developed a theory of statistical causal inference. In his presentation at the Notre Dame

In the last decade, there has been considerable progress in understanding a certain class of statistical models, known as directed acyclic graph (DAG) models, which encode independence, and conditional independence constraints. (See Pearl, 1988). This research has had fruitful results in many areas: there is now a relatively clear causal interpretation

A method is given which uses subject matter assumptions to discriminate recursive models and thus point toward possible causal explanations. The assumptions alone do not specify any order among the variables --- rather just a theoretical absence of direct association. We show how these assumptions, while not specifying any ordering, can when combined with the data through the likelihood function yield information about an underlying recursive order. We derive details of the method for multi-normal random variables. 4.1 INTRODUCTION Starting from Sewall Wright (1934), directed graphs have been used to represent structures in which variables `cause' or `influence' other variables. Nodes of the graph are used to represent variables and an arrow from one variable to another indicates that the first has a direct causal influence on the second, an influence not blocked by holding constant others considered. If the graphs are restricted to directed acyclic graphs (DAGs) by prohibiting direct...

The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of tetrad differences in a linear correlation structure. This note simplifies their proof and generalizes the theorem. This generalization can strengthen procedures used to search for structural equation models for large data sets. -- 1 -- 1 Introduction In a linear "structural equation" model, it is assumed that there is a set of variables V , and for each variable X i in V , there is a unique associated error term E i with non-zero variance. For each variable X i in V a linear equation relates X i to a subset of V (excluding X i ) and its error term E i ; the variables that do not appear in the equation for X i are assumed to have coefficients fixed at zero. We assume that the error terms are jointly independent (although in what follows, this assumption can easily be relaxed.) Associated with each such set of equations is a direct...

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A principal aim of many sciences is to model causal systems well enough to provide insight into their structures and mechanisms and to provide reliable predictions about the effects of policy interventions. To

Structural equation modeling (SEM) has advanced considerably in the social sciences. The direction of advances has varied by the substantive problems faced by individual disciplines. For example, path analysis developed to model inheritance in population genetics, and later to model status attainment in sociology. Factor analysis developed in psychology to explore the structure of intelligence, and simultaneous equation models developed in economics to examine supply and demand. These largely discipline-specific advances came together in the early 1970s to create a multidisciplinary approach to SEM. Later, during the 1980s, responding to criticisms of SEM for failing to meet assumptions implied by maximum likelihood estimation and testing, SEM proponents responded with estimators for data that departed from multivariate normality, and for modeling categorical, ordinal, and limited dependent variables. More recently, advances in SEM have incorporated additional statistical models (growth models, latent class growth models, generalized linear models, and multi-level models), drawn upon artificial intelligence research to attempt to “discover ” causal structures, and finally, returned to the question of causality with formal methods for specifying assumptions necessary for inferring causality with nonexperimental