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21
Chain Graph Models and their Causal Interpretations
 B
, 2001
"... Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultim ..."
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Cited by 48 (4 self)
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Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...
Graphs, Causality, And Structural Equation Models
, 1998
"... Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers. ..."
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Cited by 44 (14 self)
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Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.
Markov properties for acyclic directed mixed graphs
 Scandinavian Journal of Statistics
, 2003
"... We consider acyclic directed mixed graphs, in which directed edges (x → y) and bidirected edges (x ↔ y) may occur. A simple extension of Pearl’s dseparation criterion, called mseparation, is applied to these graphs. We introduce a local Markov property which is equivalent to the global property r ..."
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Cited by 36 (5 self)
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We consider acyclic directed mixed graphs, in which directed edges (x → y) and bidirected edges (x ↔ y) may occur. A simple extension of Pearl’s dseparation criterion, called mseparation, is applied to these graphs. We introduce a local Markov property which is equivalent to the global property resulting from the mseparation criterion.
Principles and practice in reporting structural equation analyses
 Psychological Methods
, 2002
"... Principles for reporting analyses using structural equation modeling are reviewed, with the goal of supplying readers with complete and accurate information. It is recommended that every report give a detailed justification of the model used, along with plausible alternatives and an account of ident ..."
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Cited by 29 (0 self)
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Principles for reporting analyses using structural equation modeling are reviewed, with the goal of supplying readers with complete and accurate information. It is recommended that every report give a detailed justification of the model used, along with plausible alternatives and an account of identifiability. Nonnormality and missing data problems should also be addressed. A complete set of parameters and their standard errors is desirable, and it will often be convenient to supply the correlation matrix and discrepancies, as well as goodnessoffit indices, so that readers can exercise independent critical judgment. A survey of fairly representative studies compares recent practice with the principles of reporting recommended here. Structural equation modeling (SEM), also known as path analysis with latent variables, is now a regularly used method for representing dependency (arguably “causal”) relations in multivariate data in the behavioral and social sciences. Following the seminal work of Jöreskog (1973), a number of models for linear structural relations have been developed
A new identification condition for recursive models with correlated errors
 Struct. Equ. Model
, 2002
"... This article establishes a new criterion for the identification of recursive linear models in which some errors are correlated. We show that identification is ensured as long as error correlation does not exist between a cause and its direct effect; no restrictions are imposed on errors associated w ..."
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Cited by 17 (0 self)
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This article establishes a new criterion for the identification of recursive linear models in which some errors are correlated. We show that identification is ensured as long as error correlation does not exist between a cause and its direct effect; no restrictions are imposed on errors associated with indirect causes. Before structural equation models (SEM) can be estimated and evaluated against data, a researcher must make sure that the parameters of the estimated model are identified, namely, that they can be determined uniquely from the population covariance matrix. The importance of testing identification prior to data analysis is summarized succinctly by Rigdon (1995): To avoid devoting research resources toward a hopeless cause (and to avoid ignoring productive research avenues out of an unfounded fear of underidentification), researchers need a way to quickly evaluate a model's identification status before data are collected. Furthermore, because models are often altered in the course of research (Joreskog, 1993), researchers need a technique that helps them understand the impact of potential structural changes on the identification status of the model, (p. 359) It is well known that, in recursive path models with correlated errors, the identification problem is unsolved. In other words, we are not in possession of a necessary and sufficient criterion for deciding whether the parameters in such a model can be computed from the population covariance matrix of the observed variables. Certain restricted classes of models are nevertheless known to be identifiable, and
A Survey of Partial Least Squares (PLS) Methods, with Emphasis on the TwoBlock Case
, 2000
"... Partial Least Squares (PLS) is a class of techniques for modeling the association between blocks of observed variables by means of latent variables. Originated by Herman Wold in the 1970's, PLS is important in many scientific disciplines, including psychology, economics, chemistry, medicine and the ..."
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Cited by 17 (0 self)
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Partial Least Squares (PLS) is a class of techniques for modeling the association between blocks of observed variables by means of latent variables. Originated by Herman Wold in the 1970's, PLS is important in many scientific disciplines, including psychology, economics, chemistry, medicine and the pharmaceutical sciences, and process modelling (Rannar et al. [10]). PLS has many variants. The algorithm can be run in two modes, called A and B. It can be applied to data that are divided into two or more blocks. The general algorithm due to Wold can be followed, or it can be modified. Wold stated his general algorithm in terms different from those customarily used by statisticians. In the current work the algorithm is placed into a more familiar notation, and the twoblock case is discussed. Canonical twoblock Mode A PLS (PLSC2A) is stated. Its properties, and the properties of the coefficients it computes, are examined in detail. In particular PLSC2A is shown to be a special case of Wold's ...
Identifying linear causal effects
 In Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI
, 2004
"... This paper concerns the assessment of linear causeeffect relationships from a combination of observational data and qualitative causal structures. The paper shows how techniques developed for identifying causal effects in causal Bayesian networks can be used to identify linear causal effects, and t ..."
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Cited by 9 (4 self)
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This paper concerns the assessment of linear causeeffect relationships from a combination of observational data and qualitative causal structures. The paper shows how techniques developed for identifying causal effects in causal Bayesian networks can be used to identify linear causal effects, and thus provides a new approach for assessing linear causal effects in structural equation models. Using this approach the paper develops a systematic procedure for recognizing identifiable direct causal effects.
A new inferential test for path models based on directed acyclic graphs. Structural Equation Modeling
"... This article introduces a new inferential test for acyclic structural equation models (SEM) without latent variables or correlated errors. The test is based on the independence relations predicted by the directed acyclic graph of the SEMs, as given by the concept of dseparation. A wide range of dis ..."
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Cited by 9 (1 self)
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This article introduces a new inferential test for acyclic structural equation models (SEM) without latent variables or correlated errors. The test is based on the independence relations predicted by the directed acyclic graph of the SEMs, as given by the concept of dseparation. A wide range of distributional assumptions and structural functions can be accommodated. No iterative fitting procedures are used, precluding problems involving convergence. Exact probability estimates can be obtained, thus permitting the testing of models with small data sets. Structural equations represent the translation of a hypothesized series of cause–effect relationships between variables into a composite statistical hypothesis concerning patterns of statistical dependencies. The development of an inferential test for such a composite statistical hypothesis (see Bollen, 1989, for a historical summary) has had a large impact on fields of study in which multivariate causal hypotheses cannot be tested through randomized experiments. The various statistical innovations that were spawned by this method have mostly followed the same basic logic. A series of hypothesized causal relationships between the variables are combined to form a directed graph (the path model). This directed graph implies a series of path coefficients, some of which are fixed to some a priori value (usually zero) and the rest of which are free to vary. These free parameters are estimated by minimizing some discrepancy measure such as the maximum likelihood loss function. The predicted variance–covariance matrix, implied by the set of fully parameterized structural equations, is then compared to the sample variance–covariance matrix using a fit statistic that has a known, usually asymptotic, probability distribution. Requests for reprints should be sent to Bill Shipley, Département de Biologie, Université de