**BOOK
REVIEWS**

Reprinted (with permission) from

**Causality:
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
Judea Pearl
Contents |

**Reference and Further Reading**

McDonald, R.P. (1997), "Haldane's Lungs: A Case Study in Path
Analysis,"

*Multivariate Behavioral Research*, 32, 1-38