Performance of Model Fit and Selection Indices for Bayesian Piecewise Growth Modeling with Missing Data

References

• Agresti, A. (2012). Categorical data analysis (3rd ed.). Wiley.
   Google Scholar
• Asparouhov, T., Muthén, B., & Morin, A. J. (2015). Bayesian structural equation modeling with cross-loadings and residual covariances: Comments on stromeyer et al. Journal of Management, 41, 1561–1577. https://doi.org/10.1177/0149206315591075
   Google Scholar
• Asparouhov, T., & Muthén, B. O. (2010). Bayesian analysis using Mplus: Technical implementation. Technical Report.
   Google Scholar
• Asparouhov, T., & Muthén, B. (2021). Advances in Bayesian model fit evaluation for structural equation models. Structural Equation Modeling, 28, 1–14. https://doi.org/10.1080/10705511.2020.1764360
   Web of Science ®Google Scholar
• Blozis, S. A. (2007). On fitting nonlinear latent curve models to multiple variables measured longitudinally. Structural Equation Modeling, 14, 179–201. https://doi.org/10.1080/10705510709336743
   Web of Science ®Google Scholar
• Cain, M. K., & Zhang, Z. (2019). Fit for a Bayesian: An evaluation of PPP and DIC for structural equation modeling. Structural Equation Modeling, 26, 39–50. https://doi.org/10.1080/10705511.2018.1490648
   Web of Science ®Google Scholar
• Can, S., van de Schoot, R., & Hox, J. (2015). Collinear latent variables in multilevel confirmatory factor analysis: A comparison of maximum likelihood and Bayesian estimations. Educational and Psychological Measurement, 75, 406–427. https://doi.org/10.1177/0013164414547959
   PubMed Web of Science ®Google Scholar
• Celeux, G., Forbes, F., Robert, C. P., & Titterington, D. M. (2006). Deviance information criteria for missing data models. Bayesian Analysis, 1, 651–673. https://doi.org/10.1214/06-BA122
   Google Scholar
• Chung, J. M., Hutteman, R., van Aken, M. A., & Denissen, J. J. (2017). High, low, and in between: Self-esteem development from middle childhood to young adulthood. Journal of Research in Personality, 70, 122–133. https://doi.org/10.1016/j.jrp.2017.07.001
   Web of Science ®Google Scholar
• Cohen, J. (2002). Statistical power analysis for the behavioral sciences. Routledge.
   Google Scholar
• Cudeck, R., & Codd, C. L. (2012). A template for describing individual differences in longitudinal data, with application to the connection between learning and ability. In J. R. Harring and G. R. Hancock (Eds.), Advances in longitudinal methods in the social and behavioral sciences (pp. 3–24). IAP Information Age Publishing.
   Google Scholar
• Daniels, M. J., & Hogan, J. W. (2008). Missing data in longitudinal studies: Strategies for Bayesian modeling and sensitivity analysis. Chapman and hall/CRC.
   Google Scholar
• Depaoli, S., Jia, F., & Heo, I. (2023). Detecting model misspecifications in Bayesian piecewise growth models. Structural Equation Modeling, 30, 574–591. https://doi.org/10.1080/10705511.2022.2144865
   Web of Science ®Google Scholar
• Diallo, T. M. O., Morin, A. J. S., & D, P. P. (2014). Statistical power of latent growth curve models to detect quadratic growth. Behavior Research Methods, 46, 357–371. https://doi.org/10.3758/s13428-013-0395-1
   PubMed Web of Science ®Google Scholar
• Edwards, K. D., & Konold, T. R. (2023). Impact of informative priors on model fit indices in Bayesian confirmatory factor analysis. Structural Equation Modeling, 30, 272–283. https://doi.org/10.1080/10705511.2022.2126359
   Web of Science ®Google Scholar
• Enders, C. K. (2011). Missing not at random models for latent growth curve analyses. Psychological Methods, 16, 1–16. https://doi.org/10.1037/a0022640
   PubMed Web of Science ®Google Scholar
• Enders, C. K., & Mansolf, M. (2018). Assessing the fit of structural equation models with multiply imputed data. Psychological Methods, 23, 76–93. https://doi.org/10.1037/met0000102
   PubMed Web of Science ®Google Scholar
• Fay, D. M., Levy, R., & Schulte, A. C. (2022). Model criticism of growth curve models via posterior predictive model checking. The Journal of Experimental Education, 90, 191–212. https://doi.org/10.1080/00220973.2020.1711697
   Web of Science ®Google Scholar
• Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural Equation Modeling, 15, 513–533. https://doi.org/10.1080/10705510802154349
   Web of Science ®Google Scholar
• Garnier-Villarreal, M., & Jorgensen, T. D. (2020). Adapting fit indices for Bayesian structural equation modeling: Comparison to maximum likelihood. Psychological Methods, 25, 46–70. https://doi.org/10.1037/met0000224
   PubMed Web of Science ®Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd edition). CRC Press Boca.
   Google Scholar
• Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24, 997–1016. https://doi.org/10.1007/s11222-013-9416-2
   Web of Science ®Google Scholar
• Grimm, K. J., Ram, N., & Estabrook, R. (2016). Growth modelling: Structural equation and multilevel modelling approaches. Guilford Publications.
   Google Scholar
• Grimm, K. J., Ram, N., & Hamagami, F. (2011). Nonlinear growth curves in developmental research. Child Development, 82, 1357–1371. https://doi.org/10.1111/j.1467-8624.2011.01630.x
   PubMed Web of Science ®Google Scholar
• Gustavson, K., von Soest, T., Karevold, E., & Røysamb, E. (2012). Attrition and generalizability in longitudinal studies: Findings from a 15-year population-based study and a Monte Carlo simulation study. BMC Public Health, 12, 918. https://doi.org/10.1186/1471-2458-12-918
   PubMed Web of Science ®Google Scholar
• Harring, J. R., Strazzeri, M. M., & Blozis, S. A. (2021). Piecewise latent growth models: Beyond modeling linear-linear processes. Behavior Research Methods, 53, 593–608. https://doi.org/10.3758/s13428-020-01420-5
   PubMed Web of Science ®Google Scholar
• Hoofs, H., van de Schoot, R., Jansen, N. W., & Kant, I. (2018). Evaluating model fit in Bayesian confirmatory factor analysis with large samples: Simulation study introducing the BRMSEA. Educational and Psychological Measurement, 78, 537–568. https://doi.org/10.1177/0013164417709314
   PubMed Web of Science ®Google Scholar
• Hu, B. Y., Fan, X., Wu, Y., LoCasale-Crouch, J., & Song, Z. (2020). Teacher–child interaction quality and Chinese children’s academic and cognitive development: New perspectives from piecewise growth modelling. Early Childhood Research Quarterly, 51, 242–255. https://doi.org/10.1016/j.ecresq.2019.10.003
   Web of Science ®Google Scholar
• Jaggars, S. S., & Xu, D. (2016). Examining the earnings trajectories of community college students using a piecewise growth curve modelling approach. Journal of Research on Educational Effectiveness, 9, 445–471. https://doi.org/10.1080/19345747.2015.1116033
   Web of Science ®Google Scholar
• Jefferys, W. H., & Berger, J. O. (1992). Ockham’s razor and Bayesian analysis. American Scientist, 80, 64–72.
   Web of Science ®Google Scholar
• Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795. https://doi.org/10.1080/01621459.1995.10476572
   Web of Science ®Google Scholar
• Kohli, N., & Harring, J. R. (2013). Modeling growth in latent variables using a piecewise function. Multivariate Behavioral Research, 48, 370–397. https://doi.org/10.1080/00273171.2013.778191
   PubMed Web of Science ®Google Scholar
• Kohli, N., Hughes, J., Wang, C., Zopluoglu, C., & Davison, M. L. (2015). Fitting a linear–linear piecewise growth mixture model with unknown knots: A comparison of two common approaches to inference. Psychological Methods, 20, 259–275. https://doi.org/10.1037/met0000034
   PubMed Web of Science ®Google Scholar
• Kohli, N., Peralta, Y., & Bose, M. (2019). Piecewise random-effects modeling software programs. Structural Equation Modeling, 26, 156–164. https://doi.org/10.1080/10705511.2018.1516507
   Web of Science ®Google Scholar
• Kroese, F. M., Adriaanse, M. A., Vinkers, C. D., van de Schoot, R., & de Ridder, D. T. (2013). The effectiveness of a proactive coping intervention targeting self-management in diabetes patients. Psychology & Health, 29, 110–125. https://doi.org/10.1080/08870446.2013.841911
   PubMed Web of Science ®Google Scholar
• Kwok, O.-M., Luo, W., & West, S. G. (2010). Using modification indexes to detect turning points in longitudinal data: A Monte Carlo study. Structural Equation Modeling, 17, 216–240. https://doi.org/10.1080/10705511003659359
   Web of Science ®Google Scholar
• Lee, I. H., & Rojewski, J. W. (2009). Development of occupational aspiration prestige: A piecewise latent growth model of selected influences. Journal of Vocational Behavior, 75, 82–90. https://doi.org/10.1016/j.jvb.2009.03.006
   Web of Science ®Google Scholar
• Lee, S.-Y. (2007). Structural equation modelling: A Bayesian approach. John Wiley & Sons.
   Google Scholar
• Leite, W. L., & Stapleton, L. M. (2011). Detecting growth shape misspecifications in latent growth models: an evaluation of fit indexes. The Journal of Experimental Education, 79, 361–381. https://doi.org/10.1080/00220973.2010.509369
   Web of Science ®Google Scholar
• Li, F., Duncan, T. E., & Hops, H. (2001). Examining developmental trajectories in adolescent alcohol use using piecewise growth mixture modelling analysis. Journal of Studies on Alcohol, 62, 199–210. https://doi.org/10.15288/jsa.2001.62.199
   PubMed Web of Science ®Google Scholar
• Li, G., Hou, G., Xie, G., Yang, D., Jian, H., & Wang, W. (2019). Trajectories of self-rated health of Chinese elders: a piecewise growth model analysis. Frontiers in Psychology, 10, 583. https://doi.org/10.3389/fpsyg.2019.00583
   PubMed Web of Science ®Google Scholar
• Lock, E. F., Kohli, N., & Bose, M. (2018). Detecting multiple random changepoints in Bayesian piecewise growth mixture models. Psychometrika, 83, 733–750. https://doi.org/10.1007/s11336-017-9594-5
   PubMed Web of Science ®Google Scholar
• Lu, Z. L., & Zhang, Z. (2021). Bayesian approach to non-ignorable missingness in latent growth models. Journal of Behavioral Data Science, 1, 1–30. https://doi.org/10.35566/jbds/v1n2/p1
   Google Scholar
• Lu, Z. L., Zhang, Z., & Lubke, G. (2011). Bayesian inference for growth mixture models with latent class dependent missing data. Multivariate Behavioral Research, 46, 567–597. https://doi.org/10.1080/00273171.2011.589261
   PubMed Web of Science ®Google Scholar
• Marcoulides, K. M. (2018). Automated latent growth curve model fitting: A segmentation and knot selection approach. Structural Equation Modeling, 25, 687–699. https://doi.org/10.1080/10705511.2018.1424548
   Web of Science ®Google Scholar
• Muthén, B. O. (2010). Bayesian analysis in Mplus: A brief introduction. Technical Report.
   Google Scholar
• Muthén, L. K., & Muthén, B. (2017). Mplus user’s guide: Statistical analysis with latent variables, user’s guide. Muthén & Muthén.
   Google Scholar
• Nicholson, J. S., Deboeck, P. R., & Howard, W. (2017). Attrition in developmental psychology: A review of modern missing data reporting and practices. International Journal of Behavioral Development, 41, 143–153. https://doi.org/10.1177/0165025415618275
   Web of Science ®Google Scholar
• Ning, L., & Luo, W. (2017). Specifying turning point in piecewise growth curve models: Challenges and solutions. Frontiers in Applied Mathematics and Statistics, 3. https://doi.org/10.3389/fams.2017.00019
   PubMedGoogle Scholar
• Ortega-Azurduy, S., Tan, F., & Berger, M. (2008). The effect of dropout on the efficiency of d-optimal designs of linear mixed models. Statistics in Medicine, 27, 2601–2617. https://doi.org/10.1002/sim.3108
   PubMed Web of Science ®Google Scholar
• Patrick, M. E., & Schulenberg, J. E. (2011). How trajectories of reasons for alcohol use relate to trajectories of binge drinking: National panel data spanning late adolescence to early adulthood. Developmental Psychology, 47, 311–317. https://doi.org/10.1037/a0021939
   PubMed Web of Science ®Google Scholar
• Ram, N., & Grimm, K. (2007). Using simple and complex growth models to articulate developmental change: Matching theory to method. International Journal of Behavioral Development, 31, 303–316. https://doi.org/10.1177/0165025407077751
   Web of Science ®Google Scholar
• Raudenbush, S. W., & Liu, X.-F. (2001). Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6, 387–401. https://doi.org/10.1037/1082-989X.6.4.387
   PubMed Web of Science ®Google Scholar
• Rhemtulla, M., Jia, F., Wu, W., & Little, T. D. (2014). Planned missing designs to optimize the efficiency of latent growth parameter estimates. International Journal of Behavioral Development, 38, 423–434. https://doi.org/10.1177/0165025413514324
   Web of Science ®Google Scholar
• Rosseel, Y. (2012). lavaan: An R package for structural equation modelling. Journal of Statistical Software, 48, 1–36. https://doi.org/10.18637/jss.v048.i02
   Web of Science ®Google Scholar
• Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464. https://doi.org/10.1214/aos/1176344136
   Web of Science ®Google Scholar
• Serang, S., Zhang, Z., Helm, J., Steele, J. S., & Grimm, K. J. (2015). Evaluation of a Bayesian approach to estimating nonlinear mixed-effects mixture models. Structural Equation Modeling, 22, 202–215. https://doi.org/10.1080/10705511.2014.937322
   Web of Science ®Google Scholar
• Shi, D., DiStefano, C., Zheng, X., Liu, R., & Jiang, Z. (2021). Fitting latent growth models with small sample sizes and non-normal missing data. International Journal of Behavioral Development, 45, 179–192. https://doi.org/10.1177/0165025420979365
   PubMed Web of Science ®Google Scholar
• Shi, D., Lee, T., & Maydeu-Olivares, A. (2019). Understanding the model size effect on SEM fit indices. Educational and Psychological Measurement, 79, 310–334. https://doi.org/10.1177/0013164418783530
   PubMed Web of Science ®Google Scholar
• Shin, T., Davison, M. L., & Long, J. D. (2017). Maximum likelihood versus multiple imputation for missing data in small longitudinal samples with nonnormality. Psychological Methods, 22, 426–449. https://doi.org/10.1037/met0000094
   PubMed Web of Science ®Google Scholar
• Smid, S. C., Depaoli, S., & Van De Schoot, R. (2020). Predicting a distal outcome variable from a latent growth model: ML versus Bayesian estimation. Structural Equation Modeling, 27, 169–191. https://doi.org/10.1080/10705511.2019.1604140
   Web of Science ®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, 583–639. https://doi.org/10.1111/1467-9868.00353
   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, 528–540. https://doi.org/10.1080/01621459.1987.10478458
   Web of Science ®Google Scholar
• Twisk, J., & de Vente, W. (2002). Attrition in longitudinal studies: How to deal with missing data. Journal of Clinical Epidemiology, 55, 329–337. https://doi.org/10.1016/s0895-4356(01)00476-0
   PubMed Web of Science ®Google Scholar
• van Buuren, S. (2018). Flexible imputation of missing data. CRC Press.
   Google Scholar
• Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C. (2021). Rank-normalization, folding, and localization: an improved R for assessing convergence of MCMC (with discussion). Bayesian Analysis, 16, 667–718. https://doi.org/10.1214/20-BA1221
   Google Scholar
• Winter, S. D., & Depaoli, S. (2022a). Performance of model fit and selection indices for Bayesian structural equation modelling with missing data. Structural Equation Modeling, (0), 1–22. https://doi.org/10.1080/10705511.2022.2164286
   Google Scholar
• Winter, S. D., & Depaoli, S. (2022b). Sensitivity of Bayesian model fit indices to the prior specification of latent growth models. Structural Equation Modeling, 29, 667–686. https://doi.org/10.1080/10705511.2022.2032078
   Web of Science ®Google Scholar
• Wu, W., & Jia, F. (2021). Applying planned missingness designs to longitudinal panel studies in developmental science: An overview. New Directions for Child and Adolescent Development, 2021, 35–63. https://doi.org/10.1002/cad.20391
   PubMedGoogle Scholar
• Wu, W., Jia, F., Rhemtulla, M., & Little, T. D. (2016). Search for efficient complete and planned missing data designs for analysis of change. Behavior Research Methods, 48, 1047–1061. https://doi.org/10.3758/s13428-015-0629-5
   PubMed Web of Science ®Google Scholar
• Wu, W., & West, S. G. (2010). Sensitivity of fit indices to misspecification in growth curve models. Multivariate Behavioral Research, 45, 420–452. https://doi.org/10.1080/00273171.2010.483378
   PubMed 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, 183–201. https://doi.org/10.1037/a0015858
   PubMed Web of Science ®Google Scholar
• Yu, C.-Y. (2002). Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes [Doctoral dissertation, University of California, Los Angeles]. ProQuest Dissertations & Theses Global.
   Google Scholar
• Zhang, Z., Hamagami, F., Lijuan Wang, L., Nesselroade, J. R., & Grimm, K. J. (2007). Bayesian analysis of longitudinal data using growth curve models. International Journal of Behavioral Development, 31, 374–383. https://doi.org/10.1177/0165025407077764
   Web of Science ®Google Scholar