Models, Reasoning, and Inference
by Judea Pearl
Cambridge University Press, 2000.
Reviewed by Roderick P. McDonald
IT IS A FAIRLY safe bet
that most readers of Chance, and of Chance reviews will have been
trained to be skeptical of causal interpretations of scientific observations,
with a possible exception for causal claims based on randomized experiments, if
free from threats of confounding factors. The influence (causal effect?) of the
positivist tradition on users of statistical methods has been so strong that
most would feel embarrassed to make claims in the form "X
causes Y." Most would seek to use disguised terminology -
"influences," "is a factor in" - or to translate the
assertion into an association, a prediction, or a distribution conditioned on
observations of X.
Over the last decade or so, Judea Pearl and his colleagues have been developing a mathernatization of causality - a calculus of causal claims - that clarifies and systematizes this difficult area of thought. The book under review is a fairly comprehensive account of this work.
The basis of this causal calculus can be briefly and imprecisely summarized here as (a) a causal model, defined as a system of generally nonparametric, nonlinear structural equations relating members of two sets of variables - predetermined (in one sense exogenous") variables whose values are determined outside the system, and endogenous variables, whose values are determined by other variables in the model - and (b) a Directed Graph - commonly a Directed Acyclic Graph - whose nodes are the observable variables in the model and whose edges correspond to the specified relationships. The predetermined variables carry a probability distribution. The reader familiar with structural equation models (SEMs) will recognize this as a generalization on linear SEMs and may be intrigued to note that for the purposes of the account the functions remain unspecified except in the familiar linear specialization.
Submodels of this causal model are obtained by setting a subset of the variables equal to constants and deleting the functions of which these are dependent variables. Parallel operations on the graph of the model give subgraphs. This setting procedure is what makes the model "causal," being interpretable as (hypothetically, counterfactually, potentially) bringing the set of variables under control and possibly giving them values other than those actually observed in data.
A clear distinction results between conditioning on observations of independent variables - wide-sense regression relationships - and conditioning on (conjectural or actual) controlled values - structural relationships. The exploitation of properties of the graphs and subgraphs by which the models and their submodels can be said to be structured enables a rigorous account of causal claims, of qualitative conditions on a specified model under which the effects of actions/interventions can be identified from nonexperimental data, and, generally, of the conclusions that can be safely drawn about causal effects in an elaborate causal network, given a correctly and completely specified causal model.
I find the account convincing and the contribution extremely important. Given the bet made in my opening paragraph, I am tempted to challenge all readers to examine Pearl's case for the "primacy of causal over associational knowledge," even if only to see if a positivist, "associational" position can be sustained in the face of his account. The challenge may prove daunting to some, not so much because the account is fairly technical, but rather because it does not rest on the forms of mathematical reasoning in which statisticians are most completely fluent.
Apart from the general thesis, there is something for everyone in this book. Many statisticians will appreciate the clear account of Simpson's paradox, confounding, and choice of covariates. Psychometricians, sociometricians, and econometricians will find a fresh view of path analysis/structural equation modeling. There is a great deal for philosophers of science, and something too for epidemiologists. There is even something for physicists - who may have learned that causal statements are crude versions of differential equations and boundary conditions - in the form of a causal/counterfactual treatment of Ohm's law and my favorite example in the book, in which we consider whether tall flagpoles cause long shadows or long shadows cause tall flagpoles.
The sequencing of topics in the book had me puzzled, but I do not wish to suggest that it is not well designed. (A list of chapter headings is appended.) According to the preface, "the sequence of discussion follows more or less the chronological order by which our team at UCLA has tackled these topics" (p. xiv). The truly dedicated reader will follow the advice of the King of Hearts to the White Rabbit in Alice in Wonderland to "begin at the beginning, and go on to the end; then stop." The preface supplies a sequence of sections to be read as an introduction to the nonmathematical aspects of causation, and an alternative sequence for "more formally driven readers." These sequences cannot, I think, be managed without considerable guesswork as to meaning or considerable backtracking. After meditating on the possibility of other sequences, and on alternative orders in which the book, counterfactually, might have been written, starting as my rough summary did, with the definition of a causal model from Chapter 7, I incline to recommend that specialist readers should go first to the chapter or section that will show them that they cannot ignore this book. They can then either follow the King of Heart's advice or decide for themselves how to find the necessary foundations for the problems and solutions of most interest. Structural equation modelers will jump to Chapter 5. (Econometricians should turn immediately to Section 7.2.1 before going to Chapter 5.) Many statisticians should be attracted first to Chapter 6, on Simpson's paradox and confounding, to discover how the treatment of causal models clarifies this problem area. Medical researchers and epidemiologists will seek applications in their fields. Philosophers will go directly to Chapter 7, where, I have quietly suggested, the story really starts. And just everyone should turn to the delightful epilogue - a public lecture that sums it all up - before beginning more serious reading. In principle, the book could be used as the basis of a specialist graduate course in a number of fields, but more likely it would serve as a resource for graduate reading.
The publication of this book is timely, if not overdue. Structural equation modeling urgently needs reexamination in the context of these ideas, which more generally offer possible reform for much of the field of multivariate data analysis. Many of the original sources of the material presented are in technical reports, conference proceedings, or journals that would not he considered mainstream by statisticians or social/behavioral scientists. Some readers will regret the fact that proofs of a number of the basic theorems are not reproduced in the text. Other readers may wish for a more extensive account, with more examples, teaching us to interrogate a graphical picture of the causal model and thereby arrive, quickly and easily - as we are assured is possible - at conclusions about the identifiability of causal effects, implied constraints on the distribution of observations, and other applications, in quite complex causal networks. The former group of readers can try to access the original accounts or wait for a technical supplement. The latter group can work carefully over the examples supplied or wait for Pearl or one of his students to write a gentler introduction to this important topic.
Most researchers in relevant fields (should) know that the Achilles heel of structural equation modeling is the problem of unknown omitted variables. (See, for example, McDonald 1997.) The causal calculus in this book cannot, of course, tell the researcher how to specify a causal model correctly and completely in an application. Nevertheless, the account of equivalent models - models that cannot be distinguished on the basis of a nonexperimental dataset - should serve as a corrective to a well-established bad practice followed by users of SEMs, of applying a global test of fit to a rather superficially and arbitrarily theorized model and ''confirming" it when the fit is good.
Directed Acyclic Graph theory yields strong results for a Markov causal network, including sets of testable constraints on the distribution of observations, in the form of conditional independences. (To avoid technicalities we will say that a Markovian causal model contains no relationships, corresponding to omitted common causes, while a semi-Markovian model may contain such relationships.) The duty of a reviewer to find fault is one I undertake with great reluctance in this case. However, I will remark that the account of the range of application of sonic of the theorems - possibly to semi-Markovian and to cyclic (nonrecursive) models - could have been made more explicit, as could the fact that theory for semi-Markovian models remains incomplete. Another mild disappointment is that the account of linear SEMs in Chapter 5 does not connect to the earlier chapters. I am left wondering, for example, what general principle accounts for unidentified causal structures - for example, Figure 3.7(c) - whose linear version is identified.
The real intent of these two mild complaints is to point to the fact that Judea Pearl has given us a justifiably confident account of the current state of what is necessarily work in progress. One of the most important effects of his book should be to encourage a larger group of workers with a wider range of backgrounds to undertake aspects of this research program. Structural equation modelers should certainly take it up in developing further theory for linear and for parametric nonlinear models. Philosophers of science, whose professional ethos directs them to unreasonable doubt, can be expected to raise difficulties about foundational issues, and just conceivable even resolve them. We should be pleased to have this book, both for what it covers and for what it points to in the way of further work on the explication of causality.
|Causality: Models, Reasoning, and Inference by
Reference and Further Reading
McDonald, R.P. (1997), "Haldane's Lungs: A Case Study in Path
Multivariate Behavioral Research, 32, 1-38
Return to CAUSALITY