Bayesian Meta-Analytic SEM: A One-Stage Approach to Modeling Between-Studies Heterogeneity in Structural Parameters

References

• Alessandri, G., & Vecchione, M. (2012). The higher-order factors of the big five as predictors of job performance. Personality and Individual Differences, 53(6), 779–784. doi:10.1016/j.paid.2012.05.037
   Web of Science ®Google Scholar
• Ando, T. (2007). Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. Biometrika, 94(2), 443–458. doi:10.1093/biomet/asm017
   Web of Science ®Google Scholar
• Asparouhov, T., & Muthén, B. (2007). Computationally efficient estimation of multilevel high-dimensional latent variable models. In Proceedings of the 2007 Joint Statistical Meetings, section on statistics in epidemiology (pp. 2531–2535).
   Google Scholar
• Asparouhov, T., & Muthén, B. (2010). Bayesian analysis of latent variable models using Mplus. Technical report, Muthén & Muthén, Los Angeles, CA.
   Google Scholar
• Baird, R., & Maxwell, S. E. (2016). Performance of time-varying predictors in multilevel models under an assumption of fixed or random effects. Psychological Methods, 21(2), 175. doi:10.1037/met0000070
   PubMed Web of Science ®Google Scholar
• Becker, B. J. (1992). Using results from replicated studies to estimate linear models. Journal of Educational Statistics, 17, 341–362. doi:10.3102/10769986017004341
   Google Scholar
• Becker, B. J. (2009). Model-based MASEM. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (pp. 377–395). New York, NY: Russell Sage Foundation.
   Google Scholar
• Becker, B. J., & Fahrbach, K. (1994). A comparison of approaches to the synthesis of correlation matrices. Paper presented at the annual meeting of the American Educational Research Association New Orleans, LA. doi:10.3168/jds.S0022-0302(94)77044-2.
   Google Scholar
• Becker, B. J., & Schram, C. M. (1994). Examining explanatory models through research synthesis. In H. Cooper & L. V. Hedges (Eds.), The handbook of research synthesis (pp. 357–381). New York, NY: Russell Sage Foundation.
   Google Scholar
• Becker, B. J., & Wu, M.-J. (2007). The synthesis of regression slopes in meta-analysis. Statistical Science, 22(3), 414–429.
   Web of Science ®Google Scholar
• Bentler, P. M. (2006). EQS 6 structural equations program manual. Encino, CA: Multivariate Software.
   Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: John Wiley & Sons.
   Google Scholar
• Briggs, N. E., & MacCallum, R. C. (2003). Recovery of weak common factors by maximum likelihood and ordinary least squares estimation. Multivariate Behavioral Research, 38, 25–56. doi:10.1207/S15327906MBR3801_2
   PubMed Web of Science ®Google Scholar
• Chang, L., Connelly, B. S., & Geeza, A. A. (2012). Separating method factors and higher order traits of the Big Five: A meta-analytic multitrait–multimethod approach. Journal of Personality and Social Psychology, 102(2), 408–426. doi:10.1093/biomet/asm017
   PubMed Web of Science ®Google Scholar
• Cheung, M. W.-L. (2014). Fixed- and random-effects meta-analytic structural equation modeling: Examples and analyses in R. Behavior Research Methods, 46(1), 29–40. doi:10.3758/s13428-013-0361-y
   PubMed Web of Science ®Google Scholar
• Cheung, M. W.-L. (2018). Issues in solving the problem of effect size heterogeneity in meta-analytic structural equation modeling: A commentary and simulation study on Yu, Downes, Carter, and OBoyle (2016). Journal of Applied Psychology, 103(7), 787–803. doi:10.1037/apl0000284
   PubMed Web of Science ®Google Scholar
• Cheung, M. W.-L., & Chan, W. (2005). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10(1), 40–64. doi:10.1037/1082-989X.10.1.40
   PubMed Web of Science ®Google Scholar
• Cheung, M. W.-L., & Chan, W. (2009). A two-stage approach to synthesizing covariance matrices in meta-analytic structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16(1), 28–53. doi:10.1080/10705510802561295
   Web of Science ®Google Scholar
• Cheung, M. W.-L., & Cheung, S. F. (2016). Random-effects models for meta-analytic structural equation modeling: Review, issues, and illustrations. Research Synthesis Methods, 7(2), 140–155. doi:10.1002/jrsm.1166
   PubMed Web of Science ®Google Scholar
• Cheung, M. W.-L., & Hafdahl, A. R. (2016). Special issue on meta-analytic structural equation modeling: Introduction from the guest editors. Research Synthesis Methods, 7(2), 112–120. doi:10.1002/jrsm.1212
   PubMed Web of Science ®Google Scholar
• Chung, Y., Gelman, A., Rabe-Hesketh, S., Liu, J., & Dorie, V. (2015). Weakly informative prior for point estimation of covariance matrices in hierarchical models. Journal of Educational and Behavioral Statistics, 40(2), 136–157. doi:10.3102/1076998615570945
   Web of Science ®Google Scholar
• Collaboration, O. S. (2015). Estimating the reproducibility of psychological science. Science, 349(6251), aac4716–aac4716. doi:10.1126/science.aac4716
   PubMed Web of Science ®Google Scholar
• Danay, E., & Ziegler, M. (2011). Is there really a single factor of personality? A multirater approach to the apex of personality. Journal of Research in Personality, 45(6), 560–567. doi:10.1016/j.jrp.2011.07.003
   Web of Science ®Google Scholar
• DeYoung, C. G. (2006). Higher-order factors of the Big Five in a multi-informant sample. Journal of Personality and Social Psychology, 91(6), 1138–1151. doi:10.1037/0022-3514.91.6.1138
   PubMed Web of Science ®Google Scholar
• DeYoung, C. G., Hasher, L., Djikic, M., Criger, B., & Peterson, J. B. (2007). Morning people are stable people: Circadian rhythm and the higher-order factors of the Big Five. Personality and Individual Differences, 43(2), 267–276. doi:10.1016/j.paid.2006.11.030
   Web of Science ®Google Scholar
• Fitzmaurice, G. M., Laird, N. M., & Ware, J. H. (2004). Applied longitudinal analysis. Hoboken, NJ: John Wiley & Sons, Inc.
   Google Scholar
• Forero, C. G. A., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing LS and ULS estimation. Structural Equation Modeling, 16, 625–641. doi:10.1080/10705510903203573
   Web of Science ®Google Scholar
• Furlow, C. F., & Beretvas, S. N. (2005). Meta-analytic methods of pooling correlation matrices for structural equation modeling under different patterns of missing data. Psychological Methods, 10(2), 227–254. doi..
   PubMed Web of Science ®Google Scholar
• Gasparrini, A., Armstrong, B., & Kenward, M. G. (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine, 31(29), 3821–3839. doi:10.1002/sim.5471
   PubMed Web of Science ®Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014). Bayesian data analysis. FL, USA: Chapman & Hall/CRC Boca Raton.
   Google Scholar
• Gelman, A., Meng, X.-L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6(4), 733–760. https://www.jstor.org/stable/24306036
   Web of Science ®Google Scholar
• Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–472. doi:10.1214/ss/1177011136
   Google Scholar
• Geweke, J. (1991).
   Google Scholar
• Gnambs, T. (2013). The elusive general factor of personality: The acquaintance effect. European Journal of Personality, 27, 507–520. doi:10.1002/per.1933
   Web of Science ®Google Scholar
• Grace, J. B., Anderson, T. M., Smith, M. D., Seabloom, E., Andelman, S. J., Meche, G., … Willig, M. R. (2007). Does species diversity limit productivity in natural grassland communities?. Ecology Letters, 10(8), 680–689. doi:10.1111/j.1461-0248.2007.01058.x
   PubMed Web of Science ®Google Scholar
• Hafdahl, A. R. (2008). Combining heterogeneous correlation matrices: Simulation analysis of fixed-effect methods. Journal of Educational and Behavioral Statistics, 33(4), 507–533. doi:10.3102/1076998607309472
   Web of Science ®Google Scholar
• Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109–1144. doi:10.1287/opre.31.6.1109
   Web of Science ®Google Scholar
• Hershberger, S. L. (2003). The growth of structural equation modeling: 1994-2001. Structural Equation Modeling, 10, 35–46. doi:10.1207/s15328007sem1001_2
   Web of Science ®Google Scholar
• Hildebrandt, A., Lüdtke, O., Robitzsch, A., Sommer, C., & Wilhelm, O. (2016). Exploring factor model parameters across continuous variables with local structural equation models. Multivariate Behavioral Research, 51, 257–258. doi:10.1080/00273171.2016.1142856
   PubMed Web of Science ®Google Scholar
• Hirsh, J. B., DeYoung, C. G., & Peterson, J. B. (2009). Metatraits of the Big Five differentially predict engagement and restraint of behavior. Journal of Personality, 77(4), 1085–1102. doi:10.1111/jopy.2009.77.issue-4
   PubMed Web of Science ®Google Scholar
• Joreskog, K. G., & Sorbom, D. (1996). LISREL 8: A user’s reference guide. Chicago, IL: Scientific Software International, Inc.
   Google Scholar
• Kane, P., & Garber, J. (2004). The relations among depression in fathers, children psychopathology, and father–child conflict: A meta-analysis. Clinical Psychology Review, 24(3), 339–360. doi:10.1016/j.cpr.2004.03.004
   PubMed Web of Science ®Google Scholar
• Koopman, J., Howe, M., Hollenbeck, J. R., & Sin, H.-P. (2015). Small sample mediation testing: Misplaced confidence in bootstrapped confidence intervals. Journal of Applied Psychology, 100(1), 194–202. doi:10.1037/a0036635
   PubMed Web of Science ®Google Scholar
• Lee, S.-Y., Lu, B., & Song, X.-Y. (2008). Semiparametric Bayesian analysis of structural equation models with fixed covariates. Statistics in Medicine, 27(13), 2341–2360. doi:10.1002/sim.3098
   PubMed Web of Science ®Google Scholar
• Lin, L. I.-K. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45, 255–268. doi:10.2307/2532051
   PubMed Web of Science ®Google Scholar
• Little, R. J. A., & Rubin, D. B. (2014). Statistical analysis with missing data (2nd ed.). Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Loehlin, J. C., & Horn, J. M. (2012). How general is the “general factor of personality”? Evidence from the Texas adoption project. Journal of Research in Personality, 46(6), 655–663. doi:10.1016/j.jrp.2012.07.004
   Web of Science ®Google Scholar
• Lunn, D., Jackson, C., Best, N., Thomas, A., & Spiegelhalter, D. (2012). The BUGS book: A practical introduction to Bayesian analysis. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The bugs project: Evolution, critique and future directions. Statistics in Medicine, 28(25), 3049–3067. doi:10.1002/sim.3680
   PubMed Web of Science ®Google Scholar
• MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51, 201–226. doi:10.1146/annurev.psych.51.1.201
   PubMed Web of Science ®Google Scholar
• Macnamara, B. N., Hambrick, D. Z., & Oswald, F. L. (2014). Delibrate practice and performance in music, games, sports, education, and professions: A meta-analysis. Psychological Science, 25(8), 1608–1618. doi:10.1177/0956797614535810
   PubMed Web of Science ®Google Scholar
• Markon, K. E., Krueger, R. F., & Watson, D. (2005). Delineating the structure of normal and abnormal personality: An integrative hierarchical approach. Journal of Personality and Social Psychology, 88(1), 139–157. doi. doi:10.1037/0022-3514.88.3.421
   PubMed Web of Science ®Google Scholar
• Mount, M. K., Barrick, M. R., Scullen, S. M., & Rounds, J. (2005). Higher-order dimensions of the Big Five personality traits and the Big Six vocational interest types. Personnel Psychology, 58(2), 447–478. doi:10.1111/j.1744-6570.2005.00468.x
   Web of Science ®Google Scholar
• Murayama, K., & Elliot, A. J. (2012). The competition–performance relation: A meta-analytic review and test of the opposing processes model of competition and performance. Psychological Bulletin, 138(6), 1035–1070. doi:10.1037/a0028324
   PubMed Web of Science ®Google Scholar
• Muthén, B., & Asparouhov, T. (2008). Growth mixture modeling: Analysis with non-Gaussian random effects. In G. Fitzmaurice, M. Davidian, G. Verbeke, & G. Molenberghs (Eds.), Longitudinal data analysis (pp. 143–165). Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Muthén, B., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313–335. doi:10.1037/a0026802
   PubMed Web of Science ®Google Scholar
• Muthén, B., & Muthén, L. K. (2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Muthén, L. K., & Muthén, B. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 9, 599–620. doi:10.1207/s15328007sem0904_8
   Web of Science ®Google Scholar
• Neale, M. C., Hunter, M. D., Pritikin, J. N., Zahery, M., Brick, T. R., Kirkpatrick, R. M., … Boker, S. M. (2016). Openmx 2.0: Extended structural equation and statistical modeling. Psychometrika, 81(2), 535–549. doi:10.1007/s11336-014-9435-8
   PubMed Web of Science ®Google Scholar
• Olkin, I., & Finn, J. (1995). Correlations redux. Psychological Bulletin, 118, 155–164. doi:10.1037//0033-2909.118.1.155
   Web of Science ®Google Scholar
• Olkin, I., & Siotani, M. (1976). Asymptotic distribution of functions of a correlation matrix. In S. Ideka (Ed.), Essays in probability and statistics (pp. 235–251). Tokyo, Japan: Shinko Tscusho.
   Google Scholar
• Paul, P. A., Lipps, P. E., & Madden, L. V. (2006). Meta-analysis of regression coefficients for the relationship between fusarium head blight and deoxynivalenol content of wheat. Phytopathology, 96(9), 951–961. doi:10.1094/PHYTO-96-0951
   PubMed Web of Science ®Google Scholar
• Pearson, K., & Filon, L. N. G. (1898). Mathematical contributions to the theory of evolution: Iv. on the probable errors of frequency constants and on the influence of random selection on variation and correlation. Philosophical Transactions of the Royal Society of London, Series A, 191, 229–311. doi:10.1098/rspl.1897.0091
   Google Scholar
• Preacher, K. J., Zyphur, M. J., & Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods, 15(3), 209–233. doi:10.1037/met0000052
   PubMed Web of Science ®Google Scholar
• Prevost, A. T., Mason, D., Griffin, S., Kinmonth, A.-L., Sutton, S., & Spiegelhalter, D. (2007). Allowing for correlations between correlations in random-effects meta-analysis of correlation matrices. Psychological Methods, 12(4), 434–450. doi:10.1037/1082-989X.12.4.434
   PubMed Web of Science ®Google Scholar
• Riemann, R., & Kandler, C. (2010). Construct validation using multitrait-multimethod-twin data: The case of a general factor of personality. European Journal of Personality, 24(3), 258–277. doi:10.1002/per.760
   Web of Science ®Google Scholar
• Rothstein, H. R., & Bushman, B. J. (2015). Methodological and reporting errors in meta-analytic reviews make other meta-analysts anry: A commentary on Ferguson (2015). Perspectives on Psychological Science, 10(5), 677–679. doi:10.1177/1745691615592235
   Web of Science ®Google Scholar
• Rushton, J. P., & Irwing, P. (2008). A general factor of personality (GFP) from two meta-analyses of the Big Five. Personality and Individual Differences, 45(7), 679–683. doi:10.1016/j.paid.2008.07.015
   Web of Science ®Google Scholar
• Rushton, J. P., & Irwing, P. (2009). A general factor of personality in 16 sets of the Big Five, the Guilford–Zimmerman temperament survey, the California psychological inventory, and the temperament and character inventory. Personality and Individual Differences, 47(6), 558–564. doi:10.1016/j.paid.2009.05.009
   Web of Science ®Google Scholar
• Savalei, V., & Bentler, P. M. (2009). A two-stage approach to missing data: Theory and application to auxiliary variables. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 477–497. doi:10.1080/10705510903008238
   Web of Science ®Google Scholar
• Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Thousand Oaks, CA: Sage Publications.
   Google Scholar
• Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583–639. doi:10.1111/1467-9868.00353
   Web of Science ®Google Scholar
• Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245–251. doi:10.1037/0033-2909.87.2.245
   Web of Science ®Google Scholar
• Sturtz, S., Ligges, U., & Gelman, A. (2005). R2WinBUGS: A package for running WinBUGS from R. Journal of Statistical Software, 12(3), 1–16. doi:10.18637/jss.v012.i03
   Web of Science ®Google Scholar
• Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528–540. doi:10.2307/2289457
   Web of Science ®Google Scholar
• Taylor, C. L. (2017). Creativity and mood disorder: A systematic review and meta-analysis. Perspectives on Psychological Science, 12(6), 1040–1076. doi:10.1177/1745691617699653
   Web of Science ®Google Scholar
• Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington, DC: American Psychological Association.
   Google Scholar
• Tong, X., & Zhang, Z. (2012). Diagnostics of robust growth curve modeling using student’s t distribution. Multivariate Behavioral Research, 47(4), 493–518. doi:10.1080/00273171.2012.692614
   PubMed Web of Science ®Google Scholar
• Tremblay, P. F., & Gardner, R. C. (1996). On the growth of structural equation modeling in psychological journals. Structural Equation Modeling, 3, 93–104. doi:10.1080/10705519609540035
   Web of Science ®Google Scholar
• Van der Linden, D., Te Nijenhuis, J., & Bakker, A. B. (2010). The general factor of personality: A meta-analysis of Big Five intercorrelations and a criterion-related validity study. Journal of Research in Personality, 44(3), 315–327. doi:10.1016/j.jrp.2010.03.0
   Web of Science ®Google Scholar
• Viswesvaran, C., & Ones, D. S. (1995). Theory testing: Combining psychometric meta-analysis and structural equation modeling. Personnel Psychology, 48(4), 865–885. doi:10.1111/j.1744-6570.1995.tb01784.x
   Web of Science ®Google Scholar
• Vonesh, E. F., Chinchilli, V. M., & Pu, K. (1996). Goodness-of-fit in generalized nonlinear mixed-effects models. Biometrics, 572–587. doi:10.2307/2532896
   PubMed Web of Science ®Google Scholar
• Ward, E. J. (2008). A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools. Ecological Modelling, 211(1), 1–10. doi:10.1016/j.ecolmodel.2007.10.030
   Web of Science ®Google Scholar
• Wu, W., West, S. G., & Taylor, A. B. (2009). Evaluating model fit for growth curve models: Integration of fit indices from SEM and MLM frameworks. Psychological Methods, 14(3), 183–201. doi:10.1037/a0015858
   PubMed Web of Science ®Google Scholar
• Yang, M., & Yuan, K.-H. (2018). Optimizing ridge generalized least squares for structural equation modeling. Structural Equation Modeling. doi:10.1080/10705511.2018.1479853
   Web of Science ®Google Scholar
• Yu, J., Downes, P. E., Carter, K. M., & O’Boyle, E. H. (2016). The problem of effect size heterogeneity in meta-analytic structural equation modeling. Journal of Applied Psychology, 101(10), 1457–1473. doi:10.1037/apl0000141
   PubMed Web of Science ®Google Scholar
• Yu, J., Downes, P. E., Carter, K. M., & O'Boyle, E. H. (2018). The heterogeneity problem in meta-analytic structural equation modeling (MASEM) revisited: A reply to Cheung. Journal of Applied Psychology, 103(7), 804–811. doi:10.1037/apl0000328
   PubMed Web of Science ®Google Scholar
• Yuan, K.-H., & Bentler, P. M. (1997). Improving parameter tests in covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 51, 289–309. doi:10.1016/s0167-9473(97)00025-x
   Web of Science ®Google Scholar
• Yuan, K.-H., & Chan, W. (2016). Structural equation modeling with unknown population distributions: Ridge generalized least squares. Structural Equation Modeling: A Multidisciplinary Journal, 23(2), 163–179. doi:10.1080/10705511.2015.1077335
   Web of Science ®Google Scholar
• Zhang, Q., Wang, L., & Bergeman, C. S. (2018). Multilevel autoregressive mediation models: Specification, estimation, and applications. Psychological Methods, 23(2), 278–297.
   PubMed Web of Science ®Google Scholar
• Zhang, Z. (2013). Bayesian growth curve models with the generalized error distribution. Journal of Applied Statistics, 40(8), 1779–1795.
   Web of Science ®Google Scholar
• Zhang, Z., Lai, K., Lu, Z., & Tong, X. (2013). Bayesian inference and application of robust growth curve models using student’s t distribution. Structural Equation Modeling, 20(1), 47–78. doi:10.1080/10705511.2013.742382
   Web of Science ®Google Scholar