Comments on: Sequences of regressions and their independencies

Abstract

A graphical model is a statistical model that is associated with a graph whose nodes correspond to random variables. The model is defined by requiring distributions to obey a factorization property determined by the graph’s edges or, alternatively, to exhibit a collection of conditional independencies associated with the pattern of edges absent from the graph. This latter point of view is the one stressed in the paper by Wermuth and Sadeghi who treat models associated with graphs that they term ‘regression graphs’. We would like to take the opportunity to briefly comment on the motivation of regression graphs, their relationship with other mixed graphs, and on constraints that are not of conditional independence type. While there has been recent progress on models for categorical data (see, for instance, Evans and Richardson 2011, and references therein), our discussion will focus on multivariate normal distributions. When variables are related through acyclic cause and effect relationships, the dependence structure they exhibit can be represented by directed acyclic graphs; see