# Chain Graph Models in R: Implementing the Cox-Wermuth Procedure

Activity: Talk or presentationScience to science

## Description

In complex research problems that involve a large number of potentially important variables or feature a complicated dependence structure, the joint probability distribution of the involved random variables can only be unsatisfactorily modelled with classical statistical models. Often some structure in the joint distribution allows to factorize it into conditionally independent components which gave rise to a class of models known as Graphical Models. By representing the joint distribution as a graph with nodes and edges, Graphical Models can exploit possible conditional independence structures in the joint distribution and allow restoring the joint distribution from the components. A subclass of Graphical Models, Chain Graph Models, are of particular interest for problems in social and behavioural sciences. A chain graph is a graph which may have both directed and undirected edges but is devoid of any directed cycles. In these models, a researcher can use substantive knowledge to categorize the variables as purely explanatory (predictor), purely dependent (response) or intermediate (response and predictor in turn). Each of these variables is assigned to a certain block, based on a partial ordering of the variables, meaning that the ordering is present between blocks but not within blocks. This approach leads to a chain of relationships between the different variables. The challenging task of fitting a full Chain Graph Model to the data is facilitated by the factorization property which allows maximizing the joint likelihood by reducing the problem to maximizing the likelihood for each factorized submodel. However, in case of different variable types in the same block (e.g., metric and categorical variables) ML estimation using the direct factorization strategy often does not converge or can computationally be very expensive. As a remedy, Cox & Wermuth (1996) propose the heuristic usage of a system of univariate models for each factorized component.
Period 14 Feb 2013 → 15 Feb 2013 Psychoco - International Workshop on Psychometric Computing Unknown International