Causal Mediation Analysis with the Parallel Process Latent Growth Curve Mediation Model

References

• Asparouhov, T., & Muthén, B. (2010). Bayesian analysis of latent variable models using Mplus. Retrieved 2024-04-07, from http://www.statmodel.com/download/BayesAdvantages18.pdf
   Google Scholar
• Asparouhov, T., & Muthén, B. (2021). Bayesian estimation of single and multilevel models with latent variable interactions. Structural Equation Modeling: A Multidisciplinary Journal, 28, 314–328. https://doi.org/10.1080/10705511.2020.1761808
   Web of Science ®Google Scholar
• Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182. https://doi.org/10.1037/0022-3514.51.6.1173
   PubMed Web of Science ®Google Scholar
• Bind, M.-A., Vanderweele, T. J., Coull, B., & Schwartz, J. (2016). Causal mediation analysis for longitudinal data with exogenous exposure. Biostatistics, 17, 122–134. https://doi.org/10.1093/biostatistics/kxv029
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. (Vol. 467). John Wiley & Sons.
   Google Scholar
• Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144–152. https://doi.org/10.1111/j.2044-8317.1978.tb00581.x
   Web of Science ®Google Scholar
• Campbell, F. A., Pungello, E. P., Miller-Johnson, S., Burchinal, M., & Ramey, C. T. (2001). The development of cognitive and academic abilities: Growth curves from an early childhood educational experiment. Developmental Psychology, 37, 231–242. https://doi.org/10.1037/0012-1649.37.2.231
   PubMed Web of Science ®Google Scholar
• Cheong, J. (2011). Accuracy of estimates and statistical power for testing meditation in latent growth curve modeling. Structural Equation Modeling: A Multidisciplinary Journal, 18, 195–211. https://doi.org/10.1080/10705511.2011.557334
   PubMed Web of Science ®Google Scholar
• Cheong, J., MacKinnon, D. P., & Khoo, S. T. (2003). Investigation of mediational processes using parallel process latent growth curve modeling. Structural Equation Modeling: A Multidisciplinary Journal, 10, 238–262. https://doi.org/10.1207/s15328007sem1002_5
   PubMed Web of Science ®Google Scholar
• Coffman, D. L., Dziak, J. J., Litson, K., Chakraborti, Y., Piper, M. E., & Li, R. (2023). A causal approach to functional mediation analysis with application to a smoking cessation intervention. Multivariate Behavioral Research, 58, 859–876. https://doi.org/10.1080/00273171.2022.2149449
   PubMed Web of Science ®Google Scholar
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). L. Erlbaum Associates.
   Google Scholar
• Congdon, P. (2003). Applied Bayesian modelling. Wiley.
   Google Scholar
• Conroy, D. E., & Coatsworth, J. D. (2004). The effects of coach training on fear of failure in youth swimmers: A latent growth curve analysis from a randomized, controlled trial. Journal of Applied Developmental Psychology, 25, 193–214. https://doi.org/10.1016/j.appdev.2004.02.007
   Web of Science ®Google Scholar
• De Stavola, B. L., Herle, M., & Pickles, A. (2022). Framing causal questions in life course epidemiology. Annual Review of Statistics and Its Application, 9, 223–248. https://doi.org/10.1146/annurev-statistics-040120-024748
   Web of Science ®Google Scholar
• Duncan, T. E., & Duncan, S. C. (2009). The ABC’s of LGM: An introductory guide to latent variable growth curve modeling. Social and Personality Psychology Compass, 3, 979–991. https://doi.org/10.1111/j.1751-9004.2009.00224.x
   PubMedGoogle Scholar
• El-Sheikh, M., Shimizu, M., Erath, S. A., Philbrook, L. E., & Hinnant, J. B. (2019). Dynamic patterns of marital conflict: Relations to trajectories of adolescent adjustment. Developmental Psychology, 55, 1720–1732. https://doi.org/10.1037/dev0000746
   PubMed Web of Science ®Google Scholar
• Ferrer, E., Balluerka, N., & Widaman, K. F. (2008). factorial invariance and the specification of second-order latent growth models. Methodology: European Journal of Research Methods for the Behavioral & Social Sciences, 4, 22–36. https://doi.org/10.1027/1614-2241.4.1.22
   PubMed Web of Science ®Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. Chapman and Hall/CRC.
   Google Scholar
• Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457–511. https://doi.org/10.1214/ss/1177011136
   Google Scholar
• Goldsmith, K. A., MacKinnon, D. P., Chalder, T., White, P. D., Sharpe, M., & Pickles, A. (2018). Tutorial: The practical application of longitudinal structural equation mediation models in clinical trials. Psychological Methods, 23, 191–207. https://doi.org/10.1037/met0000154
   PubMed Web of Science ®Google Scholar
• Gonzalez, O., & Valente, M. J. (2023). Accommodating a latent XM interaction in statistical mediation analysis. Multivariate Behavioral Research, 58, 659–674. https://doi.org/10.1080/00273171.2022.2119928
   PubMed Web of Science ®Google Scholar
• Guglielmi, R. S. (2023). Probing gaps in educational outcomes within the U.S.: A dual moderation multiple mediator latent growth model. Journal of School Psychology, 97, 123–151. https://doi.org/10.1016/j.jsp.2023.01.001
   PubMed Web of Science ®Google Scholar
• Hamaker, E. L., Asparouhov, T., Brose, A., Schmiedek, F., & Muthén, B. (2018). At the frontiers of modeling intensive longitudinal data: Dynamic structural equation models for the affective measurements from the cogito study. Multivariate Behavioral Research, 53, 820–841. https://doi.org/10.1080/00273171.2018.1446819
   PubMed Web of Science ®Google Scholar
• Hertzog, C., von Oertzen, T., Ghisletta, P., & Lindenberger, U. (2008). Evaluating the power of latent growth curve models to detect individual differences in change. Structural Equation Modeling: A Multidisciplinary Journal, 15, 541–563. https://doi.org/10.1080/10705510802338983
   Web of Science ®Google Scholar
• Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945–960. https://doi.org/10.1080/01621459.1986.10478354
   Web of Science ®Google Scholar
• Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models. Sociological Methodology, 18, 449–484. http://www.jstor.org/stable/271055 https://doi.org/10.2307/271055
   Google Scholar
• Hong, G. (2015). Causality in a social world: Moderation, mediation and spill-over. John Wiley & Sons.
   Google Scholar
• Huang, J., & Yuan, Y. (2017). Bayesian dynamic mediation analysis. Psychological Methods, 22, 667–686. https://doi.org/10.1037/met0000073
   PubMed Web of Science ®Google Scholar
• Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15, 309–334. https://doi.org/10.1037/a0020761
   PubMed Web of Science ®Google Scholar
• Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25, 51–71. https://doi.org/10.1214/10-STS321
   Web of Science ®Google Scholar
• Jeffreys, H. (1961). Theory of probability. (3rd ed.). Oxford University Press: Oxford.
   Google Scholar
• Kaplan, D. (2014). Bayesian statistics for the social sciences. Guilford Publications.
   Google Scholar
• Ke, Z., & Wang, L. (2015). Detecting individual differences in change: Methods and comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 22, 382–400. https://doi.org/10.1080/10705511.2014.936096
   Web of Science ®Google Scholar
• Lee, S.-Y., & Song, X.-Y. (2003). Model comparison of nonlinear structural equation models with fixed covariates. Psychometrika, 68, 27–47. https://doi.org/10.1007/BF02296651
   Web of Science ®Google Scholar
• Lee, S.-Y., & Song, X.-Y. (2012). Basic and advanced Bayesian structural equation modeling: With applications in the medical and behavioral sciences. John Wiley & Sons.
   Google Scholar
• Lee, S.-Y., Song, X. Y., & Poon, W.-Y. (2004). Comparison of approaches in estimating interaction and quadratic effects of latent variables. Multivariate Behavioral Research, 39, 37–67. https://doi.org/10.1207/s15327906mbr3901_2
   PubMed Web of Science ®Google Scholar
• Lee, S.-Y., Song, X.-Y., & Tang, N.-S. (2007). Bayesian methods for analyzing structural equation models with covariates, interaction, and quadratic latent variables. Structural Equation Modeling: A Multidisciplinary Journal, 14, 404–434. https://doi.org/10.1080/10705510701301511
   Web of Science ®Google Scholar
• Li, F., Duncan, T. E., & Acock, A. (2000). Modeling interaction effects in latent growth curve models. Structural Equation Modeling: A Multidisciplinary Journal, 7, 497–533. https://doi.org/10.1207/S15328007SEM0704_1
   Web of Science ®Google Scholar
• Lin, S.-H., Young, J. G., Logan, R., & VanderWeele, T. J. (2017). Mediation analysis for a survival outcome with time-varying exposures, mediators, and confounders. Statistics in Medicine, 36, 4153–4166. https://doi.org/10.1002/sim.7426
   PubMed Web of Science ®Google Scholar
• Liu, H., Yuan, K.-H., & Liu, F. (2020). A two-level moderated latent variable model with single level data. Multivariate Behavioral Research, 55, 873–893. https://doi.org/10.1080/00273171.2019.1689350
   PubMed Web of Science ®Google Scholar
• Liu, X. (2022). Causal mediation analysis with the latent growth curve mediation model. [Unpublished doctoral dissertation]. University of Notre Dame.). https://curate.nd.edu/show/1j92g735c0q
   Google Scholar
• Liu, X., Zhang, Z., Valentino, K., & Wang, L. (2023). The impact of omitting confounders in parallel process latent growth curve mediation models: Three sensitivity analysis approaches. Structural Equation Modeling: A Multidisciplinary Journal, 31, 132–150. Advanced Online Publication. https://doi.org/10.1080/10705511.2023.2189551
   PubMed Web of Science ®Google Scholar
• Loh, W. W., Moerkerke, B., Loeys, T., & Vansteelandt, S. (2021). Disentangling indirect effects through multiple mediators without assuming any causal structure among the mediators. Psychological Methods, 27, 982–999. https://doi.org/10.1037/met0000314
   PubMed Web of Science ®Google Scholar
• MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. Taylor & Francis Group/Lawrence Erlbaum Associates.
   Google Scholar
• MacKinnon, D. P., & Fairchild, A. J. (2009). Current directions in mediation analysis. Current Directions in Psychological Science, 18, 16–20. https://doi.org/10.1111/j.1467-8721.2009.01598.x
   PubMed Web of Science ®Google Scholar
• MacKinnon, D. P., Fritz, M. S., Williams, J., & Lockwood, C. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods, 39, 384–389. https://doi.org/10.3758/BF03193007
   PubMed Web of Science ®Google Scholar
• MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83–104. https://doi.org/10.1037/1082-989X.7.1.83
   PubMed Web of Science ®Google Scholar
• MacKinnon, D. P., Valente, M. J., & Gonzalez, O. (2019). The correspondence between causal and traditional mediation analysis: The link is the mediator by treatment interaction. Prevention Science: The Official Journal of the Society for Prevention Research, 21, 147–157. https://doi.org/10.1007/s11121-019-01076-4
   Web of Science ®Google Scholar
• McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577–605. https://doi.org/10.1146/annurev.psych.60.110707.163612
   PubMed Web of Science ®Google Scholar
• McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110–133. https://doi.org/10.2307/1130295
   PubMed Web of Science ®Google Scholar
• McArdle, J. J., & Nesselroade, J. R. (2014). Longitudinal data analysis using structural equation models. American Psychological Association. https://doi.org/10.1037/14440-000
   Google Scholar
• McNeish, D. M. (2016). Using data-dependent priors to mitigate small sample bias in latent growth models: A discussion and illustration using m plus. Journal of Educational and Behavioral Statistics, 41, 27–56. https://doi.org/10.3102/1076998615621299
   Web of Science ®Google Scholar
• Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122. https://doi.org/10.1007/BF02294746
   Web of Science ®Google Scholar
• Miles, C. H. (2023). On the causal interpretation of randomised interventional indirect effects. Journal of the Royal Statistical Society Series B: Statistical Methodology, 85, 1154–1172. Retrieved 2023-10-22, from https://doi.org/10.1093/jrsssb/qkad066
   Web of Science ®Google Scholar
• Miočević, M., Gonzalez, O., Valente, M. J., & MacKinnon, D. P. (2018). A tutorial in Bayesian potential outcomes mediation analysis. Structural Equation Modeling: A Multidisciplinary Journal, 25, 121–136. https://doi.org/10.1080/10705511.2017.1342541
   PubMed Web of Science ®Google Scholar
• Moreno-Betancur, M., & Carlin, J. B. (2018). Understanding interventional effects: A more natural approach to mediation analysis? Epidemiology, 29, 614–617. https://doi.org/10.1097/EDE.0000000000000866
   PubMed Web of Science ®Google Scholar
• Muthén, B., Muthén, L. K., & Asparouhov, T. (2010). Bayesian analysis in Mplus: A brief introduction (Tech. Rep.). Mplus technical report. www. statmodel. com.
   Google Scholar
• Muthén, L. K., & Muthén, B. O. (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. https://doi.org/10.1146/annurev-psych-010814-015258
   Web of Science ®Google Scholar
• Nguyen, T. Q., Schmid, I., & Stuart, E. A. (2021). Clarifying causal mediation analysis for the applied researcher: Defining effects based on what we want to learn. Psychological Methods, 26, 255–271. https://doi.org/10.1037/met0000299
   Web of Science ®Google Scholar
• O'Laughlin, K. D., Martin, M. J., & Ferrer, E. (2018). Cross-sectional analysis of longitudinal mediation processes. Multivariate Behavioral Research, 53, 375–402. https://doi.org/10.1080/00273171.2018.1454822
   PubMed Web of Science ®Google Scholar
• Parker, P. D., Thoemmes, F., Duineveld, J. J., & Salmela-Aro, K. (2015). I wish I had (not) taken a gap-year? The psychological and attainment outcomes of different post-school pathways. Developmental Psychology, 51, 323–333. https://doi.org/10.1037/a0038667
   PubMed Web of Science ®Google Scholar
• Pearl, J. (2001). Direct and indirect effects. In J. Breese & D. Koller (Eds.), UAI’01: Proceedings of the seventeenth conference on uncertainty in artificial intelligence (pp. 411–420). Morgan Kaufmann Publishers. http://dl.acm.org/citation.cfm?id=2074022.2074073
   Google Scholar
• Plummer, M. (2015). JAGS Version 4.0.0 user manual [Computer software manual]. Lyon, France. https://sourceforge.net/projects/mcmc-jags/files/Manuals/4.x/
   Google Scholar
• Preacher, K. J. (2015). Advances in mediation analysis: A survey and synthesis of new developments. Annual Review of Psychology, 66, 825–852. https://doi.org/10.1146/annurev-psych-010814-015258
   PubMed Web of Science ®Google Scholar
• Rast, P., & Hofer, S. M. (2014). Longitudinal design considerations to optimize power to detect variances and covariances among rates of change: Simulation results based on actual longitudinal studies. Psychological Methods, 19, 133–154. https://doi.org/10.1037/a0034524
   PubMed Web of Science ®Google Scholar
• Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143–155. https://doi.org/10.1097/00001648-199203000-00013
   PubMed Web of Science ®Google Scholar
• Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701. https://doi.org/10.1037/h0037350
   Web of Science ®Google Scholar
• Rubin, D. B. (1980). Randomization analysis of experimental data: The fisher randomization test comment. Journal of the American Statistical Association, 75, 591–593. https://doi.org/10.2307/2287653
   Web of Science ®Google Scholar
• Rubin, D. B. (1986). Statistics and causal inference: Comment, which ifs have causal answers. Journal of the American Statistical Association, 81, 961–962. https://doi.org/10.1080/01621459.1986.10478355
   Web of Science ®Google Scholar
• Selig, J. P., & Preacher, K. J. (2009). Mediation models for longitudinal data in developmental research. Research in Human Development, 6, 144–164. https://doi.org/10.1080/15427600902911247
   Web of Science ®Google Scholar
• Singer, J. D., Willett, J. B., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford University Press.
   Google Scholar
• Smid, S. C., McNeish, D., Miočević, M., & van de Schoot, R. (2020). Bayesian versus frequentist estimation for structural equation models in small sample contexts: A systematic review. Structural Equation Modeling: A Multidisciplinary Journal, 27, 131–161. https://doi.org/10.1080/10705511.2019.1577140
   Web of Science ®Google Scholar
• Song, X.-Y., & Lee, S.-Y. (2001). Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations. British Journal of Mathematical and Statistical Psychology, 54, 237–263. https://doi.org/10.1348/000711001159546
   PubMed Web of Science ®Google Scholar
• Speidel, R., Wang, L., Cummings, E. M., & Valentino, K. (2020). Longitudinal pathways of family influence on child self-regulation: The roles of parenting, family expressiveness, and maternal sensitive guidance in the context of child maltreatment. Developmental Psychology, 56, 608–622. https://doi.org/10.1037/dev0000782
   PubMed Web of Science ®Google Scholar
• Sun, R., Zhou, X., & Song, X. (2021). Bayesian causal mediation analysis with latent mediators and survival outcome. Structural Equation Modeling: A Multidisciplinary Journal, 28, 778–790. https://doi.org/10.1080/10705511.2020.1863154
   Web of Science ®Google Scholar
• Sung, J., & Wickrama, K. A. S. (2018). Longitudinal relationship between early academic achievement and executive function: Mediating role of approaches to learning. Contemporary Educational Psychology, 54, 171–183. https://doi.org/10.1016/j.cedpsych.2018.06.010
   Web of Science ®Google Scholar
• Thoemmes, F., MacKinnon, D. P., & Reiser, M. R. (2010). Power analysis for complex mediational designs using Monte Carlo methods. Structural Equation Modeling: A Multidisciplinary Journal, 17, 510–534. https://doi.org/10.1080/10705511.2010.489379
   PubMed Web of Science ®Google Scholar
• Tofighi, D., Hsiao, Y. Y., Kruger, E. S., MacKinnon, D. P., Van Horn, M. L., & Witkiewitz, K. (2019). Sensitivity analysis of the no-omitted confounder assumption in latent growth curve mediation models. Structural Equation Modeling: A Multidisciplinary Journal, 26, 94–109. https://doi.org/10.1080/10705511.2018.1506925
   PubMed Web of Science ®Google Scholar
• Tran, D., Braungart-Rieker, J., & Wang, L. (2021). Indirect effects of parental physical discipline on child literacy through child externalizing and internalizing problems: A longitudinal mediation. Developmental Psychology, 57, 47–59. https://doi.org/10.1037/dev0001129
   PubMed Web of Science ®Google Scholar
• Valente, M. J., Rijnhart, J. J., Smyth, H. L., Muniz, F. B., & MacKinnon, D. P. (2020). Causal mediation programs in R, Mplus, SAS, SPSS, and Stata. Structural Equation Modeling: A Multidisciplinary Journal, 27, 975–984. https://doi.org/10.1080/10705511.2020.1777133
   PubMed Web of Science ®Google Scholar
• Valente, M. J., Rijnhart, J. J. M., & Miočević, M. (2023). Causal mediation effects in single case experimental designs. Psychological Methods, 28, 488–506. https://doi.org/10.1037/met0000497
   PubMed Web of Science ®Google Scholar
• Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure–mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 18, 137–150. https://doi.org/10.1037/a0031034
   PubMed Web of Science ®Google Scholar
• VanderWeele, T. J. (2010). Direct and indirect effects for neighborhood-based clustered and longitudinal data. Sociological Methods & Research, 38, 515–544. https://doi.org/10.1177/0049124110366236
   PubMed Web of Science ®Google Scholar
• VanderWeele, T. J. (2015). Explanation in causal inference: Methods for mediation and interaction. Oxford University Press.
   Google Scholar
• VanderWeele, T. J., & Tchetgen, E. J. T. (2017). Mediation analysis with time varying exposures and mediators. Journal of the Royal Statistical Society Series B: Statistical Methodology, 79, 917–938. https://doi.org/10.1111/rssb.12194
   PubMed Web of Science ®Google Scholar
• VanderWeele, T. J., & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457–468. https://doi.org/10.4310/SII.2009.v2.n4.a7
   Web of Science ®Google Scholar
• Van De Schoot, R., & Depaoli, S., et al. (2014). Bayesian analyses: Where to start and what to report. The European Health Psychologist, 16, 75–84. http://www.ehps.net/ehp/index.php/contents/issue/view/ehp.v16.i2/showToc
   Google Scholar
• Vansteelandt, S., & Daniel, R. M. (2017). Interventional effects for mediation analysis with multiple mediators. Epidemiology, 28, 258–265. https://doi.org/10.1097/EDE.0000000000000596
   PubMed Web of Science ®Google Scholar
• von Soest, T., & Hagtvet, K. A. (2011). Mediation analysis in a latent growth curve modeling framework. Structural Equation Modeling: A Multidisciplinary Journal, 18, 289–314. https://doi.org/10.1080/10705511.2011.557344
   Web of Science ®Google Scholar
• Wang, L., & Preacher, K. J. (2015). Moderated mediation analysis using Bayesian methods. Structural Equation Modeling: A Multidisciplinary Journal, 22, 249–263. https://doi.org/10.1080/10705511.2014.935256
   Web of Science ®Google Scholar
• Wen, Z., Marsh, H. W., & Hau, K.-T. (2002). Interaction effects in growth modeling: A full model. Structural Equation Modeling: A Multidisciplinary Journal, 9, 20–39. https://doi.org/10.1207/S15328007SEM0901_2
   Web of Science ®Google Scholar
• Wen, Z., Marsh, H. W., Hau, K.-T., Wu, Y., Liu, H., & Morin, A. J. S. (2014). Interaction effects in latent growth models: Evaluation of alternative estimation approaches. Structural Equation Modeling: A Multidisciplinary Journal, 21, 361–374. https://doi.org/10.1080/10705511.2014.915205
   Web of Science ®Google Scholar
• Widaman, K. F., Ferrer, E., & Conger, R. D. (2010). Factorial invariance within longitudinal structural equation models: Measuring the same construct across time. Child Development Perspectives, 4, 10–18. https://doi.org/10.1111/j.1750-8606.2009.00110.x
   PubMed Web of Science ®Google Scholar
• Willett, J. B. (1989). Some results on reliability for the longitudinal measurement of change: Implications for the design of studies of individual growth. Educational and Psychological Measurement, 49, 587–602. https://doi.org/10.1177/0013164489049003
   Web of Science ®Google Scholar
• Wu, W., West, S. G., & Hughes, J. N. (2008). Effect of retention in first grade on children’s achievement trajectories over 4 years. Journal of Educational Psychology, 100, 727–740. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2662684/ https://doi.org/10.1037/a0013098
   PubMed Web of Science ®Google Scholar
• Yuan, Y., & MacKinnon, D. P. (2009). Bayesian mediation analysis. Psychological Methods, 14, 301–322. https://doi.org/10.1037/a0016972
   PubMed Web of Science ®Google Scholar
• Zeng, S., Rosenbaum, S., Alberts, S. C., Archie, E. A., & Li, F. (2021). Causal mediation analysis for sparse and irregular longitudinal data. The Annals of Applied Statistics, 15, 747–767. Publisher: Institute of Mathematical Statistics) https://doi.org/10.1214/20-AOAS1427
   Web of Science ®Google Scholar
• Zheng, W., & van der Laan, M. (2017). Longitudinal mediation analysis with time-varying mediators and exposures, with application to survival outcomes. Journal of Causal Inference, 5, 20160006. https://doi.org/10.1515/jci-2016-0006
   PubMed Web of Science ®Google Scholar
• Zhong, M., Huang, X., Huebner, E. S., & Tian, L. (2021). Association between bullying victimization and depressive symptoms in children: The mediating role of self-esteem. Journal of Affective Disorders, 294, 322–328. https://doi.org/10.1016/j.jad.2021.07.016
   PubMed Web of Science ®Google Scholar
• Zhou, X., & Song, X. (2023). Causal mediation analysis for multivariate longitudinal data and survival outcomes. Structural Equation Modeling: A Multidisciplinary Journal, 30, 749–760. https://doi.org/10.1080/10705511.2022.2162406
   Web of Science ®Google Scholar