Linear Causal Modeling with Structural Equations / Edition 1

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $69.04
Usually ships in 1-2 business days
(Save 27%)
Other sellers (Hardcover)
  • All (7) from $69.04   
  • New (3) from $76.45   
  • Used (4) from $69.04   


Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal relations directly by perceiving quantities in magnitudes and motions of causes that are conserved in the effects of causal exchanges.

The author surveys the basic concepts of graph theory useful in the formulation of structural models. Focusing on SEM, he shows how to write a set of structural equations corresponding to the path diagram, describes two ways of computing variances and covariances of variables in a structural equation model, and introduces matrix equations for the general structural equation model. The text then discusses the problem of identifying a model, parameter estimation, issues involved in designing structural equation models, the application of confirmatory factor analysis, equivalent models, the use of instrumental variables to resolve issues of causal direction and mediated causation, longitudinal modeling, and nonrecursive models with loops. It also evaluates models on several dimensions and examines the polychoric and polyserial correlation coefficients and their derivation.

Covering the fundamentals of algebra and the history of causality, this book provides a solid understanding of causation, linear causal modeling, and SEM. It takes readers through the process of identifying, estimating, analyzing, and evaluating a range of models.

Read More Show Less

Editorial Reviews

From the Publisher
"…an accessible yet rigorous treatment of the subject and is likely to be appealing to a wide statistical audience. … I enjoyed reading this book and suspect others will too. I would recommend this book for students and researchers [who] are familiar with standard applied statistics and causal inference but are looking for an introduction to structural equation modeling."
—Eric Laber, Journal of the American Statistical Association, September 2013

"The book is written by one of the most prominent researchers in the field of structural equation models (SEM). … It is primarily a useful textbook for graduate students but could also be very useful for researchers in quantitative methods. … the book presents the standard methods of SEM in a form that makes them interesting to students and researchers with interests in the philosophical treatment of causality using SEM. … a very useful textbook for graduate students. It stands out for its rigorous treatment of SEM as a whole and for a particularly useful philosophical treatment of causality. … Stanley Mulaik’s book is one of the most useful ones with which to start a journey in this field."
—Spiridon Penev, Australian & New Zealand Journal of Statistics, 2011

"The book benefits very substantially from the author’s mixed background in multivariate analysis, psychometrics, and philosophy of science—a background which is ideally suited to the eclectic issues raised by considerations of causality. I am sure the volume will prove to be a very useful contribution to the literature, an excellent text for someone intending to research in this area, and a useful reference source for those already doing so."
—David J. Hand, International Statistical Review (2011), 79

Read More Show Less

Product Details

Meet the Author

Stanley A. Mulaik is Professor Emeritus in the School of Psychology at the Georgia Institute of Technology.

Read More Show Less

Table of Contents


The Rise of Structural Equation Modeling

An Example of Structural Equation Modeling

Mathematical Foundations for Structural Equation Modeling


Scalar Algebra


Matrix Algebra


Treatment of Variables as Vectors

Maxima and Minima of Functions


Historical Background

Perception of Causation


Conditions for Causal Inference

Nonlinear Causation

Science as Knowledge of Objects Demands Testing of Causal Hypotheses

Summary and Conclusion

Graph Theory for Causal Modeling

Directed Acyclic Graphs

Structural Equation Models

Basics of Structural Equation Models

Path Diagrams

From Path Diagrams to Structural Equations

Formulas for Variances and Covariances in Structural Equation Models

Matrix Equations


Incompletely Specified Models


Estimation of Parameters

Discrepancy Functions

Derivatives of Elements of Matrices

Parameter Estimation Algorithms

Designing SEM Studies

Preliminary Considerations

Multiple Indicators

The Four-Step Procedure

Testing Invariance across Groups of Subjects

Modeling Mean Structures

Confirmatory Factor Analysis


Early Attempts at Confirmatory Factor Analysis

An Example of Confirmatory Factor Analysis

Faceted Classification Designs

Multirater-Multioccasion Studies

Multitrait-Multimethod Covariance Matrices

Equivalent Models


Definition of Equivalent Models

Replacement Rule

Equivalent Models That Do Not Fit Every Covariance Matrix

A Conjecture about Avoiding Equivalent Models by Specifying Nonzero Parameters

Instrumental Variables


Instrumental Variables and Mediated Causation


Multilevel Models


Multilevel Factor Analysis on Two Levels

Multilevel Path Analysis

Longitudinal Models


Simplex Models

Latent Curve Models

Reality or Just Saving Appearances?

Nonrecursive Models


Flow Graph Analysis

Mason’s Direct Rule

Covariances and Correlations with Nonrecursive-Related Variables




Model Evaluation


Errors of Fit

Chi-Square Test of Fit

Properties of Chi-Square and Noncentral Chi-Square

Goodness-of-Fit Indices, CFI, and Others

The Meaning of Degrees of Freedom

"Badness-of-Fit" Indices, RMSEA, and ER


Information Theoretic Measures of Model Discrepancy

AIC Does Not Correct for Parsimony

Is the Noncentral Chi-Square Distribution Appropriate?


Cross-Validation Index

Confusion of "Likelihoods" in the AIC

Other Information Theoretic Indices, ICOMP

LM, WALD, and LR Tests

Modifying Models Post hoc

Recent Developments

Criticisms of Indices of Approximation


Polychoric Correlation and Polyserial Correlation


Polychoric Correlation

Polyserial Correlation




Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)