A Qualitative Approach to Causal Modeling

Abstract

Linear causal models are often constructed to explain statistical data in domains in which experiments cannot be performed. We can distinguish two types of causal models. A quantitative linear causal model can be represented by a set of simultaneous linear equations, distributional assumptions about the independent variables, and a graph that represents the causal connections between variables. A qualitative causal model contains only the graph that represents the causal connections between variables. Great progress has been made in recent years in finding the correct quantitative causal model, given sample covariance matrices and the correct qualitative causal model. However, relatively little work has been done on finding the correct qualitative causal model from statistical data and background knowledge. Recently, several programs (including LISREL VI and EQS) have added a feature that uses numerical algorithms on an initially specified quantitative model to search for better qualitative and quantitative models. In contrast, we have developed a program, TETRAD II, that searches for and evaluates alternative qualitative causal models with fast graph algorithms that entirely bypass parameter estimation. We discuss the two approaches to model search and compare their reliability with a simulation study of 360 data sets generated from nine different linear causal models. We also discuss how our methods can be used to do more than search for modifications of an initial model. We show how TETRAD II can construct initial models from just covariance data and background knowledge.