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Original Articles

Evaluation of Structural Relationships in Autoregressive Cross-Lagged Models Under Longitudinal Approximate Invariance:A Bayesian Analysis

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References

  • Arruda, E. H., & Bentler, P. M. (2017). A regularized GLS for structural equation modeling. Structural Equation Modeling, 24(5), 657–665. doi:10.1080/10705511.2017.1318392
  • Asparouhov, T., & Muthén, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling, 21(4), 495–508. doi:10.1080/10705511.2014.919210
  • Asparouhov, T., & Muthén, B. O. (2010). Bayesian analysis using Mplus: Technical implementation. Mplus Technical Report. Retrieved from http://statmodel2.com/download/Bayes3.pdf
  • Bandalos, D. L., & Leite, W. L. (2013). The use of Monte Carlo studies in structural equation modeling research. In G. R. Hancock, & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 625–666). Charlotte, NC: IAP.
  • Berry, D., & Willoughby, M. T. (2016). On the practical interpretability of cross‐lagged panel models: Rethinking a developmental workhorse. Child Development, 88(4), 1186–1206. doi:10.1111/cdev.12660
  • Bishop, J., Geiser, C., & Cole, D. A. (2015). Modeling latent growth with multiple indicators: A comparison of three approaches. Psychological Methods, 20(1), 43–62. doi:10.1037/met0000018
  • Bohrnstedt, G. W. (1969). Observations on the measurement of change. Sociological Methodology, 1, 113–133. doi:10.2307/270882
  • Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NY: John Wiley & Sons.
  • Browne, M. W. (2000). Cross-validation methods. Journal of Mathematical Psychology, 44(1), 108–132. doi:10.1006/jmps.1999.1279
  • Campbell, D. T. (1963). From description to experimentation: Interpreting trends as quasi-experiments. In C. W. Harris (Ed.), Problems in measuring change (pp. 212–242). Madison, WI: University of Wisconsin Press.
  • Carvalho, C. M., Polson, N. G., & Scott, J. G. (2010). The horseshoe estimator for sparse signals. Biometrika, 97(2), 465–480. doi:10.1093/biomet/asq017
  • Chan, D. (1998). The conceptualization and analysis of change over time: An integrative approach incorporating longitudinal mean and covariance structures analysis (LMACS) and multiple indicator latent growth modeling (MLGM). Organizational Research Methods, 1(4), 421–483. doi:10.1177/109442819814004
  • Cudeck, R., & O’Dell, L. L. (1994). Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations. Psychological Bulletin, 115(3), 475–487. doi:10.1037/0033-2909.115.3.475
  • Curran, P. J., & Bauer, D. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models of change. Annual Review of Psychology, 62, 583–619. doi:10.1146/annurev.psych.093008.100356
  • Deboeck, P. R., & Preacher, K. J. (2016). No need to be discrete: A method for continuous time mediation analysis. Structural Equation Modeling, 23(1), 61–75. doi:10.1080/10705511.2014.973960
  • Duncan, O. D. (1969). Some linear models for two-wave, two-variable panel analysis. Psychological Bulletin, 72(3), 177–182. doi:10.1037/h0027876
  • Dunson, D. B., Palomo, J., & Bollen, K. A. (2005). Bayesian structural equation modeling. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.190.5937&rep=rep1&type=pdf
  • Ferrer, E., Balluerka, N., & Widaman, K. F. (2008). Factorial invariance and the specification of second-order latent growth models. Methodology, 4(1), 22–36. doi:10.1027/1614-2241.4.1.22
  • Gelman, A. (2006a). Multilevel (hierarchical) modeling: What it can and cannot do. Technometrics, 48(3), 432–435. doi:10.1198/004017005000000661
  • Gelman, A. (2006b). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515–534. doi:10.1214/06-BA117A
  • Gelman, A., Meng, X. L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6(4), 733–807.
  • Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–472. doi:10.1214/ss/1177011136
  • George, E. I., & McCulloch, R. E. (1993). Variable selection via Gibbs sampling. Journal of the American Statistical Association, 88(423), 881–889. doi:10.1080/01621459.1993.10476353
  • Gollob, H. F., & Reichardt, C. S. (1987). Taking account of time lags in causal models. Child Development, 28(1), 80–92. doi:10.2307/1130293
  • Hakanen, J. J., Schaufeli, W. B., & Ahola, K. (2008). The job demands-resources model: A three-year cross-lagged study of burnout, depression, commitment, and work engagement. Work & Stress, 22(3), 224–241. doi:10.1080/02678370802379432
  • Hamaker, E. L. (2012). Why researchers should think “within-person”: A paradigmatic rationale. In M. R. Mehl, & T. S. Conner (Eds.), Handbook of research methods for studying daily life (pp. 43–61). New York, NY:Guilford Press.
  • Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20(1), 102–116. doi:10.1037/a0038889
  • Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67. doi:10.1080/00401706.1970.10488634
  • Hong, S., Yoo, S.-K., You, S., & Wu, -C.-C. (2010). The reciprocal relationship between parental involvement and mathematics achievement: Autoregressive cross-lagged modeling. The Journal of Experimental Education, 78(4), 419–439. doi:10.1080/00220970903292926
  • Hoogland, J. J., & Boomsma, A. (1998). Robustness studies in covariance structure modeling: An overview and a meta-analysis. Sociological Methods & Research, 26(3), 329–367. doi:10.1177/0049124198026003003
  • Huang, P., Chen, H., & Weng, L. (2017). A penalized likelihood method for structural equation modeling. Psychometrika, 82(2), 329–354. doi:10.1007/s11336-017-9566-9
  • Ishwaran, H., & Rao, J. S. (2005). Spike and slab variable selection: Frequentist and Bayesian strategies. Annals of Statistics, 33(2), 730–773. doi:10.1214/009053604000001147
  • Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling, 23(4), 555–566. doi:10.1080/10705511.2016.1154793
  • Jöreskog, K. G. (1974). Analyzing psychological data by structural analysis of covariance matrices. In R. C. Atkinson, D. H. Krantz, R. D. Luce, & P. Suppas (Eds.), Contemporary developments in mathematical psychology (Vol. 2, pp. 1–56). San Francisco, CA: Freeman.
  • Jöreskog, K. G. (1979). Statistical models and methods for analysis of longitudinal data. In K. G. Jöreskog, & D. Sörbom (Eds.), Advances in factor analysis and structural equation models (pp. 129–169). Cambridge, MA: Abt.
  • Kenny, D. A., & Milan, S. (2012). Identification: A non-technical discussion of a technical issue. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 145–163). New York, NY: Guilford Press.
  • Kyung, M., Gill, J., Ghosh, M., & Casella, G. (2010). Penalized regression, standard errors, and Bayesian lassos. Bayesian Analysis, 5(2), 369–411. doi:10.1214/10-BA607
  • Leite, W. L. (2007). A comparison of latent growth models for constructs measured by multiple items. Structural Equation Modeling, 14(4), 581–610. doi:10.1080/10705510701575438
  • Liang, X. (2014). The estimation and specification search of structural equation modeling using frequentist and Bayesian methods. Florida State University Libraries. Retrieved from http://diginole.lib.fsu.edu/islandora/object/fsu%3A254459
  • 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. doi:10.1080/00273171.2016.1168279
  • MacCallum, R. C. (1986). Specification searches in covariance structure modeling. Psychological Bulletin, 100(1), 107–120. doi:10.1037/0033-2909.100.1.107
  • Maxwell, S. E., Cole, D. A., & Mitchell, M. A. (2011). Bias in cross-sectional analyses of longitudinal mediation: Partial and complete mediation under an autoregressive model. Multivariate Behavioral Research, 46(5), 816–841. doi:10.1080/00273171.2011.606716
  • Mayer, L. S. (1986). On cross-lagged panel models with serially correlated errors. Journal of Business & Economic Statistics, 4(3), 347–357.
  • McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577–605. doi:10.1146/annurev.psych.60.110707.163612
  • Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525–543. doi:10.1007/BF02294825
  • Millsap, R. E. (2011). Statistical approaches to measurement invariance. New York, NY: Taylor and Francis Group.
  • Millsap, R. E., & Cham, H. (2012). Investigating factorial invariance in longitudinal data. In B. Laursen, T. D. Little, & N. A. Card (Eds.), Handbook of developmental research methods (pp. 109–126). New York, NY: Guilford.
  • Mitchell, T. J., & Beauchamp, J. J. (1988). Bayesian variable selection in linear regression. Journal of the American Statistical Association, 83(404), 1023–1032. doi:10.1080/01621459.1988.10478694
  • Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313–335. doi:10.1037/a0026802
  • Muthén, B. O., & Asparouhov, T. (2013a). BSEM measurement invariance analysis. Mplus Web Notes 17. Retrieved from https://www.statmodel.com/examples/webnotes/webnote17.pdf
  • Muthén, B. O., & Asparouhov, T. (2013b). New methods for the study of measurement invariance with many groups. Retrieved from http://statmodel2.com/download/PolAn.pdf
  • O’Hara, R. B., & Sillanpää, M. J. (2009). A review of Bayesian variable selection methods: What, how and which. Bayesian Analysis, 4(1), 85–117. doi:10.1214/09-BA403
  • Olivera-Aguilar, M. (2013). Impact of violations of longitudinal measurement invariance in latent growth models and autoregressive quasi-simplex models. Arizona State University. Retrieved from https://repository.asu.edu/items/18699
  • Oud, J. H., & Delsing, M. J. (2010). Continuous time modeling of panel data by means of SEM. In K. Van Montfort, J. H. Oud, & A. Satorra (Eds.), Longitudinal research with latent variables (pp. 201–244). Berlin, Heidelberg: Springer.
  • Park, T., & Casella, G. (2008). The bayesian lasso. Journal of the American Statistical Association, 103(482), 681–686. doi:10.1198/016214508000000337
  • Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–164. doi:10.2307/271063
  • Schlueter, E., Davidov, E., & Schmidt, P. (2007). Applying autoregressive cross-lagged and latent growth curve models to a three-wave panel study. In K. Van Montfort, J. Oud, & A. Satorra (Eds.), Longitudinal models in the behavioral and related sciences (pp. 315–336). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Schuurman, N., Grasman, R., & Hamaker, E. (2016). A comparison of inverse-wishart prior specifications for covariance matrices in multilevel autoregressive models. Multivariate Behavioral Research, 51(2–3), 185–206. doi:10.1080/00273171.2015.1065398
  • Schuurman, N. K., Ferrer, E., De Boer-Sonnenschein, M., & Hamaker, E. L. (2016). How to compare cross-lagged associations in a multilevel autoregressive model. Psychological Methods, 21(2), 206. doi:10.1037/met0000062
  • Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. doi:10.1214/aos/1176344136
  • Selig, J. P., & Little, T. D. (2012). Autoregressive and cross-lagged panel analysis for longitudinal data. In B. Laursen, T. D. Little, & N. A. Card (Eds.), Handbook of developmental research methods (pp. 265–278). New York, NY: The Guilford Press.
  • Song, T. M., An, J.-Y., Hayman, L. L., Kim, G. S., Lee, J. Y., & Jang, H. L. (2012). A three-year autoregressive cross-lagged panel analysis on nicotine dependence and average smoking. Healthcare Informatics Research, 18(2), 115–124. doi:10.4258/hir.2012.18.2.115
  • Sörbom, D. (1989). Model modification. Psychometrika, 54(3), 371–384. doi:10.1007/BF02294623
  • 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
  • Thompson, M. S., & Green, S. B. (2006). Evaluating between-group differences in latent variable means. In G. R. Hancock, & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 163–218). Charlotte, NC: IAP.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288.
  • Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301–320. doi:10.1111/rssb.2005.67.issue-2
  • Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of Computational and Graphical Statistics, 15(2), 265–286. doi:10.1198/106186006X113430

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