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

Authors

  • İlkay ALTINDAĞ Department of Banking, Faculty of Applied Sciences, Necmettin Erbakan University, 42060, Konya, Turkey

Keywords:

Bayesian Structural Equation Modeling, Latent Variables, Path Analysis, Residential Satisfaction.

Abstract

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.

References

Akaike, H., 1973. “Information theory and an extension of the maximum likelihood principle”. In B. N. Petrox and F. Caski (eds), Second International Symposium on Information Theory, p. 267. Budapest, Hungary: Akademiai Kiado.

Ansari, A., and Jedidi, K., 2000. “Bayesian factor analysis for multilevel binary observations.” Psychometrika, 65; 475–498.

Ansari, A., Jedidi, K., and Jagpal, S., 2000. “A hierarchical Bayesian methodology for treating heterogeneity in structural equation models.” Marketing Science, 19; .328–347.

Ansari, A., Jedidi, K., and Dube, L., 2002. “Heterogeneous factor analysis models: A Bayesian approach.” Psychometrika, 67. 49–78.

Arhonditsis, G., B., Stow, C., A., Steinberg, L. J., Kenney, M. A., Lathrop, R. C., and McBride, S., J., 2006. “Exploring ecological patterns with structural equation modeling and Bayesian analysis.” Ecological Modelling”, 192; pp. 385–409.

Arbuckle, J., L., 1994. “Amos: Analysis of moment structures.” Psychhometrika, 59; 115-137.

Arminger, G., and Muthen, B., 1998. “A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis–Hastings algorithm.” Psychometrika, 63; 271-300.

Bentler, P., M., 1989. “EQS, Structural Equations, Program Manual, Program Version 3.0.” Los Angeles: BMDP Statistical Software, Inc.

Bentler, P., M., 1995. “EQS, Structural Equations Program Manual, Program Version 5.0.” Encino, CA: Multivariate Software. “Testing

Berger J., B., and Sellke, T., 1987. “Testing a Point Null Hypothesis: The Irrenocilability of $P$ Values and Evidence.” Journal of the American Statistical Association, Volume 82, Issue 397; 112-122.

Berger, J., O., Delampady, M., 1987. “Testing Pracise Hypotheses.” Statistical, Science, Vol. 2, No. 3;317-335.

Bollen, K., A., 1989. “Structural Equation Models with Latent Variables.” NJ: John Wiley & Sons, Inc.

Browne, M., W., 1974. “Generalized least-squares estimators in the analysis of covariance structures.” South African Statistical Journal, 8;1-24.

Browne, M., W., 1984. “Asymptotic distribution free methods in analysis of covariance structures.” British Journal of Mathematical and Statistical Psychology, 37;62-83

Carlin, B., P., and Louis, T., A., 1996. “Bayes and Empirical Bayes Methods for Data Analysis.” London: Chapman and Hall.

Congdon, P., 2003. “Applied Bayesian Modeling.” Hoboken, NJ: John Wiley & Sons, Inc.

Dunson, D., B., 2000. “Bayesian latent variable models for clustered mixed outcomes.” Journal of the Royal Statistical Society, Series B, 62; 355-366.

Dunson, D., B., and Herring, A., 2005. “Bayesian latent variable models for mixed discrete outcomes.” Biostatistics, 6; 11-25.

Dunson, D., B.,, Palomo, J., and Bollen, K., 2005. “Bayesian Structural Equation Modeling, Handbook of latent variable and related models.” Vol. 1, ISSN:1871-0301.

Dunson, D., B,. 2003. “Dynamic latent trait models for multidimensional longitudinal data. Journal of American Statistical Association.” 98; 555-563.

Ganzach, Y., 1997. “Misleading interaction and curvilinear terms.” Psychological Methods, 3; 235-247.

Gelman, A., Meng, X., L., and Stern, H., 1996. “Posterior predictive assessment of model fitness via realized discrepancies.” Statistica Sinica, 6; 733-759.

Hall, J., Pitt, M., K., Kohna, R., 2014. “Bayesian inference for nonlinear structural time series models.” Journal of Econometrics, 179; 99-111.

Hartmann, W., M., 1992. “The CALIS procedure: Extended user’s guide.” Cary, NC: SAS Institute.

Hoyle, R. H., 1995. “Structural equation modeling: Concepts, issues, and applications,” Thousand Oaks, California: Sage Publications, 312.

Jiang, X., and Mahadevan, S., 2009. “Bayesian structural equation modeling method for hierarchical model validation.” Reliability Engineering and System Safety, 94; 796-809. “L

Jöreskog, K., G., and Sörbom, D., 1993. “LISREL 8: User’s guide.” Chicago: Scientific Software.

Kalelioğlu, M., R., and Özgür, E., M., 2013. “İkametgâh Memnuniyeti Bağlamında Konut Yeri Seçimi ve İkametgâh Hareketliliği: Bolu Kenti Örneği.” Coğrafi Bilimler Dergisi, CBD 11 (2); 149-168.

Lee, S., Y., 2007. “Structural Equation Modeling A Bayesian Approach.” John Wiley & Sons, London.

Lee, S., Y., and Song, X., Y., 2010. “Structural Equation Models.” Elsevier Ltd.

Lee, S., Y., and Song, X., Y., 2004. “Evaluation of the Bayesian and maximum likelihood approaches in analyzing structural equation models with small sample sizes.” Multivariate Behavioral Research, 39; 653-686.

Lee, S., Y., and Song, X., Y., 2003. “Model comparison of nonlinear structural equation models with fixed covariates.” Psychometrika, 68; 27-47.

Lee, S., Y., and Shi, J., Q., 2000. “Bayesian analysis of structural equation model with fixed covariates.” Structural Equation Modeling, 7; 411-430.

Lei, P., W., and Wu, Q., 2007, “Introduction to Structural Equation Modeling: Issues and Practical Considerations.” Educational Measurement: Issues and Practice, 26; 33–43.

Meng, X., L., 1994. “Multiple-Imputation Inference with Uncongenial Sources of Input (with discussion).” Statistical Science 9; 538-573. Main paper (538-558) and Rejoinder (pp. 566-573).

Muthen, B., O., 1988. “LISCOMP: Analysis of Linear Structural Equations with a Comprehensive Measurement Model: a Program for Advanced Research.” Scientific Software.

Muthen, L.K. and Muthen, B., O., 1998. “MPlus user's guide.” Los Angeles, California

Neale, M., C., 1997. “MX: Statistical Modeling.” Department of Psychiatry, Box 710 MCV, Richmond, VA 23298.

Özgür, E., M., 2009. “İkametgâh Memnuniyeti ve Şehir İçi İkametgâh Hareketliliği.” Coğrafi Bilimler Dergisi, CBD 7 (2); 111-127.

Rubin, D., B., 1984. “Bayesianly justifiable and relevant frequency calculations for the applied statistician.” The Annals of Statistics, 12; 1151-1172.”

Scheines, R., Spirtes, P., Glymour, C., and Meek, C., 1994. “Tetrad II: User Manual.” Erlbaum.

Schermelleh-Engel, K., Werner, C. S., Klein, A. G., and Moosbrugger, H. 2010. “Nonlinear Structural Equation Modeling: Is Partial Least Squares an Alternative?.” AStA Advances in Statistical Analysis, 94, 167-184.

Schwarz, G., 1978. “Estimating the dimension of a model.” The Annals of Statistics, 6; 461-464.

Song, X., Y., and Lee, S., Y., 2002. “Analysis of structural equation model with ignorable missing continuous and polytomous data.” Psychometrika, 67; 261-288.

Song, X., Y., Lee, S., Y., Ma, R., C., W., So, W., Y., Cai, J., H., and Ying, W., 2009a. “Phenotype–genotype interactions on renal function in type 2 diabetes an analysis using structural equation modeling.” Diabetologia, 52; 1543-1553.

Song, X., Y., Xia, Y., M., and Lee, S., Y., 2009b. “Bayesian semiparametric analysis of structural equation models with mixed continuous and unordered categorical variables.” Statistics in Medicine, 28; 2253–2276.

Song, X., Y., Lu, Z., H., Hser, Y., I., and Lee, S., Y., 2011. “A Bayesian approach for analyzing longitudinal structural equation models.” Structural Equation Modeling: A Multidisciplinary Journal, 18; 183-194.

Song, X., Y., Tang, N., S., and Chow, S., M., 2012. “A Bayesian approach for generalized random coefficient structural equation models for longitudinal data with adjacent time effects.” Computational Statistics and Data Analysis, 56; 4190-4203.

Song, X., Y., and Lee, S., Y., 2012a. “A tutorial on the Bayesian approach for analyzing structural equation models.” Journal of Mathematical Psychology, 56; 135-148.

Song, X., Y., and Lee, S., Y., 2012b. “Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences.” John Wiley & Sons, London.

Spiegelhalter, D., J., Best, N., G., Carlin, B., P., and Linde, A., 2002. “Bayesian measures of model complexity and fit (with discussion).” J. Roy. Statist. Soc. B. 64; 583-640.

Turkish Statistical Institute, “Life Satisfaction Survey”, 2013.

Van Onna, M., J., H., 2002. “Bayesian estimation and model selection in ordered latent class models for polytomous items.” Psychometrika, 67; 519-538.

Yang, M., G., and Dunson, D., B., 2010. “Bayesian semiparametric structural equation models with latent variables.” Psychometrika, 75; 675-693.

Yanuar, F., 2014. “The Estimation Process in Bayesian Structural Equation Modeling Approach.” Journal of Physics: Conference Series, 495, 012047.

Wang, Y., F., and Fan, T., H., 2010. “A Bayesian analysis on time series structural equation models.” Journal of Statistical Planning and Inference, 141; 2071-2078.

Yuan, S., X., Fei, C., and Zhao-Hua, L., 2013. “A Bayesian semiparametric dynamic two-level structural equation model for analyzing non-normal longitudinal data.” Journal of Multivariate Analysis, 121;87-108.

Wu, X., L., Heringstad, B., and Gianola, D., 2010. “Bayesian structural equation models for inferring relationships between phenotypes: a review of methodology, identifiability, and applications.” Journal of Animal Breeding and Genetics, 127; 3-15.

Downloads

Published

2017-10-20

How to Cite

ALTINDAĞ, İlkay. (2017). Application of Bayesian Nonlinear Structural Equation Modeling for Exploring Relationships on Residential Satisfaction in Turkey. International Journal of Sciences: Basic and Applied Research (IJSBAR), 36(4), 132–149. Retrieved from https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/8183

Issue

Section

Articles