A Bayesian Regularized Approach to Exploratory Factor Analysis in One Step

Structural Equation Modeling

Volumn 28, Issue 4, 2021, Pages 518-528

  Chen, Jinsong ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

bayesian regularization; bilevel selection; Factor analysis; factor extraction; spike and slab prior

Indexed keywords

MARKOV CHAINS; MULTIVARIANT ANALYSIS; PARAMETER ESTIMATION;

EXPLORATORY FACTOR ANALYSIS; EXPLORATORY FACTOR ANALYSIS (EFA); INTERVAL ESTIMATE; MARKOV CHAIN MONTE-CARLO; MODEL INTERPRETATIONS; NUMBER OF FACTORS; REAL DATA ANALYSIS; SIGNIFICANCE TESTING;

FACTOR ANALYSIS;

EID: 85099827698     PISSN: 10705511     EISSN: 15328007     Source Type: Journal    
DOI: 10.1080/10705511.2020.1854763     Document Type: Article

References (43)

1. Asparouhov, T., & Muthén, B., (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397–438. https://doi.org/10.1080/10705510903008204
2. Auerswald, M., & Moshagen, M., (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods, 24, 468–491. https://doi.org/10.1037/met0000200
3. Bernaards, C. A., & Jennrich, R. I., (2005). Gradient projection algorithms and software for arbitrary rotation criteria in factor analysis. Educational and Psychological Measurement, 65, 676–696. https://doi.org/10.1177/0013164404272507
4. Box, G. E. P., & Tiao, G. C., (1973). Bayesian inference in statistical analysis. Addison-Wesley.
5. Browne, M. W., (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111–150. https://doi.org/10.1207/S15327906MBR3601_05
6. Casella, G., (2001). Empirical Bayes Gibbs sampling. Biostatistics, 2, 485–500. https://doi.org/10.1093/biostatistics/2.4.485
7. Casella, G., & George, E. I., (1992). Explaining the Gibbs sampler. The American Statistician, 46, 167–174. https://doi.org/10.1080/00031305.1992.10475878
8. Conti, G., Frühwirth-Schnatter, S., Heckman, J. J., & Piatek, R., (2014). Bayesian exploratory factor analysis. Journal of Econometrics, 183, 31–57. https://doi.org/10.1016/j.jeconom.2014.06.008
9. Feng, X.-N., Wu, H.-T., & Song, X.-Y., (2017). Bayesian regularized multivariate generalized latent variable models. Structural Equation Modeling, 24, 341–358. https://doi.org/10.1080/10705511.2016.1257353
10. Frühwirth-Schnatter, S., & Lopes, H. F., (2018). Sparse Bayesian factor analysis when the number of factors is unknown. arXiv.org. https://arxiv.org/abs/1804.04231
11. Gelman, A., (1996). Inference and monitoring convergence. In W. R., Gilks, S., Richardson, & D. J., Spiegelharter (Eds.), Markov chain Monte Carlo in practice (pp. 131–144). Chapman & Hall.
12. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B., (2004). Bayesian data analysis (2nd ed.). Chapman & Hall.
13. Geman, S., & Geman, D., (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741. https://doi.org/10.1109/TPAMI.1984.4767596
14. Gilks, W. R., Richardson, S., & Spiegelhalter, D. J., (Eds). (1996). Markov chain Monte Carlo in practice. Chapman & Hall.
15. Hastings, W. K., (1970). Monte Carlo sampling methods using Markov chains and their application. Biometrika, 57, 97–109. https://doi.org/10.1093/biomet/57.1.97
16. Heintz, S., (2017). Putting a spotlight on daily humor behaviors: Dimensionality and relationships with personality, subjective well-being, and humor styles. Personality and Individual Differences, 104, 407–412. https://doi.org/10.1016/j.paid.2016.08.042
17. Horn, J. L., (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179–185. https://doi.org/10.1007/BF02289447
18. Huang, P.-H., (2018). A penalized likelihood method for multi-group structural equation modelling. British Journal of Mathematical and Statistical Psychology, 71, 499–522. https://doi.org/10.1111/bmsp.12130
19. Huang, P.-H., Chen, H., & Weng, L.-J., (2017). A penalized likelihood method for structural equation modeling. Psychometrika, 82, 329–354. https://doi.org/10.1007/s11336-017-9566-9
20. Jacobucci, R., Grimm, K. J., & McArdle, J. J., (2016). Regularized structural equation modeling. Structural Equation Modeling, 23, 555–566. https://doi.org/10.1080/10705511.2016.1154793
21. Liu, X., (2008). Parameter expansion for sampling a correlation matrix: An efficient GPX-RPMH algorithm. Journal of Statistical Computation and Simulation, 78, 1065–1076. https://doi.org/10.1080/00949650701519635
22. Liu, X., & Daniels, M. J., (2006). A new efficient algorithm for sampling a correlation matrix based on parameter expansion and re-parameterization. Journal of Computational and Graphical Statistics, 15, 897–914. https://doi.org/10.1198/106186006X160681
23. Lu, Z. H., Chow, S. M., & Loken, E., (2016). Bayesian factor analysis as a variable-selection problem: Alternative priors and consequences. Multivariate Behavioral Research, 51, 519–539. https://doi.org/10.1080/00273171.2016.1168279
24. Martin, R. A., Puhlik-Doris, P., Larsen, G., Gray, J., & Weir, K., (2003). Individual differences in uses of humor and their relation to psychological well-being: Development of the humor styles questionnaire. Journal of Research in Personality, 37, 48–75. https://doi.org/10.1016/S0092-6566(02)00534-2
25. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E., (1953). Equations of state calculations by fast computing machine. Journal of Chemical Physics, 21, 1087–1091. https://doi.org/10.1063/1.1699114
26. Mulaik, S. A., (2010). Foundations of factor analysis (2nd ed.). Chapman & Hall/CRC.
27. Muthén, B. O., & Asparouhov, T., (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17, 313–335. https://doi.org/10.1037/a0026802
28. Papastamoulis, P., (2020). Clustering multivariate data using factor analytic Bayesian mixtures with an unknown number of components. Statistics and Computing, 30, 485–506. https://doi.org/10.1007/s11222-019-09891-z
29. Park, T., & Casella, G., (2008). The Bayesian lasso. Journal of the American Statistical Association, 103, 681–686. https://doi.org/10.1198/016214508000000337
30. Piatek, R., (2020). BayesFM: Bayesian inference for factor modeling (R package version 0.1.4). CRAN. https://CRAN.R-project.org/package=BayesFM
31. Plummer, M., Best, N., Cowles, K., & Vines, K., (2006). CODA: Convergence diagnosis and output analysis for MCMC. R News, 6, 7–11. https://cran.r-project.org/doc/Rnews/Rnews_2006-1.pdf#page=7
32. R Development Core Team. (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing. http://www.R-project.org
33. Revelle, W., (2020). psych: Procedures for psychological, psychometric, and personality research (R package version 2.0.9). CRAN. https://CRAN.R-project.org/package=psych
34. Sass, D. A., & Schmitt, T. A., (2010). A comparative investigation of rotation criteria within exploratory factor analysis. Multivariate Behavioral Research, 45, 73–103. https://doi.org/10.1080/00273170903504810
35. Scharf, F., & Nestler, S., (2019). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling, 26, 576–590. https://doi.org/10.1080/10705511.2018.1558060
36. Simon, N., Friedman, J., Hastie, T., & Tibshirani, R., (2013). A sparse-group Lasso. Journal of Computational and Graphical Statistics, 22, 231–245. https://doi.org/10.1080/10618600.2012.681250
37. Tibshirani, R., (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B, 58, 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
38. Trendafilov, N. T., Fontanella, S., & Adachi, K., (2017). Sparse exploratory factor analysis. Psychometrika, 82, 778–794. https://doi.org/10.1007/s11336-017-9575-8
39. Van Erp, S., Mulder, J., & Oberski, D. L., (2017). Prior sensitivity analysis in default Bayesian structural equation modeling. Psychological Methods, 23, 363–388. https://doi.org/10.1037/met0000162
40. Xu, X., & Ghosh, M., (2015). Bayesian variable selection and estimation for group Lasso. Bayesian Analysis, 10, 909–936. https://doi.org/10.1214/14-BA929
41. Yates, A., (1987). Multivariate exploratory data analysis: A perspective on exploratory factor analysis. State Univ. of New York Press.
42. Yuan, M., & Lin, Y., (2005). Efficient empirical Bayes variable selection and estimation in linear models. Journal of the American Statistical Association, 100, 1215–1225. https://doi.org/10.1198/016214505000000367
43. Yuan, M., & Lin, Y., (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68, 49–67. https://doi.org/10.1111/j.1467-9868.2005.00532.x