Bayesian Analysis of Multi-Factorial Experimental Designs Using SEM

References

• Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Sage Publications.
   Google Scholar
• Asparouhov, T., Muthén, B. (2010). Bayesian analysis using Mplus: Technical implementation (Version 3) [Technical report]. http://statmodel.com/download/Bayes3.pdf
   Google Scholar
• Asparouhov, T., & Muthén, B. (2020). Advances in Bayesian model fit evaluation for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 28(1), 1–14. https://doi.org/10.1080/10705511.2020.1764360
   Web of Science ®Google Scholar
• Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of Statistical Psychology, 3(2), 77–85. https://doi.org/10.1111/j.2044-8317.1950.tb00285.x
   Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. Wiley.
   Google Scholar
• Box, G. E. P. (1980). Sampling and Bayes’ inference in scientific modelling and robustness. Journal of the Royal Statistical Society. Series A (General), 143(4), 383. https://doi.org/10.2307/2982063
   Web of Science ®Google Scholar
• Buse, A. (1982). The likelihood ratio, wald, and Lagrange multiplier tests: An expository note. American Statistician, 36(3), 153–157. https://doi.org/10.2307/2683166
   Web of Science ®Google Scholar
• Can, S., van de Schoot, R., & Hox, J. (2014). Collinear latent variables in multilevel confirmatory factor analysis. Educational and Psychological Measurement, 75(3), 406–427. https://doi.org/10.1177/0013164414547959
   PubMed Web of Science ®Google Scholar
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.) Routledge.
   Google Scholar
• Depaoli, S. (2013). Mixture class recovery in GMM under varying degrees of class separation: Frequentist versus Bayesian estimation. Psychological Methods, 18(2), 186–219. https://doi.org/10.1037/a0031609
   PubMed Web of Science ®Google Scholar
• Engle, R. F. (1984). Wald, likelihood ratio, and lagrange multiplier tests in econometrics. In Z. Griliches & M. D. Intriligator (Eds.), Handbook of econometrics (1st ed., Vol. 2, pp. 775–825). North Holland.
   Google Scholar
• Fahrmeir, L., Kneib, T., Lang, S., & Marx, B. (2013). Regression. Springer.
   Google Scholar
• Fouladi, R. T. (2000). Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality. Structural Equation Modeling: A Multidisciplinary Journal, 7(3), 356–410. https://doi.org/10.1207/S15328007SEM0703_2
   Web of Science ®Google Scholar
• Fox, J., & Weisberg, S. (2019). An R companion to applied regression (3rd ed.). Sage.
   Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B., & Dunson, D. B. (2013). Bayesian data analysis (3rd ed.). Taylor & Francis.
   Google Scholar
• Green, S. B., & Babyak, M. A. (1997). Control of type I errors with multiple tests of constraints in structural equation modeling. Multivariate Behavioral Research, 32(1), 39–51. https://doi.org/10.1207/s15327906mbr3201_2
   PubMed Web of Science ®Google Scholar
• Hallquist, M. N., & Wiley, J. F. (2018). MplusAutomation: An R package for facilitating large-scale latent variable analyses in Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 621–638. https://doi.org/10.1080/10705511.2017.1402334
   PubMed Web of Science ®Google Scholar
• Hart, S. G., & Staveland, L. E. (1988). Development of NASA-TLX (task load index): results of empirical and theoretical research. In P. A. Hancock & N. Meshkati (Eds.), Human mental workload. (Vol. 52, pp. 139–183). North-Holland.
   Google Scholar
• Herzog, W., Boomsma, A., & Reinecke, S. (2007). The model-size effect on traditional and modified tests of covariance structures. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 361–390. https://doi.org/10.1080/10705510701301602
   Web of Science ®Google Scholar
• Hu, L-t., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112(2), 351–362. https://doi.org/10.1037/0033-2909.112.2.351
   PubMed Web of Science ®Google Scholar
• IBM Corp. (2020). IBM SPSS statistics for windows (Version 27.0).
   Google Scholar
• JASP Team. (2021). JASP (Version 0.16) [Computer software]. https://jasp-stats.org/
   Google Scholar
• Jöreskog, K. G. (1969). A general approach to confirmatory factor analysis. Psychometrika, 34(2), 183–202. https://doi.org/10.1007/BF02289343
   Web of Science ®Google Scholar
• Judd, C. M., McClelland, G. H., & Ryan, C. S. (2017). Data analysis: A model comparison approach to regression, ANOVA, and beyond (3rd ed.). Routledge.
   Google Scholar
• Kaplan, D., & Depaoli, S. (2012). Bayesian structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 650–673). The Guilford Press.
   Google Scholar
• Karageorghis, C. I., Kuan, G., Mouchlianitis, E., Payre, W., Howard, L. W., Reed, N., & Parkes, A. M. (2022). Interactive effects of task load and music tempo on psychological, psychophysiological, and behavioural outcomes during simulated driving. Ergonomics, 65(7), 915–932. https://doi.org/10.1080/00140139.2021.2003872
   PubMed Web of Science ®Google Scholar
• Keselman, H. J. (1975). A Monte Carlo investigation of three estimates of treatment magnitude: Epsilon squared, eta squared, and omega squared. Canadian Psychological Review/Psychologie Canadienne, 16(1), 44–48. https://doi.org/10.1037/h0081789
   Google Scholar
• Keselman, H. J., Huberty, C. J., Lix, L. M., Olejnik, S., Cribbie, R. A., Donahue, B., Kowalchuk, R. K., Lowman, L. L., Petoskey, M. D., Keselman, J. C., & Levin, J. R. (1998). Statistical practices of educational researchers: An analysis of their anova, manova, and ancova analyses. Review of Educational Research, 68(3), 350–386. https://doi.org/10.3102/00346543068003350
   Web of Science ®Google Scholar
• Kohler, D. F. (1982). The relation among the likelihood ratio-, wald-, and lagrange multiplier tests and their applicability to small samples. Rand Paper Series, P-6756, 1–10.
   Google Scholar
• Langenberg, B., Helm, J. L., Günther, T., & Mayer, A. (2023). Understanding, testing, and relaxing sphericity of repeated measures ANOVA with manifest and latent variables using SEM. Methodology, 19(1), 60–95. https://doi.org/10.5964/meth.8415
   Web of Science ®Google Scholar
• Langenberg, B., Helm, J. L., & Mayer, A. (2022). Repeated measures ANOVA with latent variables to analyze interindividual differences in contrasts. Multivariate Behavioral Research, 57(1), 2–19. https://doi.org/10.1080/00273171.2020.1803038
   PubMed Web of Science ®Google Scholar
• Langenberg, B., Mayer, A. (2022). Differences in longitudinal trajectories between groups – The multi-group latent growth components approach. Proceedings of the 9th European Congress of Methodology, Valencia, Spain.
   Google Scholar
• Lu, Y., & Zhang, G. (2010). The equivalence between likelihood ratio test and f-test for testing variance component in a balanced one-way random effects model. Journal of Statistical Computation and Simulation, 80(4), 443–450. https://doi.org/10.1080/00949650802695664
   Web of Science ®Google Scholar
• Maples-Keller, J. L., Williamson, R. L., Sleep, C. E., Carter, N. T., Campbell, W. K., & Miller, J. D. (2019). Using item response theory to develop a 60-item representation of the NEO PI–r using the international personality item pool: Development of the IPIP–NEO–60. Journal of Personality Assessment, 101(1), 4–15. https://doi.org/10.1080/00223891.2017.1381968
   PubMed Web of Science ®Google Scholar
• Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (2nd ed.). Lawrence Erlbaum Associates.
   Google Scholar
• Maxwell, S. E., Kelley, K., & Rausch, J. R. (2008). Sample size planning for statistical power and accuracy in parameter estimation. Annual Review of Psychology, 59(1), 537–563. https://doi.org/10.1146/annurev.psych.59.103006.093735
   PubMed Web of Science ®Google Scholar
• Mayer, A., Steyer, R., & Mueller, H. (2012). A general approach to defining latent growth components. Structural Equation Modeling: A Multidisciplinary Journal, 19(4), 513–533. https://doi.org/10.1080/10705511.2012.713242
   Web of Science ®Google Scholar
• McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In J. R. Nesselroade & R. B. Cattell (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 561–614). Plenum Press.
   Google Scholar
• McArdle, J. J., & Epstein, D. B. (1987). Latent growth curves within developmental structural equation models. Child Development, 58(1), 110–133. https://doi.org/10.2307/1130295
   PubMed Web of Science ®Google Scholar
• McNeish, D. M. (2016a). On using Bayesian methods to address small sample problems. Structural Equation Modeling: A Multidisciplinary Journal, 23(5), 750–773. https://doi.org/10.1080/10705511.2016.1186549
   Web of Science ®Google Scholar
• McNeish, D. M. (2016b). Using data-dependent priors to mitigate small sample bias in latent growth models. Journal of Educational and Behavioral Statistics, 41(1), 27–56. https://doi.org/10.3102/1076998615621299
   Web of Science ®Google Scholar
• Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55(1), 107–122. https://doi.org/10.1007/BF02294746
   Web of Science ®Google Scholar
• Merkle, E. C., & Rosseel, Y. (2018). blavaan: Bayesian structural equation models via parameter expansion. Journal of Statistical Software, 85(4), 1–30. https://doi.org/10.18637/jss.v085.i04
   PubMed Web of Science ®Google Scholar
• 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. https://doi.org/10.1080/10705511.2017.1312407
   PubMed Web of Science ®Google Scholar
• Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313–335. https://doi.org/10.1037/a0026802
   PubMed Web of Science ®Google Scholar
• Muthén, B. O., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38(2), 171–189. https://doi.org/10.1111/j.2044-8317.1985.tb00832.x
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2017). Mplus user’s guide (8th ed.). Mutheén & Mutheén.
   Google Scholar
• Olejnik, S., & Algina, J. (2000). Measures of effect size for comparative studies: Applications, interpretations, and limitations. Contemporary Educational Psychology, 25(3), 241–286. https://doi.org/10.1006/ceps.2000.1040
   PubMed Web of Science ®Google Scholar
• Perugini, M., Gallucci, M., & Costantini, G. (2018). A practical primer to power analysis for simple experimental designs. International Review of Social Psychology, 31(1), 20. https://doi.org/10.5334/irsp.181
   Web of Science ®Google Scholar
• Quintana, S. M., & Maxwell, S. E. (1994). A Monte Carlo comparison of seven ϵ-adjustment procedures in repeated measures designs with small sample sizes. Journal of Educational Statistics, 19(1), 57–71. https://doi.org/10.3102/10769986019001057
   Google Scholar
• R Core Team. (2021). R: A language and environment for statistical computing (Computer software).
   Google Scholar
• Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–163. https://doi.org/10.2307/271063
   Web of Science ®Google Scholar
• Raykov, T., & Widaman, K. F. (1995). Issues in applied structural equation modeling research. Structural Equation Modeling: A Multidisciplinary Journal, 2(4), 289–318. https://doi.org/10.1080/10705519509540017
   Web of Science ®Google Scholar
• Rencher, A. C., & Christensen, W. F. (2012). Methods of multivariate analysis (3rd ed.) John Wiley & Sons.
   Google Scholar
• Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56(5), 356–374. https://doi.org/10.1016/j.jmp.2012.08.001
   Web of Science ®Google Scholar
• Rouder, J. N., Morey, R. D., Verhagen, J., Swagman, A. R., & Wagenmakers, E.-J. (2017). Bayesian analysis of factorial designs. Psychological Methods, 22(2), 304–321. https://doi.org/10.1037/met0000057
   PubMed Web of Science ®Google Scholar
• Rovine, M. J., & McDermott, P. A. (2018). Latent growth curve and repeated measures anova contrasts: What the models are telling you. Multivariate Behavioral Research, 53(1), 90–101. https://doi.org/10.1080/00273171.2017.1387511
   PubMed Web of Science ®Google Scholar
• Rovine, M. J., & Molenaar, P. C. M. (1998). A LISREL model for the analysis of repeated measures with a patterned covariance matrix. Structural Equation Modeling: A Multidisciplinary Journal, 5(4), 318–343. https://doi.org/10.1080/10705519809540110
   Web of Science ®Google Scholar
• Rovine, M. J., & Molenaar, P. C. M. (2003). Estimating analysis of variance models as structural equation models. In B. H. Pugesek, A. Tomer, & A. von Eye (Eds.), Structural equation modeling: Applications in ecological and evolutionary biology (pp. 235–280). Cambridge University Press.
   Google Scholar
• Satorra, A., & Bentler, P. M. (1988). Scaling corrections for statistics in covariance structure analysis. Department of Statistics, UCLA.
   Google Scholar
• Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Sage Publications.
   Google Scholar
• Searle, S. R., Casella, G., & McCulloch, C. E. (1992). Variance components. John Wiley & Sons.
   Google Scholar
• Seber, G. A. F., & Lee, A. J. (2003). Linear regression analysis. Wiley.
   Google Scholar
• Smid, S. C., McNeish, D., Miočević, M., & van de Schoot, R. (2019). Bayesian versus frequentist estimation for structural equation models in small sample contexts: A systematic review. Structural Equation Modeling: A Multidisciplinary Journal, 27(1), 131–161. https://doi.org/10.1080/10705511.2019.1577140
   Web of Science ®Google Scholar
• Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9(2), 164–182. https://doi.org/10.1037/1082-989X.9.2.164
   PubMed Web of Science ®Google Scholar
• Swain, A. J. (1975). Analysis of parametric structures for variance matrices [Doctoral dissertation]. University of Adelaide. https://hdl.handle.net/2440/21286
   Google Scholar
• Ünal, A. B., Steg, L., & Epstude, K. (2012). The influence of music on mental effort and driving performance. Accident; Analysis and Prevention, 48, 271–278. https://doi.org/10.1016/j.aap.2012.01.022
   PubMed Web of Science ®Google Scholar
• van de Schoot, R., Broere, J. J., Perryck, K. H., Zondervan-Zwijnenburg, M., & van Loey, N. E. (2015). Analyzing small data sets using Bayesian estimation: The case of posttraumatic stress symptoms following mechanical ventilation in burn survivors. European Journal of Psychotraumatology, 6(1), 25216. https://doi.org/10.3402/ejpt.v6.25216
   PubMed Web of Science ®Google Scholar
• 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. Psychological Methods, 22(2), 217–239. https://doi.org/10.1037/met0000100
   PubMed Web of Science ®Google Scholar
• van Erp, S., Mulder, J., & Oberski, D. L. (2018). Prior sensitivity analysis in default Bayesian structural equation modeling. Psychological Methods, 23(2), 363–388. https://doi.org/10.1037/met0000162
   PubMed Web of Science ®Google Scholar
• Voelkle, M. C. (2007). Latent growth curve modeling as an integrative approach to the analysis of change. Psychology Science, 49(4), 375–414.
   Google Scholar
• Wagenmakers, E.-J., Lee, M., Lodewyckx, T., & Iverson, G. J. (2008). Bayesian versus frequentist inference. In H. Hoijtink, I. Klugkist, & P. A. Boelen (Eds.), Bayesian evaluation of informative hypotheses (pp. 181–207). Springer Science + Business Media. https://doi.org/10.1007/978-0-387-09612-4_9
   Google Scholar
• Weijters, B., & Baumgartner, H. (2018). Analyzing policy capturing data using structural equation modeling for within-subject experiments (SEMWISE). Organizational Research Methods, 22(3), 623–648. https://doi.org/10.1177/1094428118756742
   Web of Science ®Google Scholar
• Winter, S. D., & Depaoli, S. (2023). Illustrating the value of prior predictive checking for Bayesian structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 1000–1021. https://doi.org/10.1080/10705511.2022.2164286
   Web of Science ®Google Scholar
• Yuan, K.-H., & Bentler, P. M. (1997). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92(438), 767–774. https://doi.org/10.1080/01621459.1997.10474029
   Web of Science ®Google Scholar
• Zijlstra, F. R. H. (1993). Efficiency in work behaviour: A design approach for modern tools [Doctoral Dissertation, Delft University]. Delft University Press. http://resolver.tudelft.nl/uuid:d97a028b-c3dc-4930-b2ab-a7877993a17f
   Google Scholar
• Zondervan-Zwijnenburg, M., Depaoli, S., Peeters, M., & van de Schoot, R. (2019). Pushing the limits. Methodology, 15(1), 31–43. https://doi.org/10.1027/1614-2241/a000162
   Google Scholar