Application of Bayesian Nonlinear Structural Equation Modeling for Exploring Relationships on Residential Satisfaction in Turkey

We introduce a Bayesian Nonlinear Structural Equation Modeling framework to explore the relationships on residential satisfaction in Turkey. The structural equation model (SEM) is a multivariate statistical method that allows assessment of relationships between observed and latent variables. SEM includes methods for regression, path analysis and factor analysis. SEM is widely used to examine the inter-relationships between latent and observed variables in psychological, social and medical research. Generally, linear relationships between observed and latent variables are modeled in SEM. Recent years, modeling of nonlinear relationship in SEM get attract great attention in the literature. A Bayesian approach to SEM may enable models that reflect hypotheses based on complex theory. The Bayesian approach analyses a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. In this study we make Bayesian non-linear structural equation modeling analysis for Residential Satisfaction

A flexible approach to parametric inference in nonlinear time series models

Many structural break and regime-switching models have been used with macroeconomic and …nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speci…cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use arti…cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth

A flexible approach to parametric inference in nonlinear and time varying time series models

Many structural break and regime-switching models have been used with macroeconomic and …nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speci…cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use arti…cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth

Factor analyses of the Hospital Anxiety and Depression Scale: a Bayesian structural equation modeling approach

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How Subdimensions of Salience Influence Each Other. Comparing Models Based on Empirical Data

Theories about salience of landmarks in GIScience have been evolving for about 15 years. This paper empirically analyses hypotheses about the way different subdimensions (visual, structural, and cognitive aspects, as well as prototypicality and visibility in advance) of salience have an impact on each other. The analysis is based on empirical data acquired by means of an in-situ survey (360 objects, 112 participants). It consists of two parts: First, a theory-based structural model is assessed using variance-based Structural Equation Modeling. The results achieved are, second, corroborated by a data-driven approach, i.e. a tree-augmented naive Bayesian network is learned. This network is used as a structural model input for further analyses. The results clearly indicate that the subdimensions of salience influence each other

A review of R-packages for random-intercept probit regression in small clusters

Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision

Regularizing Structural Equation Models via the Lasso : Generalizability and Reproducibility Issues

학위논문 (석사)-- 서울대학교 대학원 : 심리학과 계량심리 전공, 2016. 8. 김청택.Generalizability and Reproducibility of research have become one of the main topics in current psychology. Previous discussions on the issue have focused on the Experimental/Procedural aspect such as incentive structure for researchers, violation in conducting an experiment, selective reporting, etc. However, sometimes statistical methods which are widely used in psychology have properties that undermine the generalizabilty of research results. The present thesis approaches the reproducibility problem based on this Analytical/Statistical aspect. For this purpose, we studied a method for improving the Structural Equation Modeling(SEM), one of dominant statistical models in psychology. The main focus of this study is implementing L1-regularization, or Lasso, to SEM. With this method, the result will enjoy less variability of estimation than the existing Maximum Likelihood method. First of all, the present thesis discusses some indices including Overall Discrepancy(OD) and Mean Squared Error(MSE) as criteria which indicate the generalizability and reproducibility of analysis results. Bayesian Lasso SEM, one of the previous attempts, is also covered with some fundamental issues. Furthermore, an algorithm for regularizing SEM via the Lasso is derived and examined by several simulation studies. The study is carried out using Factor Analysis Model and Structural Equation Modeling, while adding several misspecified parameters. The purpose of this approach is to test Lasso SEMs complete shrinkage ability, which is able to detect and remove unnecessary parameters from the original model so that the method yields the result close to the true population-generating process. It is also investigated whether Lasso can improve generalizability and reproducibility by observing and comparing OD and MSE. The simulation deals with various conditions including model error, sample sizes, and magnitudes of covariance matrix, in order to examine in which condition Lasso SEM yields better results than the Maximum Likelihood Estimation. The result reveals that Lasso SEM works well in various conditionsit improves generalizability indices, detects and removes misspecified parameters in the original model. However, the performance depends on the conditions, which implies that the Lasso SEM should be applied with careful scrutiny on characteristics of practical data. Especially, the model error, one of the component affecting the data-generating process, has turned out to be the most influential factor that hinders proper function of the Lasso SEM. We suggest modifying the optimization of Lasso SEM, which is currently rely upon the value of OD, or its cross-validation estimate. The improvement can be achieved by replacing criteria or objective function in the optimization procedure. This will minimize problems including those generated from the model error. A correlation analysis shows that Sample Discrepancy, which is a criterion of the existing estimation method, and goodness of model fit indices widely used in SEM have considerably low correlations with OD. This outcome implies the SEM result obtained by the original method may be hard to be generalized to other independent samples including the future data, and the phenomenon that researchers are interested in.Introduction 1 Reproducibility Issues in Psychological Researches 1 Analytical/Statistical Approach to Reproducibility Issues 3 Generalizability in Structural Equation Modeling 7 Thesis Organization 11 Chapter 1 Structural Equation Modeling 13 1.1 Introduction to SEM 13 1.1.1 Measurement Model Part 13 1.1.2 Structural Model Part 16 1.2 Estimation of SEM 20 1.3 Fit Indices for Model Evaluation 24 1.4 Reproducibility and Generalizability Issues in SEM 32 Chapter 2 Regularization 41 2.1 Bias, Variance and MSE 41 2.2 Shrinkage Estimation 45 2.3 Regularization 47 2.3.1 Ridge (Hoerl & Kennard, 1970a, b) 50 2.3.2 Lasso (Tibshirani, 1996) 52 2.3.3 Elastic Net (Zou & Hastie, 2005) 54 2.4 The Connection between Regularization and Bayesian Analysis 57 2.4.1 Bayesian Linear Regression Analysis 57 2.4.2 BLasso: Bayesian Lasso 59 2.5 Regularization and Structural Equation Modeling 64 2.6 Some optimization methods for Lasso 71 2.6.1 LARS Algorithm 71 2.6.2 MM-Algorithm 76 Chapter 3 Bayesian Structural Equation Modeling 81 3.1 Basic Approach 81 3.1.1 Bayesian Factor Analysis 82 3.1.2 Bayesian Structural Equation Modeling 84 3.2 Bayesian Regularization for SEM 86 3.2.1 Bayesian Lasso for Factor Analysis 86 3.2.2 Bayesian Lasso for Structural Equation Modeling 88 3.3 Limitation 90 Chapter 4 Implementing Lasso to Structural Equation Modeling 95 4.1 Likelihood Functions in SEM 96 4.1.1 Measurement Model Part 96 4.1.2 Structural Model Part 98 4.2 Double EM-algorithm for L1-Regularized SEM 103 4.2.1 E-step : Compute Conditional Expectations of Likelihood Functions 105 4.2.2 M-step : Minimizing the target function 110 4.2.3 Optimization Methods for M-step 113 4.3 Further Issues in fitting Lasso SEM 121 4.3.1 Rescaling Issue for the Measurement Model 121 4.3.2 A Standardization Issue in M-step 125 4.3.3 Tuning Methods for L1-Regularized SEM 129 4.4 Result Algorithm for Lasso SEM 132 Chapter 5 Simulation Study : Method 135 5.1 Purposes of Research 135 5.2 Generating Population 137 5.3 Research Models 141 5.4 Research Conditions 149 5.5 Indices in Simulation Study 159 5.6 Flow of Simulation 162 Chapter 6 Simulation Study : Result 165 6.1 Research 1: Factor Analysis Model 165 6.2 Research 2: Structural Equation Model 189 6.3 Research 3: Additional Analyses 207 6.3.1 DA and Bias Analysis 207 6.3.2 Correlation Analysis of Fit Indices 214 Chapter 7 Discussion 221 References 239 Appendix 249 Appendix A : Result Tables 249 A1. Result Tables for Lasso 249 A2. Result Tables for BLasso 262 Appendix B : Standardization of SEM 275 B1. Factor Analysis Model 275 B2. Structural Equation Model 276 Appendix C : Some Derivations 277 C1. Derivation of Latent Variable Covariance Matrix 277 C2. Derivations for Some Posterior Distributions of BLasso SEM 278 Appendix D : R functions for Lasso SEM 282 Appendix E : Generating Population in SEM 290 초록 297Maste