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Learning the structure of linear latent variable models
 Journal of Machine Learning Research
, 2006
"... We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are dseparated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the ..."
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We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are dseparated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is pointwise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we
The TETRAD Project: Constraint Based Aids to Causal Model Specification
 MULTIVARIATE BEHAVIORAL RESEARCH
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Generalized measurement models
, 2004
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document without permission of its author may be prohibited by law.
Conducting tetrad tests of model fit and contrasts of tetradnested models: a new SAS macro
 Struct. Equ. Model
"... This article describes a SAS macro to assess model fit of structural equation models by employing a test of the modelimplied vanishing tetrads. Use of this test has been limited in the past, in part due to the lack of software that fully automates the test in a userfriendly way. The current SAS m ..."
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This article describes a SAS macro to assess model fit of structural equation models by employing a test of the modelimplied vanishing tetrads. Use of this test has been limited in the past, in part due to the lack of software that fully automates the test in a userfriendly way. The current SAS macro provides a straightforward method for researchers touse thevanishing tetrads impliedbymodels toassess the fitof (a) structural equation models containing continuous endogenous variables; (b) structural equation models containing continuous endogenous variables nested for vanishing tetrads; and (c) structural equation models containing dichotomous, ordinal, or censored endogenous variables. Besides providing an alternative assessment of model fit to the usual likelihoodratio test (LRT), thevanishing tetrads testoccasionallyprovidesastatistical assessment of competing models nested for vanishing tetrads but not nested for the LRT. The macro permits formal comparisons between tetradnested structural equation models containing dichotomous, ordinal, or censored endogenous variables. A key focus of structural equation modeling (SEM) is the assessment of model fit. The usual test applied for assessing model fit is the likelihoodratio chisquare test
Generalization of the Tetrad Representation Theorem
"... Abstract. The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and su cient for the vanishing of tetrad di erences in a linear correlation structure. This note simpli es their proof and generalizes the theorem. This generalization can ..."
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Abstract. The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and su cient for the vanishing of tetrad di erences in a linear correlation structure. This note simpli es their proof and generalizes the theorem. This generalization can strengthen procedures used to search for structural equation models for large data sets.
Generalization of the Tetrad Representation Theorem
 Preliminary Papers of the Fifth International Workshop on Artificial Intelligence and
, 1993
"... The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of tetrad differences in a linear correlation structure. This note simplifies their proof and generalizes the theorem. This generalization can stren ..."
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The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of tetrad differences in a linear correlation structure. This note simplifies their proof and generalizes the theorem. This generalization can strengthen procedures used to search for structural equation models for large data sets.  1  1 Introduction In a linear "structural equation" model, it is assumed that there is a set of variables V , and for each variable X i in V , there is a unique associated error term E i with nonzero variance. For each variable X i in V a linear equation relates X i to a subset of V (excluding X i ) and its error term E i ; the variables that do not appear in the equation for X i are assumed to have coefficients fixed at zero. We assume that the error terms are jointly independent (although in what follows, this assumption can easily be relaxed.) Associated with each such set of equations is a direct...
Chapter 15 Eight Myths About Causality and Structural Equation Models
"... Abstract Causality was at the center of the early history of structural equation models (SEMs) which continue to serve as the most popular approach to causal analysis in the social sciences. Through decades of development, critics and defenses of the capability of SEMs to support causal inference ha ..."
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Abstract Causality was at the center of the early history of structural equation models (SEMs) which continue to serve as the most popular approach to causal analysis in the social sciences. Through decades of development, critics and defenses of the capability of SEMs to support causal inference have accumulated. A variety of misunderstandings and myths about the nature of SEMs and their role in causal analysis have emerged, and their repetition has led some to believe they are true. Our chapter is organized by presenting eight myths about causality and SEMs in the hope that this will lead to a more accurate understanding. More specifically, the eight myths are the following: (1) SEMs aim to establish causal relations from associations alone, (2) SEMs and regression are essentially equivalent, (3) no causation without manipulation, (4) SEMs are not equipped to handle nonlinear causal relationships, (5) a potential outcome framework is more principled than SEMs, (6) SEMs are not applicable to experiments with randomized treatments, (7) mediation analysis in SEMs is inherently noncausal, and (8) SEMs do not test any major part of the theory against the data. We present the facts that dispel these myths, describe what SEMs can and cannot do, and briefly present our critique of current practice using SEMs. We conclude that the current capabilities of SEMs to formalize and implement causal inference tasks are indispensible; its potential to do more is even