multidimensional contingency tables. We provide a practical example of how we used log-linear analysis to study efficiency in a men’s basketball competition played by Spain’s top teams using a model containing three dimensions (and their respective categories): position of last pass before a shot, position of shot, and result of shot. The best-fit and most parsimonious model (i.e., the model that provided the best explanation of the observed frequencies in the contingency table and that contained the fewest effects) was a conditional independence model in which last pass position and shot position were associated independently of the categories in the shot result dimension and the interaction between shot position and shot result was not affected by the categories in the last pass dimension. Estimation and subsequent interpretation of the significant parameters in the selected model showed how log-linear modeling can provide basketball coaches with practical insights within an observational methodology study.