What assumptions and methods allow us to turn observations into causal knowledge, and how can even incomplete causal knowledge be used in planning and prediction to influence and control our environment? In this book Peter Spirtes, Clark Glymour, and Richard Scheines address these questions using the formalism of Bayes networks, with results that have been applied in diverse areas of research in the social, behavioral, and physical sciences. The authors show that although experimental and observational study designs may not always permit the same inferences, they are subject to uniform principles. They axiomatize the connection between causal structure and probabilistic independence, explore several varieties of causal indistinguishability, formulate a theory of manipulation, and develop asymptotically reliable procedures for searching over equivalence classes of causal models, including models of categorical data and structural equation models with and without latent variables. The authors show that the relationship between causality and probability can also help to clarify such diverse topics in statistics as the comparative power of experimentation versus observation, Simpson's paradox, errors in regression models, retrospective versus prospective sampling, and variable selection. The second edition contains a new introduction and an extensive survey of advances and applications that have appeared since the first edition was published in 1993.

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Causation, prediction, and search

The regression models appropriate for counted data have seen little use in psychology. This article describes problems that occur when ordinary linear regression is used to analyze count data and presents 3 alternative regression models. The simplest, the Poisson regression model, is likely to be misleading unless restrictive assumptions are met because individual counts are usually more variable ("overdispersed") than is implied by the model. This model can be modified in 2 ways to accomodate this problem. In the overdispersed model, a factor can be estimated that corrects the regression model's inferential statistics. In the second alternative, the negative binomial regression model, a random term reflecting unexplained between-subject differences is included in the regression model. The authors compare the advantages of these approaches.

Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models

Structural equation modeling (SEM) is an extremely flexible linear-in-parameters multivariate statistical modeling technique. It has been used in modeling travel behavior and values since about 1980, and its use is rapidly accelerating, partially due to the availability of improved software. The number of published studies, now known to be more than 50, has approximately doubled in the past three years. This review of SEM is intended to provide an introduction to the field for those who have not used the method, and a compendium of applications for those who wish to compare experiences and avoid the pitfall of reinventing previous research.

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Structural equation modeling for travel behavior research

Gauging the robustness of regression estimates is especially important in small-sample analyses. Here, we examine recent developments in the detection and analysis of outliers and influential cases...

Regression Diagnostics: An Expository Treatment of Outliers and Influential Cases

Introduction.- Vector and Matrix Algebra.- The Multivariate Normal Distribution, Multivariate Normality, and Covariance Structure.- One- and Two-Sample Tests.- Multivariate Analysis of Variance.- Discriminant Analysis.- Canonical Correlation.- Principal Component Analysis.- Factor Analysis.- Structural Equations.

John Fox

Papers

Linear statistical models and related methods