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1

Lee, Sik-Yum, and Xin-Yuan Song. "Bayesian structural equation model." Wiley Interdisciplinary Reviews: Computational Statistics 6, no. 4 (June 16, 2014): 276–87. http://dx.doi.org/10.1002/wics.1311.

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Wang, Yifan, Xiang-Nan Feng, and Xin-Yuan Song. "Bayesian Quantile Structural Equation Models." Structural Equation Modeling: A Multidisciplinary Journal 23, no. 2 (July 25, 2015): 246–58. http://dx.doi.org/10.1080/10705511.2015.1033057.

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Song, Xin-Yuan, Ye-Mao Xia, Jun-Hao Pan, and Sik-Yum Lee. "Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models." Structural Equation Modeling: A Multidisciplinary Journal 18, no. 1 (January 13, 2011): 55–72. http://dx.doi.org/10.1080/10705511.2011.532720.

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Feng, Xiang-Nan, Yifan Wang, Bin Lu, and Xin-Yuan Song. "Bayesian regularized quantile structural equation models." Journal of Multivariate Analysis 154 (February 2017): 234–48. http://dx.doi.org/10.1016/j.jmva.2016.11.002.

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Stenling, Andreas, Andreas Ivarsson, Urban Johnson, and Magnus Lindwall. "Bayesian Structural Equation Modeling in Sport and Exercise Psychology." Journal of Sport and Exercise Psychology 37, no. 4 (August 2015): 410–20. http://dx.doi.org/10.1123/jsep.2014-0330.

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Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.
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Jiang, Xiaomo, and Sankaran Mahadevan. "Bayesian structural equation modeling method for hierarchical model validation." Reliability Engineering & System Safety 94, no. 4 (April 2009): 796–809. http://dx.doi.org/10.1016/j.ress.2008.08.008.

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7

Levy, Roy. "Bayesian Data-Model Fit Assessment for Structural Equation Modeling." Structural Equation Modeling: A Multidisciplinary Journal 18, no. 4 (October 5, 2011): 663–85. http://dx.doi.org/10.1080/10705511.2011.607723.

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Lee, Sik-Yum, and Jian-Qing Shi. "Bayesian Analysis of Structural Equation Model With Fixed Covariates." Structural Equation Modeling: A Multidisciplinary Journal 7, no. 3 (July 2000): 411–30. http://dx.doi.org/10.1207/s15328007sem0703_3.

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Guo, Ruixin, Hongtu Zhu, Sy-Miin Chow, and Joseph G. Ibrahim. "Bayesian Lasso for Semiparametric Structural Equation Models." Biometrics 68, no. 2 (February 29, 2012): 567–77. http://dx.doi.org/10.1111/j.1541-0420.2012.01751.x.

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Chen, Ji, Pengfei Liu, and Xinyuan Song. "Bayesian diagnostics of transformation structural equation models." Computational Statistics & Data Analysis 68 (December 2013): 111–28. http://dx.doi.org/10.1016/j.csda.2013.06.012.

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Yang, Seoeun. "Bayesian Semiparametric Structural Equation Model with Dirichlet Process and Splines." Korean Data Analysis Society 21, no. 6 (December 31, 2019): 2829–45. http://dx.doi.org/10.37727/jkdas.2019.21.6.2829.

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Akbarzadeh, Mahdi, Abbas Moghimbeigi, Nathan Morris, Maryam S. Daneshpour, Hossein Mahjub, and Ali Reza Soltanian. "A Bayesian structural equation model in general pedigree data analysis." Statistical Analysis and Data Mining: The ASA Data Science Journal 12, no. 5 (July 24, 2019): 404–11. http://dx.doi.org/10.1002/sam.11434.

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Qin, Lu. "Estimating Nonlinear Indirect Effects in Bayesian Semiparametric Structural Equation Model." Multivariate Behavioral Research 53, no. 1 (January 2, 2018): 130–31. http://dx.doi.org/10.1080/00273171.2017.1404896.

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14

Lafifa. "Restructuring and Expanding Technology Acceptance Model Structural Equation Model and Bayesian Approach." American Journal of Applied Sciences 9, no. 4 (April 1, 2012): 496–504. http://dx.doi.org/10.3844/ajassp.2012.496.504.

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Lee, Sik-Yum, and Xin-Yuan Song. "On Bayesian estimation and model comparison of an integrated structural equation model." Computational Statistics & Data Analysis 52, no. 10 (June 2008): 4814–27. http://dx.doi.org/10.1016/j.csda.2008.03.029.

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Rahmadita, Astari, Ferra Yanuar, and Dodi Devianto. "The Construction of Patient Loyalty Model Using Bayesian Structural Equation Modeling Approach." CAUCHY 5, no. 2 (May 21, 2018): 73. http://dx.doi.org/10.18860/ca.v5i2.5039.

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<pre>The information on the health status of an individual is often gathered based on a health survey. Patient assessment on the quality of hospital services is important as a reference in improving the service so that it can increase a patient satisfaction and patient loyalty. The concepts of health service are often involve multivariate factors with multidimensional sructure of corresponding factors. One of the methods that can be used to model such these variables is SEM (Structural Equation Modeling). Structural Equation Modelling (SEM) is a multivariate method that incorporates ideas from regression, path-analysis and factor analysis. A Bayesian approach to SEM may enable models that reflect hypotheses based on complex theory. Bayesian SEM is used to construct the model for describing the patient loyalty at <em>Puskesmas</em> in Padang City. The convergence test with the history of trace plot, density plot and the model consistency test were performed with three different prior types. Based on Bayesian SEM approach, it is found that the quality of service and patient satisfaction significantly related to the patient loyalty.</pre>
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Sari, Dewi Kurnia, Ni Wayan Surya Wardhani, and Suci Astutik. "Parameter Estimation of Structural Equation Modeling Using Bayesian Approach." CAUCHY 4, no. 2 (May 31, 2016): 86. http://dx.doi.org/10.18860/ca.v4i2.3492.

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Leadership is a process of influencing, directing or giving an example of employees in order to achieve the objectives of the organization and is a key element in the effectiveness of the organization. In addition to the style of leadership, the success of an organization or company in achieving its objectives can also be influenced by the commitment of the organization. Where organizational commitment is a commitment created by each individual for the betterment of the organization. The purpose of this research is to obtain a model of leadership style and organizational commitment to job satisfaction and employee performance, and determine the factors that influence job satisfaction and employee performance using SEM with Bayesian approach. This research was conducted at Statistics FNI employees in Malang, with 15 people. The result of this study showed that the measurement model, all significant indicators measure each latent variable. Meanwhile in the structural model, it was concluded there are a significant difference between the variables of Leadership Style and Organizational Commitment toward Job Satisfaction directly as well as a significant difference between Job Satisfaction on Employee Performance. As for the influence of Leadership Style and variable Organizational Commitment on Employee Performance directly declared insignificant.
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R.M., Harindranath, and Jayanth Jacob. "Bayesian structural equation modelling tutorial for novice management researchers." Management Research Review 41, no. 11 (November 19, 2018): 1254–70. http://dx.doi.org/10.1108/mrr-11-2017-0377.

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Purpose This paper aims to popularize the Bayesian methods among novice management researchers. The paper interprets the results of Bayesian method of confirmatory factor analysis (CFA), structural equation modelling (SEM), mediation and moderation analysis, with the intention that the novice researchers will apply this method in their research. The paper made an attempt in discussing various complex mathematical concepts such as Markov Chain Monte Carlo, Bayes factor, Bayesian information criterion and deviance information criterion (DIC), etc. in a lucid manner. Design/methodology/approach Data collected from 172 pharmaceutical sales representatives were used. The study will help the management researchers to perform Bayesian CFA, Bayesian SEM, Bayesian moderation analysis and Bayesian mediation analysis using SPSS AMOS software. Findings The interpretation of the results of Bayesian CFA, Bayesian SEM and Bayesian mediation analysis were discussed. Practical implications The management scholars are non-statisticians and are not much aware of the benefits offered by Bayesian methods. Hitherto, the management scholars use predominantly traditional SEM in validating their models empirically, and this study will give an exposure to “Bayesian statistics” that has practical advantages. Originality/value This is one paper, which discusses the following four concepts: Bayesian method of CFA, SEM, mediation and moderation analysis.
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19

Hirose, Kei, Shuichi Kawano, Daisuke Miike, and Sadanori Konishi. "HYPER-PARAMETER SELECTION IN BAYESIAN STRUCTURAL EQUATION MODELS." Bulletin of informatics and cybernetics 42 (December 2010): 55–70. http://dx.doi.org/10.5109/25906.

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20

Song, Xin-Yuan, Jun-Hao Pan, Timothy Kwok, Liesbeth Vandenput, Claes Ohlsson, and Ping-Chung Leung. "A semiparametric Bayesian approach for structural equation models." Biometrical Journal 52, no. 3 (June 2010): 314–32. http://dx.doi.org/10.1002/bimj.200900135.

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21

Yang, Mingan, and David B. Dunson. "Bayesian Semiparametric Structural Equation Models with Latent Variables." Psychometrika 75, no. 4 (July 27, 2010): 675–93. http://dx.doi.org/10.1007/s11336-010-9174-4.

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22

Scheines, Richard, Herbert Hoijtink, and Anne Boomsma. "Bayesian estimation and testing of structural equation models." Psychometrika 64, no. 1 (March 1999): 37–52. http://dx.doi.org/10.1007/bf02294318.

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23

Ouyang, Ming, Xiaodong Yan, Ji Chen, Niansheng Tang, and Xinyuan Song. "Bayesian local influence of semiparametric structural equation models." Computational Statistics & Data Analysis 111 (July 2017): 102–15. http://dx.doi.org/10.1016/j.csda.2017.01.007.

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24

Thanoon, Thanoon Y., and Robiah Adnan. "Model comparison of linear and nonlinear Bayesian structural equation models with dichotomous data." Communications in Statistics - Simulation and Computation 46, no. 6 (February 3, 2017): 4578–99. http://dx.doi.org/10.1080/03610918.2015.1122052.

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25

Thanoon, Thanoon Y., Robiah Adnan, and Muhamad Alias Bin Md Jedi. "Model comparison of Bayesian structural equation models with mixed ordered categorical and dichotomous data." Journal of Statistics and Management Systems 20, no. 1 (January 2, 2017): 113–31. http://dx.doi.org/10.1080/09720510.2016.1238111.

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26

Chatterjee, Snehamoy. "Development of uncertainty-based work injury model using Bayesian structural equation modelling." International Journal of Injury Control and Safety Promotion 21, no. 4 (October 11, 2013): 318–27. http://dx.doi.org/10.1080/17457300.2013.825629.

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27

Miočević, Milica. "A Tutorial in Bayesian Mediation Analysis With Latent Variables." Methodology 15, no. 4 (October 1, 2019): 137–46. http://dx.doi.org/10.1027/1614-2241/a000177.

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Abstract. Maximum Likelihood (ML) estimation is a common estimation method in Structural Equation Modeling (SEM), and parameters in such analyses are interpreted using frequentist terms and definition of probability. It is also possible, and sometimes more advantageous ( Lee & Song, 2004 ; Rindskopf, 2012 ), to fit structural equation models in the Bayesian framework ( Kaplan & Depaoli, 2012 ; Levy & Choi, 2013 ; Scheines, Hoijtink, & Boomsma, 1999 ). Bayesian mediation analysis has been described for manifest variable models ( Enders, Fairchild, & MacKinnon, 2013 ; Yuan & MacKinnon, 2009 ). This tutorial outlines considerations in the analysis and interpretation of results for the single mediator model with latent variables. The reader is guided through model specification, estimation, and the interpretations of results obtained using two kinds of diffuse priors and one set of informative priors. Recommendations are made for applied researchers and annotated syntax is provided in R2OpenBUGS and Mplus. The target audience for this article are researchers wanting to learn how to fit the single mediator model as a Bayesian SEM.
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28

Wang, Yi-Fu, and Tsai-Hung Fan. "A Bayesian analysis on time series structural equation models." Journal of Statistical Planning and Inference 141, no. 6 (June 2011): 2071–78. http://dx.doi.org/10.1016/j.jspi.2010.12.017.

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29

Lee, Sik-Yum, and Xin-Yuan Song. "Bayesian analysis of structural equation models with dichotomous variables." Statistics in Medicine 22, no. 19 (2003): 3073–88. http://dx.doi.org/10.1002/sim.1544.

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30

Song, Xin-Yuan, Zhao-Hua Lu, Yih-Ing Hser, and Sik-Yum Lee. "A Bayesian Approach for Analyzing Longitudinal Structural Equation Models." Structural Equation Modeling: A Multidisciplinary Journal 18, no. 2 (April 6, 2011): 183–94. http://dx.doi.org/10.1080/10705511.2011.557331.

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31

Lee, Sik-Yum. "Bayesian analysis of stochastic constraints in structural equation models." British Journal of Mathematical and Statistical Psychology 45, no. 1 (May 1992): 93–107. http://dx.doi.org/10.1111/j.2044-8317.1992.tb00979.x.

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32

Zhang, Yanqing, and Niansheng Tang. "Bayesian empirical likelihood estimation of quantile structural equation models." Journal of Systems Science and Complexity 30, no. 1 (February 2017): 122–38. http://dx.doi.org/10.1007/s11424-017-6254-x.

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33

Liang, Xinya. "Prior Sensitivity in Bayesian Structural Equation Modeling for Sparse Factor Loading Structures." Educational and Psychological Measurement 80, no. 6 (February 26, 2020): 1025–58. http://dx.doi.org/10.1177/0013164420906449.

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Bayesian structural equation modeling (BSEM) is a flexible tool for the exploration and estimation of sparse factor loading structures; that is, most cross-loading entries are zero and only a few important cross-loadings are nonzero. The current investigation was focused on the BSEM with small-variance normal distribution priors (BSEM-N) for both variable selection and model estimation. The prior sensitivity in BSEM-N was explored in factor analysis models with sparse loading structures through a simulation study (Study 1) and an empirical example (Study 2). Study 1 examined the prior sensitivity in BSEM-N based on the model fit, population model recovery, true and false positive rates, and parameter estimation. Seven shrinkage priors on cross-loadings and five noninformative/vague priors on other model parameters were examined. Study 2 provided a real data example to illustrate the impact of various priors on model fit and parameter selection and estimation. Results indicated that when the 95% credible intervals of shrinkage priors barely covered the population cross-loading values, it resulted in the best balance between true and false positives. If the goal is to perform variable selection, a sparse cross-loading structure is required, preferably with a minimal number of nontrivial cross-loadings and relatively high primary loading values. To improve parameter estimates, a relatively large prior variance is preferred. When cross-loadings are relatively large, BSEM-N with zero-mean priors is not recommended for the estimation of cross-loadings and factor correlations.
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MI, XIAOJUAN, KENT ESKRIDGE, DONG WANG, P. STEPHEN BAENZIGER, B. TODD CAMPBELL, KULVINDER S. GILL, and ISMAIL DWEIKAT. "Bayesian mixture structural equation modelling in multiple-trait QTL mapping." Genetics Research 92, no. 3 (June 2010): 239–50. http://dx.doi.org/10.1017/s0016672310000236.

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SummaryQuantitative trait loci (QTLs) mapping often results in data on a number of traits that have well-established causal relationships. Many multi-trait QTL mapping methods that account for correlation among the multiple traits have been developed to improve the statistical power and the precision of QTL parameter estimation. However, none of these methods are capable of incorporating the causal structure among the traits. Consequently, genetic functions of the QTL may not be fully understood. In this paper, we developed a Bayesian multiple QTL mapping method for causally related traits using a mixture structural equation model (SEM), which allows researchers to decompose QTL effects into direct, indirect and total effects. Parameters are estimated based on their marginal posterior distribution. The posterior distributions of parameters are estimated using Markov Chain Monte Carlo methods such as the Gibbs sampler and the Metropolis–Hasting algorithm. The number of QTLs affecting traits is determined by the Bayes factor. The performance of the proposed method is evaluated by simulation study and applied to data from a wheat experiment. Compared with single trait Bayesian analysis, our proposed method not only improved the statistical power of QTL detection, accuracy and precision of parameter estimates but also provided important insight into how genes regulate traits directly and indirectly by fitting a more biologically sensible model.
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Lee, Sik-Yum, and Xin-Yuan Song. "Bayesian model selection for mixtures of structural equation models with an unknown number of components." British Journal of Mathematical and Statistical Psychology 56, no. 1 (May 2003): 145–65. http://dx.doi.org/10.1348/000711003321645403.

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Lee, Sik-Yum, and Xin-Yuan Song. "Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data." British Journal of Mathematical and Statistical Psychology 57, no. 1 (May 2004): 131–50. http://dx.doi.org/10.1348/000711004849204.

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37

Li, Yun Xian. "A Bayesian Method for Model Optimization in Structural Equation Models with Mixed Continuous and Ordered Categorical Data." Applied Mechanics and Materials 110-116 (October 2011): 2655–61. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.2655.

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In this paper, a Bayesian criterion-based method called the Lv measure, as well as its calibration distribution, is introduced and applied to model optimization of structural equation models with mixed continuous and categorical data. A simulation study is presented to illustrate the satisfactory performance of the Lv measure in model optimization.
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38

Kaplan, David, and Chansoon Lee. "Optimizing Prediction Using Bayesian Model Averaging: Examples Using Large-Scale Educational Assessments." Evaluation Review 42, no. 4 (April 11, 2018): 423–57. http://dx.doi.org/10.1177/0193841x18761421.

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This article provides a review of Bayesian model averaging as a means of optimizing the predictive performance of common statistical models applied to large-scale educational assessments. The Bayesian framework recognizes that in addition to parameter uncertainty, there is uncertainty in the choice of models themselves. A Bayesian approach to addressing the problem of model uncertainty is the method of Bayesian model averaging. Bayesian model averaging searches the space of possible models for a set of submodels that satisfy certain scientific principles and then averages the coefficients across these submodels weighted by each model’s posterior model probability (PMP). Using the weighted coefficients for prediction has been shown to yield optimal predictive performance according to certain scoring rules. We demonstrate the utility of Bayesian model averaging for prediction in education research with three examples: Bayesian regression analysis, Bayesian logistic regression, and a recently developed approach for Bayesian structural equation modeling. In each case, the model-averaged estimates are shown to yield better prediction of the outcome of interest than any submodel based on predictive coverage and the log-score rule. Implications for the design of large-scale assessments when the goal is optimal prediction in a policy context are discussed.
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39

Lee, Sik-Yum, Bin Lu, and Xin-Yuan Song. "Semiparametric Bayesian analysis of structural equation models with fixed covariates." Statistics in Medicine 27, no. 13 (2008): 2341–60. http://dx.doi.org/10.1002/sim.3098.

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40

Song, Xin-Yuan, Zhao-Hua Lu, Jing-Heng Cai, and Edward Hak-Sing Ip. "A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models." Psychometrika 78, no. 4 (February 1, 2013): 624–47. http://dx.doi.org/10.1007/s11336-013-9323-7.

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41

Dong, Weihua, Yuhao Jiang, Liangyu Zheng, Bing Liu, and Liqiu Meng. "Assessing Map-Reading Skills Using Eye Tracking and Bayesian Structural Equation Modelling." Sustainability 10, no. 9 (August 28, 2018): 3050. http://dx.doi.org/10.3390/su10093050.

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Map reading is an important skill for acquiring spatial information. Previous studies have mainly used results-based assessments to learn about map-reading skills. However, how to model the relationship between map-reading skills and eye movement metrics is not well documented. In this paper, we propose a novel method to assess map-reading skills using eye movement metrics and Bayesian structural equation modelling. We recruited 258 participants to complete five map-reading tasks, which included map visualization, topology, navigation, and spatial association. The results indicated that map-reading skills could be reflected in three selected eye movement metrics, namely, the measure of first fixation, the measure of processing, and the measure of search. The model fitted well for all five tasks, and the scores generated by the model reflected the accuracy and efficiency of the participants’ performance. This study might provide a new approach to facilitate the quantitative assessment of map-reading skills based on eye tracking.
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42

Li, Yan, Dayou Liu, Jianfeng Chu, Yungang Zhu, Jie Liu, and Xiaochun Cheng. "A Sparse Bayesian Learning Method for Structural Equation Model-Based Gene Regulatory Network Inference." IEEE Access 8 (2020): 40067–80. http://dx.doi.org/10.1109/access.2020.2976743.

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43

Song, Xin-Yuan, and Sik-Yum Lee. "A tutorial on the Bayesian approach for analyzing structural equation models." Journal of Mathematical Psychology 56, no. 3 (June 2012): 135–48. http://dx.doi.org/10.1016/j.jmp.2012.02.001.

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44

Cai, Jingheng, Ming Ouyang, Kai Kang, and Xinyuan Song. "Bayesian Diagnostics of Hidden Markov Structural Equation Models with Missing Data." Multivariate Behavioral Research 53, no. 2 (January 11, 2018): 151–71. http://dx.doi.org/10.1080/00273171.2017.1407233.

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45

Ansari, Asim, Kamel Jedidi, and Sharan Jagpal. "A Hierarchical Bayesian Methodology for Treating Heterogeneity in Structural Equation Models." Marketing Science 19, no. 4 (November 2000): 328–47. http://dx.doi.org/10.1287/mksc.19.4.328.11789.

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46

Lee, Sik-Yum. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data." Psychometrika 71, no. 3 (August 25, 2006): 541–64. http://dx.doi.org/10.1007/s11336-006-1177-1.

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47

Lee, Sik-Yum, and Ye-Mao Xia. "A Robust Bayesian Approach for Structural Equation Models with Missing Data." Psychometrika 73, no. 3 (February 16, 2008): 343–64. http://dx.doi.org/10.1007/s11336-008-9060-5.

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48

Kaplan, David, and Chansoon Lee. "Bayesian Model Averaging Over Directed Acyclic Graphs With Implications for the Predictive Performance of Structural Equation Models." Structural Equation Modeling: A Multidisciplinary Journal 23, no. 3 (November 18, 2015): 343–53. http://dx.doi.org/10.1080/10705511.2015.1092088.

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49

Kleibergen, Frank, and Herman K. van Dijk. "BAYESIAN SIMULTANEOUS EQUATIONS ANALYSIS USING REDUCED RANK STRUCTURES." Econometric Theory 14, no. 6 (December 1998): 701–43. http://dx.doi.org/10.1017/s0266466698146017.

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Diffuse priors lead to pathological posterior behavior when used in Bayesian analyses of simultaneous equation models (SEM's). This results from the local nonidentification of certain parameters in SEM's. When this a priori known feature is not captured appropriately, it results in an a posteriori favoring of certain specific parameter values that is not the consequence of strong data information but of local nonidentification. We show that a proper consistent Bayesian analysis of a SEM explicitly has to consider the reduced form of the SEM as a standard linear model on which nonlinear (reduced rank) restrictions are imposed, which result from a singular value decomposition. The priors/posteriors of the parameters of the SEM are therefore proportional to the priors/posteriors of the parameters of the linear model under the condition that the restrictions hold. This leads to a framework for constructing priors and posteriors for the parameters of SEM's. The framework is used to construct priors and posteriors for one, two, and three structural equation SEM's. These examples together with a theorem, showing that the reduced forms of SEM's accord with sets of reduced rank restrictions on standard linear models, show how Bayesian analyses of generally specified SEM's can be conducted.
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Gerassis, S., M. T. D. Albuquerque, J. F. García, C. Boente, E. Giráldez, J. Taboada, and J. E. Martín. "Understanding complex blasting operations: A structural equation model combining Bayesian networks and latent class clustering." Reliability Engineering & System Safety 188 (August 2019): 195–204. http://dx.doi.org/10.1016/j.ress.2019.03.032.

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