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Sik-yum Lee - One of the best experts on this subject based on the ideXlab platform.
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Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models.
Structural Equation Modeling, 2011Co-Authors: Xin Yuan Song, Ye-mao Xia, Junhao Pan, Sik-yum LeeAbstract:Structural Equation Models have wide applications. One of the most important issues in analyzing Structural Equation Models is model comparison. This article proposes a Bayesian model comparison statistic, namely the L ν-measure for both semiparametric and parametric Structural Equation Models. For illustration purposes, we consider a Bayesian semiparametric approach for estimation and model comparison in the context of Structural Equation Models with fixed covariates. A finite dimensional Dirichlet process is used to model the crucial latent variables, and a blocked Gibbs sampler is implemented for estimation. Empirical performance of the L ν-measure is evaluated through a simulation study. Results obtained indicate that the L ν-measure, which additionally requires very minor computational effort, gives satisfactory performance. Moreover, the methodologies are demonstrated through an example with a real data set on kidney disease. Finally, the application of the L ν-measure to Bayesian semiparametric non...
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A Robust Bayesian Approach for Structural Equation Models with Missing Data
Psychometrika, 2008Co-Authors: Sik-yum Lee, Ye-mao XiaAbstract:In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing Structural Equation Models with complete or missing data. In the context of a nonlinear Structural Equation model with fixed covariates, robust Bayesian methods are developed for estimation and model comparison. Results from simulation studies are reported to reveal the characteristics of estimation. The methods are illustrated by using a real data set obtained from diabetes patients.
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a unified maximum likelihood approach for analyzing Structural Equation Models with missing nonstandard data
Sociological Methods & Research, 2007Co-Authors: Sik-yum Lee, Xin Yuan SongAbstract:In this article, the authors present a unified approach for maximum likelihood analysis of Structural Equation Models that involve subtle model formulations and nonstandard data structures. Based on the idea of data augmentation, they describe a generic Monte Carlo expectation-maximization algorithm for estimation. They propose path sampling for computing the observed data likelihood functions that usually involve complicated integrals and show how to apply this method for computing the Bayesian information criterion for model comparison. An application of the proposed unified approach to a two-level nonlinear Structural Equation model with missing continuous and ordered categorical data is presented. An illustrative example with a real data set is given.
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a maximum likelihood approach for multisample nonlinear Structural Equation Models with missing continuous and dichotomous data
Structural Equation Modeling, 2006Co-Authors: Xin Yuan Song, Sik-yum LeeAbstract:Structural Equation Models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and Models with a linear Structural Equation. However, discrete nonnormal data and missing data are rather common, and sometimes it is necessary to incorporate nonlinear Structural Equations for assessing the impact of nonlinear terms of the exogenous latent variables to the endogenous latent variables. Moreover, to study the behaviors of different populations, it is necessary to extend from a single sample model to a multisample model. In this article, a maximum likelihood (ML) approach is developed for analyzing a multisample nonlinear Structural Equation model, in the context of mixed continuous and dichotomous data that involve data that are missing at random. The article demonstrates the newly developed method...
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maximum likelihood analysis of nonlinear Structural Equation Models with dichotomous variables
Multivariate Behavioral Research, 2005Co-Authors: Xin Yuan Song, Sik-yum LeeAbstract:In this article, a maximum likelihood approach is developed to analyze Structural Equation Models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the Structural Equation in the model is defined by a nonlinear function. The basic idea of the development is to augment the observed dichotomous data with the hypothetical missing data that involve the latent underlying continuous measurements and the latent variables in the model. An EM algorithm is implemented. The conditional expectation in the E-step is approximated via observations simulated from the appropriate conditional distributions by a Metropolis-Hastings algorithm within the Gibbs sampler, whilst the M-step is completed by conditional maximization. Convergence is monitored by bridge sampling. Standard errors are also obtained. Results from a simulation study and a real example are presented to illustrate the methodology.
Xin Yuan Song - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Quantile Structural Equation Models
Structural Equation Modeling, 2015Co-Authors: Yifan Wang, Xiang-nan Feng, Xin Yuan SongAbstract:Structural Equation modeling is a common multivariate technique for the assessment of the interrelationships among latent variables. Structural Equation Models have been extensively applied to behavioral, medical, and social sciences. Basic Structural Equation Models consist of a measurement Equation for characterizing latent variables through multiple observed variables and a mean regression-type Structural Equation for investigating how explanatory latent variables influence outcomes of interest. However, the conventional Structural Equation does not provide a comprehensive analysis of the relationship between latent variables. In this article, we introduce the quantile regression method into Structural Equation Models to assess the conditional quantile of the outcome latent variable given the explanatory latent variables and covariates. The estimation is conducted in a Bayesian framework with Markov Chain Monte Carlo algorithm. The posterior inference is performed with the help of asymmetric Laplace di...
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Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models.
Structural Equation Modeling, 2011Co-Authors: Xin Yuan Song, Ye-mao Xia, Junhao Pan, Sik-yum LeeAbstract:Structural Equation Models have wide applications. One of the most important issues in analyzing Structural Equation Models is model comparison. This article proposes a Bayesian model comparison statistic, namely the L ν-measure for both semiparametric and parametric Structural Equation Models. For illustration purposes, we consider a Bayesian semiparametric approach for estimation and model comparison in the context of Structural Equation Models with fixed covariates. A finite dimensional Dirichlet process is used to model the crucial latent variables, and a blocked Gibbs sampler is implemented for estimation. Empirical performance of the L ν-measure is evaluated through a simulation study. Results obtained indicate that the L ν-measure, which additionally requires very minor computational effort, gives satisfactory performance. Moreover, the methodologies are demonstrated through an example with a real data set on kidney disease. Finally, the application of the L ν-measure to Bayesian semiparametric non...
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Structural Equation Models
International Encyclopedia of Education, 2010Co-Authors: Sungyoung Lee, Xin Yuan SongAbstract:In this article, we introduce Structural Equation Models which are powerful multivariate tools in analyzing interrelationships among observed and latent variables. Useful Models, including the standard linear model and its generalizations such as the nonlinear Models, multilevel Models, and Models with ordered categorical data are discussed. In addition, the maximum likelihood approach, a Bayesian approach for estimation and model comparison, as well as the freely available software WinBUGS for obtaining the Bayesian results are described.
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a unified maximum likelihood approach for analyzing Structural Equation Models with missing nonstandard data
Sociological Methods & Research, 2007Co-Authors: Sik-yum Lee, Xin Yuan SongAbstract:In this article, the authors present a unified approach for maximum likelihood analysis of Structural Equation Models that involve subtle model formulations and nonstandard data structures. Based on the idea of data augmentation, they describe a generic Monte Carlo expectation-maximization algorithm for estimation. They propose path sampling for computing the observed data likelihood functions that usually involve complicated integrals and show how to apply this method for computing the Bayesian information criterion for model comparison. An application of the proposed unified approach to a two-level nonlinear Structural Equation model with missing continuous and ordered categorical data is presented. An illustrative example with a real data set is given.
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a maximum likelihood approach for multisample nonlinear Structural Equation Models with missing continuous and dichotomous data
Structural Equation Modeling, 2006Co-Authors: Xin Yuan Song, Sik-yum LeeAbstract:Structural Equation Models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and Models with a linear Structural Equation. However, discrete nonnormal data and missing data are rather common, and sometimes it is necessary to incorporate nonlinear Structural Equations for assessing the impact of nonlinear terms of the exogenous latent variables to the endogenous latent variables. Moreover, to study the behaviors of different populations, it is necessary to extend from a single sample model to a multisample model. In this article, a maximum likelihood (ML) approach is developed for analyzing a multisample nonlinear Structural Equation model, in the context of mixed continuous and dichotomous data that involve data that are missing at random. The article demonstrates the newly developed method...
Yutaka Kano - One of the best experts on this subject based on the ideXlab platform.
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Identifiability of nonrecursive Structural Equation Models
Statistics & Probability Letters, 2017Co-Authors: Mario Nagase, Yutaka KanoAbstract:An approach to studying reciprocal-effects in a cross-sectional data is to apply nonrecursive Structural Equation Models. This article takes a theoretical approach to study the identifiability problem of reciprocal-effect Models. Identifiability conditions are presented under a variety of settings.
Bernhard Scholkopf - One of the best experts on this subject based on the ideXlab platform.
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causal consistency of Structural Equation Models
Uncertainty in Artificial Intelligence, 2017Co-Authors: Paul K Rubenstein, Sebastian Weichwald, Stephan Bongers, Joris M Mooij, Dominik Janzing, Moritz Grossewentrup, Bernhard ScholkopfAbstract:Complex systems can be modelled at various levels of detail. Ideally, causal Models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) Models with large numbers of variables versus Models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level Models versus macro-level Models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series Models versus Models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.
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causal inference on time series using restricted Structural Equation Models
Neural Information Processing Systems, 2013Co-Authors: Jonas Peters, Dominik Janzing, Bernhard ScholkopfAbstract:Causal inference uses observational data to infer the causal structure of the data generating system. We study a class of restricted Structural Equation Models for time series that we call Time Series Models with Independent Noise (TiMINo). These Models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. This work contains two main contributions: (l) Theoretical: By restricting the model class (e.g. to additive noise) we provide general identifiability results. They cover lagged and instantaneous effects that can be nonlinear and unfaithful, and non-instantaneous feedbacks between the time series. (2) Practical: If there are no feedback loops between time series, we propose an algorithm based on non-linear independence tests of time series. We show empirically that when the data are causally insufficient or the model is misspecified, the method avoids incorrect answers. We extend the theoretical and the algorithmic part to situations in which the time series have been measured with different time delays. TiMINo is applied to artificial and real data and code is provided.
Tenko Raykov - One of the best experts on this subject based on the ideXlab platform.
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On measures of explained variance in nonrecursive Structural Equation Models.
Journal of Applied Psychology, 2000Co-Authors: Peter M. Bentler, Tenko RaykovAbstract:: Whereas measures of explained variance in a regression and an Equation of a recursive Structural Equation model can be simply summarized by a standard R2 measure, this is not possible in nonrecursive Models in which there are reciprocal interdependencies among variables. This article provides a general approach to defining variance explained in latent dependent variables of nonrecursive linear Structural Equation Models. A new method of its estimation, easily implemented in EQS or LISREL and available in EQS 6, is described and illustrated.
