Causality: Models, Reasoning, and Inference. Judea Pearl. Cambridge, UK. Cambridge University Press, 2000.
by Bill Shipley
Départment of Biologie
Universite de Sherbrooke
Wright introduced causal modeling, in the form of path analysis, in 1921. His
method had two important defects. First, although he could decompose statistical associations into direct and indirect effects given a causal
structure, he had no way of statistically testing for an agreement between the
empirical data and the assumed causal structure. Second, the link between
causality and probability distributions was intuitive, largely unstated, and
contrary to the views of leading statisticians and philosophers of science at
the turn of the 20th century. Wright was one of the leading evolutionary
biologists of his time and he continued to publish on this method
until 1984 and yet, because of these two defects, path analysis was stillborn in
biology and largely ignored. A similar fate could still await structural
equation modeling (SEM), but the new book by Judea Pearl will go a long way to
avoiding this possibility.
Despite the fact that modem SEM has partially solved the first defect of Wright's method, that of testing for an agreement between empirical data and an assumed causal structure, it has largely ignored the second defect. Is SEM simply a method of reproducing or approximating a covariance matrix (and there are other, simpler methods of doing this) or does it permit causal interpretations? If the former, then why not use simpler methods of statistical prediction? If the latter, then what is the relation between causal claims and structural equations? What is the link (if any) between causal claims and probability distributions? These questions are dealt with in SEM in one of three ways: by ignoring them, by appealing to the same intuitive links between causality and probability that Wright used, or by publicly denying any causal content to SEM while continuing to apply it to overtly causal research questions. Until the relation between causality and probability distributions is rigorously defined, critics can justifiably compare SEM to the prestidigitation of conjurers.
Unknown to most users of SEM there is a small group of computer scientists, statisticians, and philosophers who have made much progress in solving just those problems that SEM has failed to resolve. One of the leading researchers in this group is Judea Pearl and his new book provides a rigorous answer to many of the criticisms of SEM. Before describing the many important insights and methods that can be found in his book, let me point out its major failing: the terse prose and mathematical notation, although comprehensible to the in-crowd, will be a barrier to most readers of this review. This is unfortunate because most of the ideas are not difficult to understand when explained in simple language and they are clearly important to the further development of SEM.
The first chapter, besides describing the various problems that are tackled in the book, lays out the axiomatic relations between directed acyclic graphs (approximately equivalent to a recursive path diagram), causal claims, and conditional independence relations in the joint probability distribution generated by the graph. These relations are linked by the graph theoretic notion of d-separation. Much of this section extends ideas first developed in Pearl's 1988 book and provides a rigorous translation, based on mathematical proofs, between causal claims and probability distributions.
The second chapter, A Theory of Inferred Causation, builds on the notion of d-separation to produce a proveably correct and intellectually elegant algorithm for discovering causal structures—or more often partial causal structures—from patterns of independence or partial independence in observational data. Some SEM programs have "modification indexes" that attempt to suggest modifications of an ill-fitting model, but these methods are both proveably incorrect and perform poorly in simulations. There are more advanced treatments of this topic in other publications, which are cited by Pearl, but he does not describe them. Almost as an afterthought, this chapter also shows how to generate all equivalent models of a given causal model using a simple graphical criterion. These two results alone would justify the effort of reading the book.
Chapters 3 and 4 develop methods to tell when and how to predict the effects of interventions based on an observational model of a causal process. These chapters lay out in detail the important but misunderstood difference between statistically conditioning on passive observations and actually manipulating some variables while passively observing others. If your causal model involves (say) the degree of early childhood education, academic achievement in secondary school, as well as variables related to the home and school environment, you might want to answer the following question: If the government were to install a program of early childhood education, by how much would the academic achievement of an average child change given a particular home and school environment? If early childhood education is not an exogenous variable, then this cannot be answered by statistically conditioning on passive observations of it, but can possibly be answered using the methods in these chapters even if some variables are latent.
Chapter 5, Causality and Structural Models in Social Science and Economics, should be of interest to most practitioners of SEM. Using the results of previous chapters it explicates the causal meaning of structural equations using proofs based on the axiomatic relations between causality, directed graphs, and probability distributions. Many of the conceptual problems of SEM, as causal models as opposed to purely statistical constructs, are sorted out. This can only be positive to anyone trying to link notions of causality to SEM.
The power of the mathematical language of causality that Pearl develops is shown in Chapter 6, in which he shows how long-standing problems in statistics (Simpson's Paradox, confounding and collapsibility) can be easily sorted out. Chapters 7 to 9 link this mathematical language of causality to the counterfactual treatment of causality used by some philosophers to relate causes to probabilities. The Epilogue is a reproduction of a public lecture of the ideas in this book for a general audience. If I had written the book, I would have put this information at the beginning rather than at the end because it is probably the easiest introduction to these ideas
Who should read this book? Anyone who wants to study causal processes using observational data. Although it is not a book about SEM it is an important development that could move current research in SEM into new territory. Be patient. Don't be intimidated by the unnecessarily difficult prose. Important conceptual advances don't appear often and so they are worth some extra effort.
Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Network of plausible inference. San Mateo, CA: Morgan Kaufman.
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