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Generalized spatial structural equation models
 Biostatistics
, 2005
"... ow nloaded from It is common in public health research to have high dimensional, multivariate, spatiallyreferenced data representing summaries of geographic regions. Often it is desirable to examine relationships among these variables both within and across regions. An existing modeling technique c ..."
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ow nloaded from It is common in public health research to have high dimensional, multivariate, spatiallyreferenced data representing summaries of geographic regions. Often it is desirable to examine relationships among these variables both within and across regions. An existing modeling technique called spatial factor analysis has been used and assumes that a common spatial factor underlies all the variables and causes them to be related to one another. An extension of this technique considers that there may be more than one underlying factor, and that relationships among the underlying latent variables are of primary interest. However, due to the complicated nature of the covariance structure of this type of data, existing methods are not satisfactory. We thus propose a generalized spatial structural equation model (GSSEM). In the rst level of the model, we assume the observed variables are related to particular underlying factors. In the second level of the model, we use the structural equation method to model the relationship among the underlying factors and use parametric spatial distributions on the covariance structure of the underlying factors. We apply the model to countylevel cancer mortality and census summary data for Minnesota, including socioeconomic status and access to public utilities.
Nonlinear and Nonparametric Regression and Instrumental
 Variables,Journal of the American Statistical Association
, 2004
"... We consider regression when the predictor is measured with error and an instrumental variable (IV) is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error mod ..."
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We consider regression when the predictor is measured with error and an instrumental variable (IV) is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identifiability. In addition, we exploit a characterization of the IV estimator as a classical “correction for attenuation ” method based on a particular estimate of the variance of the measurement error. This estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution. The functional estimators uses simulation extrapolation or deconvolution kernels and the structural method uses Bayesian Markov chain Monte Carlo. The Bayesian estimator is found to significantly outperform the functional approach.
Quasi Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects
"... The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficie ..."
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Cited by 14 (0 self)
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The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficient methods is complicated by the fact that a nonlinear model structure implies specifically nonnormal multivariate distributions for the indicator variables. In this paper, nonlinear structural equation models with quadratic forms are introduced and a new QuasiMaximum Likelihood method for simultaneous estimation of model parameters is developed with the focus on statistical efficiency and computational practicability. The QuasiML method is based on an approximation of the nonnormal density function of the joint indicator vector by a product of a normal and a conditionally normal density. The results of MonteCarlo studies for the new QuasiML method indicate that the parameter estimation is almost as efficient as ML estimation, whereas ML estimation is only computationally practical for elementary models. Also, the QuasiML method outperforms other currently available methods with respect to efficiency. It is demonstrated in a MonteCarlo study that the QuasiML method permits computationally feasible and very efficient analysis of models with multiple latent nonlinear effects. Finally, the applicability of the QuasiML method is illustrated by an empirical example of an aging study in psychology. Key words: structural equation modeling, quadratic form of normal variates, latent interaction effect, moderator effect, QuasiML estimation, variance function model. 1 1.
Automatic discovery of latent variable models
 Machine Learning Dpt., CMU
, 2005
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Cited by 9 (4 self)
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representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.
Latent variable modelling: A survey
 Scandinavian Journal of Statistics
"... ABSTRACT. Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of ‘traditional ’ latent variable models include latent class models, item–response models, common factor mode ..."
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Cited by 8 (2 self)
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ABSTRACT. Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of ‘traditional ’ latent variable models include latent class models, item–response models, common factor models, structural equation models, mixed or random effects models and covariate measurement error models. Although latent variables have widely different interpretations in different settings, the models have a very similar mathematical structure. This has been the impetus for the formulation of general modelling frameworks which accommodate a wide range of models. Recent developments include multilevel structural equation models with both continuous and discrete latent variables, multiprocess models and nonlinear latent variable models.
Simple, Efficient and Distributionfree Approach to Interaction Effects in Complex Structural Equation Models
"... Abstract. Structural equation models with mean structure and nonlinear constraints are the most frequent choice for estimating interaction effects when measurement errors are present. This article proposes eliminating the mean structure and all the constraints but one, which leads to a more easily ..."
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Abstract. Structural equation models with mean structure and nonlinear constraints are the most frequent choice for estimating interaction effects when measurement errors are present. This article proposes eliminating the mean structure and all the constraints but one, which leads to a more easily handled model that is more robust to nonnormality and more general as it can accommodate endogenous interactions and thus indirect effects. Our approach is compared to other approaches found in the literature with a Monte Carlo simulation and is found to be equally efficient under normality and less biased under nonnormality. An empirical illustration is included. Key words: Interaction effects; structural equation models; indirect effects; nonlinear constraints; mean structure; normality assumption. 1.
Isotone additive latent variable models
, 2011
"... additive latent variable models ..."
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Joint Statistical Meetings Business & Economic Statistics Section PSEUDO LIKELIHOOD APPROACH FOR NONLINEAR AND NONNORMAL STRUCTURAL EQUATION ANALYSIS
"... standard error estimation, deconvolution, bootstrap, latent variable modeling. Structural equation analysis is widely used in economics and social sciences. The model considered in this paper consists of two parts; a linear measurement model relating observed measurements to underlying latent variab ..."
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standard error estimation, deconvolution, bootstrap, latent variable modeling. Structural equation analysis is widely used in economics and social sciences. The model considered in this paper consists of two parts; a linear measurement model relating observed measurements to underlying latent variables, and a nonlinear structural model representing relationships among the latent variables. When the distributional form of the latent variables is unspecified, a pseudo likelihood approach based on a hypothetical normal mixture assumption is proposed. To obtain the pseudo likelihood parameter estimates, the Monte Carlo EM algorithm is developed. Standard error estimates for the estimated structural parameters are obtained combining an empirical observed information estimates and a bootstrap estimated covariance matrix for the nuisance parameters. Simulation studies are reported. 1.
IN STRUCTURAL EQUATION MODELING: A COMPARISON OF ALTERNATIVE ESTIMATION APPROACHES
"... The estimation of nonlinear relations between variables is an important concern in different areas of the social and behavioral sciences. Several theories do not only incorporate linear but also nonlinear relations between variables. The mostoften investigated nonlinear effects are interaction and ..."
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The estimation of nonlinear relations between variables is an important concern in different areas of the social and behavioral sciences. Several theories do not only incorporate linear but also nonlinear relations between variables. The mostoften investigated nonlinear effects are interaction and quadratic effects.