We consider joint probability distributions generated recursively in terms of univariate conditional distributions satisfying conditional independence restrictions. The independences are captured by missing edges in a directed graph. A matrix form of such a graph, called the generating edge...

The multivariate regression of a p - 1 vector Y of random variables on a q - 1 vector X of explanatory variables is considered. It is assumed that linear transformations of the components of Y can be the basis for useful interpretation whereas the components of X have strong individual identity....

Undetected confounding may severely distort the effect of an explanatory variable on a response variable, as defined by a stepwise data-generating process. The best known type of distortion, which we call direct confounding, arises from an unobserved explanatory variable common to a response and...

The paper examines the effect of marginalizing over a possibly unobserved background variable on the conditional relation between a response and an explanatory variable. In particular it is shown that some conclusions derived from least squares regression theory apply in general to testing...