Two Algorithms for Inducing Structural Equation Models from Data

We present two algorithms for inducing structural equation models from data. Assuming no latent variables, these models have a causal interpretation and their parameters may be estimated by linear multiple regression. Our algorithms are comparable with PC [Spirtes93] and IC [Pearl91a, Pearl91b], which rely on conditional independence. We present the algorithms and empirical comparisons with PC and IC. 1.1 Structural Equation Models Given a dependent variable x 0 and a set of predictor variables P = fx 1 ; x 2 ; : : : ; x k g, multiple regression algorithms find subsets p ae P that account for "much" of the variance in x 0 . These are search algorithms, and they are not guaranteed to find the "best" p---the one that makes R 2 as big as possible, especially when p is a proper subset of P [Mosteller77, Cohen75, Draper66]. The question arises, what should be done with the variables in T = P \Gamma p? T is the set of variables that are not selected as predictors of x 0 . In many data..