贝叶斯结构方程模型及其研究现状

doi:10.3724/SP.J.1042.2019.01812

摘要/Abstract

摘要：

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。

关键词: 结构方程模型, 贝叶斯估计, 极大似然估计

Abstract:

Structural equation modeling (SEM) has been widely used in psychological researches to investigate the casual relationship among latent variables. Model estimation can be conducted under both the frequentist framework (e.g., maximum-likelihood approach) and the Bayesian framework. In recent years, with the prevalence of Bayesian statistics and its advantages in dealing with small samples, missing data and complex models in SEM, Bayesian structural equation modeling (BSEM) has developed rapidly. However, in China its application in the field of psychology is still insufficient. Therefore, this paper mainly focuses on presenting this new research method to applied researchers. We explain the theoretical and methodological basis of BSEM, as well as its advantages and disadvantages compared with the traditional frequentist approach. We also introduce several commonly used BSEM models and their applications.

Key words: structural equation modeling, Bayesian estimation, maximum-likelihood estimation

中图分类号:

B841

张沥今, 陆嘉琦, 魏夏琰, 潘俊豪. (2019). 贝叶斯结构方程模型及其研究现状. 心理科学进展 , 27(11), 1812-1825.

ZHANG Lijin, LU Jiaqi, WEI Xiayan, PAN Junhao. (2019). Bayesian structural equation modeling and its current researches. Advances in Psychological Science, 27(11), 1812-1825.

图/表 3

参考文献 80

1	侯杰泰, 温忠麟, 成子娟, 张雷 . (2004). 结构方程模型及其应用. 北京: 教育科学出版社.
2	李锡钦 . (2011). 结构方程模型:贝叶斯方法 (蔡敬衡, 潘俊豪, 周影辉译). 北京: 高等教育出版社.
3	刘红云, 孟庆茂 . ( 2003). 纵向数据分析方法. 心理科学进展, 11( 5), 586-592.
4	罗胜强, 姜嬿 . (2014). 管理学问卷调查研究方法. 重庆大学出版社.
5	王济川, 王小倩, 姜宝法 . (2011). 结构方程模型:方法与应用. 北京: 高等教育出版社.
6	王孟成 . (2014). 潜变量建模与Mplus应用(基础篇). 重庆大学出版社.
7	王孟成, 邓倩文, 毕向阳 . ( 2017). 潜变量建模的贝叶斯方法. 心理科学进展, 25( 10), 1682-1695.
8	温忠麟, 叶宝娟 . ( 2014). 中介效应分析: 方法和模型发展. 心理科学进展, 22( 5), 731-745.
9	叶素静, 唐文清, 张敏强, 曹魏聪 . ( 2014). 追踪研究中缺失数据处理方法及应用现状分析. 心理科学进展, 22( 12), 1985-1994.
10	Alessandri, G., & de Pascalis V. 2017). Double dissociation between the neural correlates of the general and specific factors of the life orientation test-revised. Cognitive Affective & Behavioral Neuroscience, 17( 5), 917-931.
11	Asparouhov, T., &Muthén B. 2009). Exploratory structural equation modeling. Structural Equation Modeling, 16( 3), 397-438.
12	Asparouhov, T., &Muthén B. 2010). Bayesian analysis of latent variable models using Mplus. (Technical Report). Retrieved June, 17, 2014.
13	Asparouhov T. ,& Muthén, B. (2012, July). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. Retrieved from .
14	Asparouhov, T., &Muthén B. 2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21( 4), 495-508.
15	Baldwin,S. A., &Fellingham,G. W . ( 2013). Bayesian methods for the analysis of small sample multilevel data with a complex variance structure. Psychological Methods, 18( 2), 151-164. doi: 10.1037/a0030642
16	Bollen,K. A., &Curran,P. J . ( 2006). Latent curve models: A structural equation approach. Hoboken, NJ: Wiley- Interscience.
17	Chou,C. P., &Bentler,P. M . ( 1990). Model modification in covariance structure modeling: A comparison among likelihood ratio, Lagrange multiplier, and Wald tests. Multivariate Behavioral Research, 25( 1), 115-136.
18	Chung Y. J., Rabe-Hesketh S., Dorie V., Gelman A., & Liu J. C . ( 2013). A nondegenerate penalized likelihood estimator for variance parameters in multilevel models. Psychometrika, 78( 4), 685-709. doi: 10.1007/s11336-013-9328-2
19	Crenshaw A. O., Christensen A., Baucom D. H., Epstein N. B., &Baucom, B. R. W. . ( 2016). Revised scoring and improved reliability for the communication patterns questionnaire. Psychological Assessment, 29( 7), 913-925.
20	de Bondt,N., & van Petegem P. 2015). Psychometric evaluation of the overexcitability questionnaire-two applying Bayesian structural equation modeling (BSEM) and multiple-group BSEM-based alignment with approximate measurement invariance. Frontiers in Psychology, 6, 1963.
21	Depaoli, S., &Clifton,J. P . ( 2015). A Bayesian approach to multilevel structural equation modeling with continuous and dichotomous outcomes. Structural Equation Modeling: A Multidisciplinary Journal, 22( 3), 327-351.
22	Depaoli, S., & van de Schoot R. 2015). Improving transparency and replication in Bayesian statistics: The wambs-checklist. Psychological Methods,22( 2), 240-261.
23	Draper, D. . ( 1995). Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society. Series B (Methodological), 57( 1), 45-97.
24	Falkenström F., Hatcher R. L., & Holmqvist R . ( 2015). Confirmatory factor analysis of the patient version of the working alliance inventory-short form revised. Assessment, 22( 5), 581-593.
25	Fong,T. C. T., &Ho,R. T. H . ( 2014). Testing gender invariance of the hospital anxiety and depression scale using the classical approach and Bayesian approach. Quality of Life Research, 23( 5), 1421-1426. doi: 10.1007/s11136-013-0594-3
26	Gelman A., Carlin J. B., Stern H. S., Dunson D. B., Vehtari A., & Rubin D. B . ( 2014). Bayesian data analysis (3rd ed.). Boca Raton, FL: CRC press.
27	Gelman A., Carlin J. B .,Stern, H. S. & Rubin, D. B. . ( 2003). Bayesian data analysis.London: Chapman and Hall/CRC.
28	Gelman A., Meng X. L., Stern H . ( 1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6, 733-807.
29	Golay P., Reverte I., Rossier J., Favez N., & Lecerf T . ( 2013). Further insights on the French WISC-IV factor structure through Bayesian structural equation modeling. Psychological Assessment, 25( 2), 496-508. doi: 10.1037/a0030676
30	Greenland, S. . ( 2001). Sensitivity analysis, Monte Carlo risk analysis, and Bayesian uncertainty assessment. Risk Analysis, 21( 4), 579-584.
31	Hox J. J., Maas C. J. M., &Brinkhuis, M. J. S. . ( 2010). The effect of estimation method and sample size in multilevel structural equation modeling. Statistica Neerlandica, 64( 2), 157-170.
32	Hsu H.-Y., Troncoso Skidmore S., Li Y., & Thompson B . ( 2014). Forced zero cross-loading misspecifications in measurement component of structural equation models: Beware of even “small” misspecifications. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 10(4), 138-152.
33	Jacobson N. C., Lord K. A., & Newman M. G . ( 2017). Perceived emotional social support in bereaved spouses mediates the relationship between anxiety and depression. Journal of Affective Disorders, 211, 83-91.
34	Johnson A. R., Schoot R. V. D., Delmar F., & Crano W. D . ( 2015). Social influence interpretation of interpersonal processes and team performance over time using Bayesian model selection. Journal of Management, 41(2), 574-606.
35	Kaplan, D. . ( 2009). Structural equation modeling: Foundations and extensions (2nd ed.). Newbury Park, CA:Sage.
36	Kaplan D. ,& Depaoli, S.( 2012). Bayesian structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 650-673). New York, NY,US:Guilford Press.
37	Kass,R. E., &Raftery,A. E . ( 1995). Bayes factors. Journal of the American Statistical Association, 90( 430), 773-795.
38	Kenny D. A., Korchmaros J. D., & Bolger N . ( 2003). Lower level mediation in multilevel models. Psychological Methods, 8( 2), 115-128.
39	Kim E. S., Cao C. H., Wang Y., & Nguyen D. T . ( 2017). Measurement invariance testing with many groups: A comparison of five approaches. Structural Equation Modeling: A Multidisciplinary Journal, 24( 4), 524-544.
40	Lee,S. Y, &Song,X. Y . ( 2012). Basic and advanced Bayesian structural equation modeling. John Wiley & Sons, Ltd.
41	Li, X., &Beretvas,S. N . ( 2013). Sample size limits for estimating upper level mediation models using multilevel SEM. Structural Equation Modeling: A Multidisciplinary Journal, 20( 2), 241-264.
42	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( 4), 519-539.
43	Lunn D. J., Thomas A., Best N., & Spiegelhalter D . ( 2000). WinBUGS-a Bayesian modelling framework: Concepts, structure, and extensibility. Statistics and Computing, 10( 4), 325-337. doi: 10.1023/A:1008929526011
44	Maccallum R. C., Roznowski M., & Necowitz L. B . ( 1992). Model modifications in covariance structure analysis: The problem of capitalization on chance. Psychological Bulletin, 111( 3), 490-504.
45	MacKinnon D. P., Lockwood C. M., & Williams J . ( 2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39( 1), 99-128.
46	Maier M. F., Bohlmann N. L., & Palacios N. A . ( 2016). Cross-language associations in the development of preschoolers’ receptive and expressive vocabulary. Early Childhood Research Quarterly, 36, 49-63.
47	Marsh H. W., Muthén B., Asparouhov T., Lüdtke O., Robitzsch A., Morin A. J. S., & Trautwein U . ( 2009). Exploratory structural equation modeling, integrating CFA and EFA: Application to students’ evaluations of university teaching. Structural Equation Modeling: A Multidisciplinary Journal, 16( 3), 439-476.
48	Meredith, W., &Tisak J. 1990). Latent curve analysis. Psychometrika, 55( 1), 107-122.
49	Merkle,E. C., &Rosseel Y. (2015). Blavaan: Bayesian structural equation models via parameter expansion.
50	Meuleman, B., &Billiet J. 2009). A Monte Carlo sample size study: How many countries are needed for accurate multilevel SEM? Survey Research Methods, 3( 1), 45-58.
51	Miočević,M. MacKinnon,D. P. &Levy R. 2017). Power in Bayesian mediation analysis for small sample research. Structural Equation Modeling: A Multidisciplinary Journal, 24( 5), 666-683.
52	Muthén, B., &Asparouhov T. 2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17( 3), 313-335.
53	Muthén, B., &Asparouhov T. (2013). BSEM measurement invariance analysis. Mplus Web Note 17. .
54	Muthén,L. K., &Muthén,B. O . (1998-2019).Mplus user’s guide. Eighth Edition. Los Angeles, CA: Muthén & Muthén.
55	Nuijten M. B., Wetzels R., Matzke D., Dolan C. V., & Wagenmakers E. J . ( 2015). A default Bayesian hypothesis test for mediation. Behavior Research Methods, 47( 1), 85-97.
56	Pan J., Ip E. H., & Dubé L . ( 2017). An alternative to post hoc model modification in confirmatory factor analysis: The Bayesian lasso. Psychological Methods, 22( 4), 687-704.
57	Plummer, M. . (2005). JAGS: Just Another Gibbs Sampler. Astrophysics Source Code Library.
58	Praetorius A. K., Koch T., Scheunpflug A., Zeinz H., & Dresel M . (2017). Identifying determinants of teachers' judgment (in) accuracy regarding students' school-related motivations using a Bayesian cross-classified multi-level model. Learning and Instruction, 52, 148-160.
59	Preacher K. J., Zhang Z., & Zyphur M. J . (2011). Alternative methods for assessing mediation in multilevel data: The advantages of multilevel SEM. Structural Equation Modeling: A Multidisciplinary Journal, 18( 2), 161-182.
60	Preacher K. J., Zyphur M. J., and Zhang Z . ( 2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods 15(3), 209-233. doi: 10.1037/a0020141.
61	Prem R., Scheel T. E., Weigelt O., Hoffmann K., & Korunka C . ( 2018). Procrastination in daily working life: A diary study on within-person processes that link work characteristics to workplace procrastination. Frontiers in Psychology, 9 1087. doi: 10.3389/fpsyg.2018.01087.
62	Rabe-hesketh S., Skrondal A., & Pickles A . ( 2004). Generalized multilevel structural equation modeling. Psychometrika, 69( 2), 167-190. doi: 10.1007/BF02295939
63	Salarzadeh H. J., Moghavvemi S., Wan C. M. R., Babashamsi P., & Arashi M . ( 2017). Testing students' e-learning via facebook through Bayesian structural equation modeling. PlosOne, 12( 9), e0182311.
64	Scherer R., Siddiq F., & Teo T . ( 2015). Becoming more specific: Measuring and modeling teachers' perceived usefulness of ICT in the context of teaching and learning. Computers & Education, 88, 202-214.
65	Schmitt, N., &Kuljanin G. 2008). Measurement invariance: Review of practice and implications. Human Resource Management Review, 18( 4), 210-222. doi: 10.1016/j.hrmr.2008.03.003
66	Schwarz, G. . ( 1978). Estimating the dimension of a model. The Annals of Statistics, 6( 2), 461-464.
67	Shuck B., Zigarmi D., & Owen J . ( 2015). Psychological needs, engagement, and work intentions: A Bayesian multi-measurement mediation approach and implications for HRD. European Journal of Training and Development, 39( 1), 2-21.
68	Sörbom, D. . ( 1989). Model modification. Psychometrika, 54( 3), 371-384.
69	Spiegelhalter D. J., Best N. G., Carlin B. P., &van der Linde, A. . ( 2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society Series B (Statistical Methodology),64, 583-616.
70	Stan Development Team . ( 2014). Stan modeling language: Users guide and reference manual, Version 2.2.0.
71	Tamminen K. A., Gaudreau P., Mcewen C. E., & Crocker P. R . ( 2016). Interpersonal emotion regulation among adolescent athletes: A Bayesian multilevel model predicting sport enjoyment and commitment . Journal of Sport and Exercise Psychology, 38(6), 541-555.
72	Tofighi, D., &MacKinnon,D. P . ( 2011). R mediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43( 3), 692-700. doi: 10.3758/s13428-011-0076-x
73	Tofighi, D., &Mackinnon,D. P . ( 2016). Monte Carlo confidence intervals for complex functions of indirect effects. Structural Equation Modeling: A Multidisciplinary Journal, 23( 2), 194-205.
74	van de Schoot R., Winter S. D., Ryan O., Zondervan- Zwijnenburg M., & Depaoli S . ( 2017). A systematic review of Bayesian articles in psychology: The last 25 years. Psychology Methods, 22( 2), 217-239.
75	Vandenberg,R. J., &Lance,C. E . ( 2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3( 1), 4-70.
76	Wang, L., &Preacher,K. J . ( 2015). Moderated mediation analysis using Bayesian methods. Structural Equation Modeling: A Multidisciplinary Journal, 22( 2), 249-263.
77	Winans-Mitrik R. L., Hula W. D., Dickey M. W., Schumacher J. G., Swoyer B., & Doyle P. J . ( 2014). Description of an intensive residential aphasia treatment program: Rationale, clinical processes, and outcomes. American Journal of Speech-Language Pathology, 23( 2), 330-342. doi: 10.1044/2014_AJSLP-13-0102
78	Yuan, Y., &Mackinnon,D. P . ( 2009). Bayesian mediation analysis. Psychological Methods, 14( 4), 301-322.
79	Zeman J. L., Dallaire D. H., Folk J. B., & Thrash T. M . ( 2017). Maternal incarceration, children’s psychological adjustment, and the mediating role of emotion regulation. Journal of Abnormal Child Psychology, 46( 2), 223-236.
80	Zhang Z. Y., Hamagami F., Wang L. L., Nesselroade J. R., & Grimm K. J . ( 2007). Bayesian analysis of longitudinal data using growth curve models. International Journal of Behavioral Development, 31( 4), 374-383.

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[11]	卞冉;车宏生;阳辉. 项目组合在结构方程模型中的应用[J]. 心理科学进展, 2007, 15(3): 567-576.
[12]	白新文，陈毅文. 测量等价性的概念及其判定条件[J]. 心理科学进展, 2004, 12(2): 231-239.
[13]	罗婷;焦书兰. 认知加工速度研究中常用的实验和统计方法[J]. 心理科学进展, 2002, 10(1): 21-28.
[14]	刘大维. 结构方程模型在跨文化心理学研究中的应用[J]. 心理科学进展, 1999, 7(2): 48-516.