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A Criterion for Parameter Identification in Structural Equation Models
, 2007
"... This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper establishes a sufficient criterion for identifying individual causal effects and provides a procedure computing identified causal effects in terms of observed covariance m ..."
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This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper establishes a sufficient criterion for identifying individual causal effects and provides a procedure computing identified causal effects in terms of observed covariance matrix.
Local Markov property for models satisfying composition axiom
 In Proceedings of the 21th Annual Conference on Uncertainty in Artificial Intelligence (UAI05
, 2005
"... The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bidirected edges in the graph, the local Markov property may invoke exponential number of conditional independencies. This paper shows that the ..."
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The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bidirected edges in the graph, the local Markov property may invoke exponential number of conditional independencies. This paper shows that the number of conditional independence relations required may be reduced if the probability distributions satisfy the composition axiom. In certain types of graphs, only linear number of conditional independencies are required. The result has applications in testing linear structural equation models with correlated errors. 1
Markov Properties for Linear Causal Models with Correlated Errors Markov Properties for Linear Causal Models with Correlated Errors
"... A linear causal model with correlated errors, represented by a DAG with bidirected edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the dseparation criterion, the set of all conditional independence relations holding ..."
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A linear causal model with correlated errors, represented by a DAG with bidirected edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the dseparation criterion, the set of all conditional independence relations holding in any model associated with a graph. A local Markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global Markov property. For DAGs with bidirected edges associated with arbitrary probability distributions, a local Markov property is given in Richardson (2003) which may invoke an exponential number of conditional independencies. In this paper, we show that for a class of linear structural equation models with correlated errors the local Markov property will invoke only linear number of conditional independence relations. For general linear models, we provide a local Markov property that often invokes far fewer conditional independencies than that in Richardson (2003). The results have applications in testing linear structural equation models with correlated errors.
On the identification of a class of linear models
 In Proceedings of the AAAI
, 2007
"... This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper provides a procedure for solving the identification problem in a special class of models. ..."
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This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper provides a procedure for solving the identification problem in a special class of models.
Identification and likelihood inference for recursive linear models with correlated errors
, 2007
"... In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by recursive systems of linear structural equations. Such models appear in particular in seemingly unrelated regressions, structural equation modelling, simultaneous equati ..."
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In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by recursive systems of linear structural equations. Such models appear in particular in seemingly unrelated regressions, structural equation modelling, simultaneous equation systems, and in Gaussian graphical modelling. We show that recursive linear models that are ‘bowfree’ are wellbehaved statistical models, namely, they are everywhere identifiable and form curved exponential families. Here, ‘bowfree ’ refers to models satisfying the condition that if a variable x occurs in the structural equation for y, then the errors for x and y are uncorrelated. For the computation of maximum likelihood estimates in ‘bowfree ’ recursive linear models we introduce the Residual Iterative Conditional Fitting (RICF) algorithm. Compared to existing algorithms RICF is easily implemented requiring only least squares computations, has clear convergence properties, and finds parameter estimates in closed form whenever possible. 1
The Limits of Causal Inference from Observational Data
"... Introduction The following quotation from Rosenbaum (1995) expresses a commonly held view about the problem of potential confounders, and how they can be dealt with. (We will take a "confounder" of treatment and response to be a variable that is a cause of both treatment and response.) An observat ..."
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Introduction The following quotation from Rosenbaum (1995) expresses a commonly held view about the problem of potential confounders, and how they can be dealt with. (We will take a "confounder" of treatment and response to be a variable that is a cause of both treatment and response.) An observational study is an empirical investigation of treatments, policies, or exposures and the effect they cause, but it differs from an experiment in that the investigator cannot control the assignment of treatments to subjects. ... Analytical adjustments are widely used in observational studies to remove overt biases, that is, differences between treated and control groups, present before treatment, that are visible in the data at hand. ... If treated and control groups differed before treatment in ways not recorded, there would be a hidden bias. ... sensitivity analyses ... ask how the findings of a study might be altered by hidden biases of various magnitudes. It turns out that
Parameter Identification in a Class of Linear Structural Equation Models
"... Linear causal models known as structural equation models (SEMs) are widely used for data analysis in the social sciences, economics, and artificial intelligence, in which random variables are assumed to be continuous and normally distributed. This paper deals with one fundamental problem in the appl ..."
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Linear causal models known as structural equation models (SEMs) are widely used for data analysis in the social sciences, economics, and artificial intelligence, in which random variables are assumed to be continuous and normally distributed. This paper deals with one fundamental problem in the applications of SEMs – parameter identification. The paper uses the graphical models approach and provides a procedure for solving the identification problem in a special class of SEMs. 1
Graphical Gaussian Modelling of Multivariate Time Series with Latent Variables
"... In time series analysis, inference about causeeffect relationships among multiple times series is commonly based on the concept of Granger causality, which exploits temporal structure to achieve causal ordering of dependent variables. One major problem in the application of Granger causality for the ..."
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In time series analysis, inference about causeeffect relationships among multiple times series is commonly based on the concept of Granger causality, which exploits temporal structure to achieve causal ordering of dependent variables. One major problem in the application of Granger causality for the identification of causal relationships is the possible presence of latent variables that affect the measured components and thus lead to socalled spurious causalities. In this paper, we describe a new graphical approach for modelling the dependence structure of multivariate stationary time series that are affected by latent variables. To this end, we introduce dynamic maximal ancestral graphs (dMAGs), in which each time series is represented by a single vertex. For Gaussian processes, this approach leads to vector autoregressive models with errors that are not independent but correlated according to the dashed edges in the graph. We discuss identifiability of the parameters and show that these models can be viewed as graphical ARMA models that satisfy the Granger causality restrictions encoded by the associated dynamic maximal ancestral graph. 1