## The TETRAD Project: Constraint Based Aids to Causal Model Specification

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Venue: | MULTIVARIATE BEHAVIORAL RESEARCH |

Citations: | 12 - 0 self |

### BibTeX

@ARTICLE{Scheines_thetetrad,

author = {Richard Scheines and Peter Spirtes and Clark Glymour and Christopher Meek and Thomas Richardson},

title = {The TETRAD Project: Constraint Based Aids to Causal Model Specification},

journal = {MULTIVARIATE BEHAVIORAL RESEARCH},

year = {},

volume = {33},

pages = {65--117}

}

### Years of Citing Articles

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### Abstract

### Citations

7072 |
Probabilistic reasoning in intelligent systems: Networks of plausible inference
- Pearl
- 1988
(Show Context)
Citation Context ...of these discoveries, offered in the hope that social and behavioral scientists will make more use of these methods and help to improve them. (Mathematical details and related results can be found in =-=Pearl, 1988-=-; Spirtes, et al., 1993; Scheines, et al., 1994). 1.5 Search Procedures Two approaches to RSEM specification have been pursued in the statistics and computer science literature. The first focuses on s... |

1079 | Bayesian method for the induction of probabilistic networks from data - Cooper, Herskovits - 1992 |

756 |
Structural Equations with Latent Variables
- Bollen
- 1989
(Show Context)
Citation Context ...ribe are very general and apply to models of categorical as well as continuous data, but for the sake of concreteness we will illustrate them with linear structural equation models (hereafter, SEMs) (=-=Bollen, 1989-=-; James, Mulaik, and Brett, 1982). SEMs include linear regression models (Weisberg, 1985), path analytic models (Wright, 1934), factor analytic models (Lawley & Maxwell, 1971), panel models (Blalock, ... |

497 |
Causation, Prediction and Search
- Spirtes, Glymour, et al.
- 2000
(Show Context)
Citation Context ...directed to Richard Scheines, Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213. E-mail: RS2L@andrew.cmu.edu.the effects of adopting different policies (Strotz & Wold, 1960; =-=Spirtes, et al., 1993-=-), the great bulk of theoretical attention on statistical causal models has been devoted to estimating their parameters, to developing statistics for testing individual parameters and overall model fi... |

391 |
Structural equation modeling in practice: A review and recommended two-step approach
- ANDERSON, GERBING
- 1988
(Show Context)
Citation Context ...pattern or a PAG. In these cases the Purify and MIMbuild modules of TETRAD II can help in RSEM specification. Purify helps locate unidimensional measurement models (Anderson, Gerbing, & Hunter, 1987; =-=Anderson & Gerbing, 1988-=-; Scheines, 1993). The basic idea of unidimensionality is that each indicator measures exactly one latent and all error terms are uncorrelated (the exact definition is more complicated, and presented ... |

238 | The ALARM Monitoring System: A Case Study with Two Probabilistic Inference Techniques for Belief Networks - Beinlich, Suernondt, et al. - 1989 |

216 |
Equivalence and synthesis of causal models
- Verma, Pearl
- 1990
(Show Context)
Citation Context ... common causes, then Build runs the PC algorithm, which is documented and traced in the appendix, and in (Spirtes, et. al, 1993; Scheines, et. al, 1994). The output of the PC algorithm is a pattern, (=-=Verma and Pearl, 1990-=-) which is a compact representation of a partial correlation (and covariance) equivalence class of RSEMs without correlated errors or latent common causes. A pattern contains a mixture of directed and... |

205 | A Theory of Inferred Causation
- Pearl, Verma
- 1991
(Show Context)
Citation Context ...r & Herskovits, 1992; Geiger, 1990; Geiger & Heckerman, 1991, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; =-=Pearl and Verma, 1991-=-; Robins, 1986; Spiegelhalter, 1986). 9 For example, the Bayesian Information Criterion (Raftery, 1993), or the posterior probability, (Geiger & Heckerman, 1994). 11satisfy a set of constraints judge... |

204 |
General intelligence, objectively determined and measured
- Spearman
- 1904
(Show Context)
Citation Context ...elations among the measured variables X = {X1, X2, X3, X4}, and there is no partial correlation involving only variables in X that is entailed to be zero by this SEM. The vanishing tetrad difference (=-=Spearman, 1904-=-), however, can provide extra information about the specification of this model. A tetrad difference involves two products of correlations, each of which involve the same four variables but in differe... |

182 | Theory refinement on Bayesian networks
- Buntine
- 1991
(Show Context)
Citation Context ...rtainty in Artificial Intelligence, Knowledge Discovery in Data Bases, and the bi-annual conference on Artificial Intelligence and Statistics. Examples of important papers in this tradition include: (=-=Buntine 1991-=-; Cooper & Herskovits, 1992; Geiger, 1990; Geiger & Heckerman, 1991, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter,... |

172 | Causal diagrams for empirical research - Pearl - 1995 |

164 |
Graphical models for associations between variables, some of which are qualitative and some quantitative’, Annals of Statistics
- Lauritzen, Wermuth
- 1989
(Show Context)
Citation Context ...mportant papers in this tradition include: (Buntine 1991; Cooper & Herskovits, 1992; Geiger, 1990; Geiger & Heckerman, 1991, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; =-=Lauritzen & Wermuth, 1984-=-; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 1986; Spiegelhalter, 1986). 9 For example, the Bayesian Information Criterion (Raftery, 1993), or the posterior probability, (Geige... |

154 |
A new approach to causal inference in mortality studies with sustained exposure periods applications to control of the healthy worker survivor effect. Mathematical Modeling 7
- Robins
- 1393
(Show Context)
Citation Context ...eiger, 1990; Geiger & Heckerman, 1991, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; =-=Robins, 1986-=-; Spiegelhalter, 1986). 9 For example, the Bayesian Information Criterion (Raftery, 1993), or the posterior probability, (Geiger & Heckerman, 1994). 11satisfy a set of constraints judged to hold in t... |

138 |
Lisrel 8: User’s Reference Guide
- Jöreskog, Sörbom
- 1997
(Show Context)
Citation Context ...ters and overall model fit (Bollen and Long, 1993), and to techniques for making minor respecifications of models that fit data poorly (Kaplan, 1990; Saris, et al., 1987; Sorbom, 1989; Bentler, 1986; =-=Jöreskog and Sörbom, 1993-=-). We believe the problem of model specification is in many respects analogous to the problem of parameter estimation, and that the same kind of rigor brought to the development and evaluation of algo... |

135 |
Tools for Statistical inference: methods for exploration of posterior distributions and likelihood functions, 3rd edition
- Tanner
- 1996
(Show Context)
Citation Context ...d model holds in the population, then asymptotically, as the sample size goes to infinity, the sampling distribution of θML goes to N(θpop, J -1 (θ)), where J(θ) is the Fisher information matrix (cf. =-=Tanner, 1993-=-, p. 16). So θML is a consistent estimator in the sense that as the sample size grows without bound the difference between θpop and θML will, with probability 1, converge to zero. The PC algorithm tak... |

122 |
Factor analysis as a statistical method
- Lawley, Maxwell
- 1971
(Show Context)
Citation Context ... equation models (hereafter, SEMs) (Bollen, 1989; James, Mulaik, and Brett, 1982). SEMs include linear regression models (Weisberg, 1985), path analytic models (Wright, 1934), factor analytic models (=-=Lawley & Maxwell, 1971-=-), panel models (Blalock, 1985; Wheaton, et al., 1977), simultaneous equation models (Goldberger & Duncan, 1973), MIMIC models (Bye, et al., 1985), and multiple indicator models (Sullivan, et. al., 19... |

112 |
Learning Gaussian networks
- Geiger, Heckerman
- 1994
(Show Context)
Citation Context ... 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 1986; Spiegelhalter, 1986). 9 For example, the Bayesian Information Criterion (Raftery, 1993), or the posterior probability, (=-=Geiger & Heckerman, 1994-=-). 11satisfy a set of constraints judged to hold in the population (e.g., Spirtes, et al., 1993). (See Richardson (1996) for a correct algorithm for searching for non-recursive SEMs without latent va... |

110 |
Identifying independence in Bayesian networks
- Geiger, Verma, et al.
- 1990
(Show Context)
Citation Context ...l conference on Artificial Intelligence and Statistics. Examples of important papers in this tradition include: (Buntine 1991; Cooper & Herskovits, 1992; Geiger, 1990; Geiger & Heckerman, 1991, 1994; =-=Geiger, Verma, and Pearl, 1990-=-, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 1986; Spiegelhalter, 1986). 9 For example, the Bayesian Information... |

105 | The chain graph Markov property - FRYDENBERG - 1990 |

82 |
Causal inference and causal explanation with background knowledge
- Meek
- 1995
(Show Context)
Citation Context ...single SEM, rather than an equivalence class of SEMs. Another search strategy based upon maximizing a score is to search not RSEMs themselves, but covariance equivalence classes of RSEMs (Spirtes and =-=Meek, 1995-=-). In contrast to a score maximization search, a constraint search uses some testing procedure for conditional independence, vanishing partial correlations, vanishing tetrad differences, or other cons... |

72 | Causal Ordering and Identifiability - Simon - 1953 |

71 |
Tests for Structural Equation Models
- Bollen, Long
- 1992
(Show Context)
Citation Context ...the great bulk of theoretical attention on statistical causal models has been devoted to estimating their parameters, to developing statistics for testing individual parameters and overall model fit (=-=Bollen and Long, 1993-=-), and to techniques for making minor respecifications of models that fit data poorly (Kaplan, 1990; Saris, et al., 1987; Sorbom, 1989; Bentler, 1986; Jöreskog and Sörbom, 1993). We believe the proble... |

70 | Discovering causal structure - Glymour, Scheines, et al. - 1987 |

56 | Learning Bayesian networks with discrete variables from data - Spirtes, Meek - 1995 |

40 | 1954) Spurious correlation: a causal interpretation - Simon |

39 | Directed cyclic graphical representations of feedback models - Spirtes - 1995 |

38 |
Recursive versus nonrecursive systems: an attempt at synthesis. Econometrica 1960;28:417–27
- Strotz, Wold
(Show Context)
Citation Context ...espondence should be directed to Richard Scheines, Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213. E-mail: RS2L@andrew.cmu.edu.the effects of adopting different policies (=-=Strotz & Wold, 1960-=-; Spirtes, et al., 1993), the great bulk of theoretical attention on statistical causal models has been devoted to estimating their parameters, to developing statistics for testing individual paramete... |

36 |
Probabilistic reasoning in predictive expert systems
- Spiegelhalter
- 1986
(Show Context)
Citation Context ...eiger & Heckerman, 1991, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 1986; =-=Spiegelhalter, 1986-=-). 9 For example, the Bayesian Information Criterion (Raftery, 1993), or the posterior probability, (Geiger & Heckerman, 1994). 11satisfy a set of constraints judged to hold in the population (e.g., ... |

34 | Issues in the comparative measurement of political democracy - Bollen - 1980 |

34 | Advances in probabilistic reasoning
- Geiger, Heckerman
- 1991
(Show Context)
Citation Context ... in Data Bases, and the bi-annual conference on Artificial Intelligence and Statistics. Examples of important papers in this tradition include: (Buntine 1991; Cooper & Herskovits, 1992; Geiger, 1990; =-=Geiger & Heckerman, 1991-=-, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 1986; Spiegelhalter, 1986). 9... |

31 | Bayesian model selection in structural equation models, in K.Bollen and J.Long, eds, ‘Testing Structural Equation Models
- Raftery
- 1993
(Show Context)
Citation Context ...; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 1986; Spiegelhalter, 1986). 9 For example, the Bayesian Information Criterion (=-=Raftery, 1993-=-), or the posterior probability, (Geiger & Heckerman, 1994). 11satisfy a set of constraints judged to hold in the population (e.g., Spirtes, et al., 1993). (See Richardson (1996) for a correct algori... |

30 |
Structural analysis of multivariate data: a review. Sociological Methodology
- Kiiveri, Speed
- 1982
(Show Context)
Citation Context ...artial Correlation Constraints In a SEM some partial correlations may be equal to zero for all values of the model’s free parameters (for which the partial correlation is defined). (See Blalock 1962; =-=Kiiveri & Speed, 1982-=-). In this case we will say that the SEM entails that the partial correlation is zero. 10 For example, in SEM S1 (Figure 1), where all of the error terms are uncorrelated, ρX1,X3.X2 = 0 for all values... |

29 |
Graphoids: a qualitative framework for probabilistic inference
- Geiger
- 1990
(Show Context)
Citation Context ...edge Discovery in Data Bases, and the bi-annual conference on Artificial Intelligence and Statistics. Examples of important papers in this tradition include: (Buntine 1991; Cooper & Herskovits, 1992; =-=Geiger, 1990-=-; Geiger & Heckerman, 1991, 1994; Geiger, Verma, and Pearl, 1990, Hand, 1993; Lauritzen, et al., 1990; Lauritzen & Wermuth, 1984; Pearl, 1988; Pearl & Dechter, 1989; Pearl and Verma, 1991; Robins, 198... |

28 | An algorithm for causal inference in the presence of latent variables and selection bias, in Cooper and Glymour - Spirtes, Meek, et al. - 1999 |

27 | Bayesian Estimation and Testing of Structural Equation Models - Scheines, Hoijtink, et al. - 1999 |

25 |
Causal analysis: Assumptions, models, and data
- James, Mulaik, et al.
- 1982
(Show Context)
Citation Context ...general and apply to models of categorical as well as continuous data, but for the sake of concreteness we will illustrate them with linear structural equation models (hereafter, SEMs) (Bollen, 1989; =-=James, Mulaik, and Brett, 1982-=-). SEMs include linear regression models (Weisberg, 1985), path analytic models (Wright, 1934), factor analytic models (Lawley & Maxwell, 1971), panel models (Blalock, 1985; Wheaton, et al., 1977), si... |

22 |
Applied linear regression. 2nd ed
- Weisberg
- 1985
(Show Context)
Citation Context ...ut for the sake of concreteness we will illustrate them with linear structural equation models (hereafter, SEMs) (Bollen, 1989; James, Mulaik, and Brett, 1982). SEMs include linear regression models (=-=Weisberg, 1985-=-), path analytic models (Wright, 1934), factor analytic models (Lawley & Maxwell, 1971), panel models (Blalock, 1985; Wheaton, et al., 1977), simultaneous equation models (Goldberger & Duncan, 1973), ... |

21 | Specification searches in covariance structure modeling - MacCallum - 1986 |

20 |
Identification, Equivalent Models and Computer Algebra
- Bekker, Merchens, et al.
- 1994
(Show Context)
Citation Context ...identifiable. When a parameter is not identifiable, it has more than one value for which the likelihood of the data is maximal given the model. Although many special cases have been solved (e.g., see =-=Becker, et al., 1994-=-), necessary and sufficient conditions for SEM parameter identifiability are not known. In the case of SEM specification procedures there is a problem analogous to parameter non-identifiability. There... |

17 |
Model modification
- Sörbom
- 1989
(Show Context)
Citation Context ...are restricted to searching a very restricted class of RSEMs. The “modification index” searches based on the Lagrange Multiplier statistic (Bentler, 1986; Kaplan, 1989, 1990; Jöreskog & Sörbom, 1993; =-=Sörbom, 1989-=-) in LISREL and EQS are restricted versions of this strategy. They typically begin with a given SEM M and perform a stepwise forward search (EQS can also perform a stepwise backward search). One diffi... |

12 |
The Robustness of LISREL against Small Sample Sizes in Factor Analysis Models
- Boomsma
- 1982
(Show Context)
Citation Context ...theory described above (θML ~ N(θpop, J -1 (θ))) as an estimate of the sampling distribution of θML. Second, we can approximate the sampling distribution of θML empirically by Monte Carlo techniques (=-=Boomsma, 1982-=-). We can do this by assuming Σ(θML) = Σ(θpop). We can then repeatedly sample from Σ(θpop), and calculate the ML estimate for each sample (Figure 6). Although for small N the sampling distribution of ... |

12 | Dependence, political exclusion, and government repression: Some cross-national evidence - Timberlake, Williams - 1984 |

11 |
On the assessment of unidimensional measurement: Internal and external consistency, and overall consistency criteria
- Anderson, Gerbing, et al.
- 1987
(Show Context)
Citation Context ...letely undirected, whether it is a pattern or a PAG. In these cases the Purify and MIMbuild modules of TETRAD II can help in RSEM specification. Purify helps locate unidimensional measurement models (=-=Anderson, Gerbing, & Hunter, 1987-=-; Anderson & Gerbing, 1988; Scheines, 1993). The basic idea of unidimensionality is that each indicator measures exactly one latent and all error terms are uncorrelated (the exact definition is more c... |

11 | An Evaluation of Machine-Learning Methods for Predicting Pneumonia Mortality - Cooper, Aliferis, et al. - 1995 |

10 | Confirmatory tetrad analysis - Bollen, Ting - 1993 |

9 |
Evaluating and modifying covariance structure models: A review and recommendation
- Kaplan
- 1990
(Show Context)
Citation Context ...rameters, to developing statistics for testing individual parameters and overall model fit (Bollen and Long, 1993), and to techniques for making minor respecifications of models that fit data poorly (=-=Kaplan, 1990-=-; Saris, et al., 1987; Sorbom, 1989; Bentler, 1986; Jöreskog and Sörbom, 1993). We believe the problem of model specification is in many respects analogous to the problem of parameter estimation, and ... |

8 | R.W.: Selecting models from data - Cheeseman, Oldfors - 1994 |

8 | Using dseparation to calculate zero partial correlations in linear models with correlated errors - Spirtes, Richardson, et al. - 1996 |

8 | The dimensionality of mixed ancestral graphs - Spirtes, Richardson, et al. - 1997 |

7 | The impact of specification error on the estimation, testing, and improvement of structural equation models - Kaplan - 1988 |