A Comparison of Regularized Maximum-Likelihood, Regularized 2-Stage Least Squares, and Maximum-Likelihood Estimation with Misspecified Models, Small Samples, and Weak Factor Structure

References

• Bentler, P. M., & Chou, C. P. (1987). Practical issues in structural modeling. Sociological Methods & Research, 16(1), 78–117. 10.1177/0049124187016001004
   Web of Science ®Google Scholar
• Bollen, K. A. (1996). An alternative two stage least squares (2SLS) estimator for latent variable equations. Psychometrika, 61(1), 109–121.
   Web of Science ®Google Scholar
• Bollen, K. A., & Bauer, D. J. (2004). Automating the selection of model-implied instrumental variables. Sociological Methods & Research, 32(4), 425–452.
   Web of Science ®Google Scholar
• Bollen, K. A., Kirby, J. B., Curran, P. J., Paxton, P., & Chen, F. (2007). Latent variable models under misspecification. Two-stage least squares (2SLS) and maximum likelihood (ML) estimators. Sociological Methods & Research, 36(1), 48–86.
   Web of Science ®Google Scholar
• Brandt, H., Cambria, J., & Kelava, A. (2018). An adaptive Bayesian lasso approach with spike-and-slab priors to identify multiple linear and nonlinear effects in structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 25(6), 946–960.
   Web of Science ®Google Scholar
• Brown, T. A. (2013). Confirmatory factor analysis for applied research. Guilford.
   Google Scholar
• Evans, D. E., & Rothbart, M. K. (2007). Development of a model for adult temperament. Journal of Research in Personality, 41(4), 868–888.
   Web of Science ®Google Scholar
• Fisher, Z., Bollen, K., Gates, K., & Ronkko, M. (2019). MIIVsem: Model implied instrumental variable estimation of structural equation models. R software library.
   Google Scholar
• Fok, C. C. T., Henry, D., & Allen, J. (2015). Maybe small is too small a term: Introduction to advancing small sample prevention science. Prevention Science, 16(7), 943–949.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. doi:10.1145/1401890.1401893
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., Tibshirani, R., Simon, N., Narasimhan, B., & Qian, J. (2019). Glmnet: Lasso and elastic-net regularized generalized linear models. R software package.
   Google Scholar
• Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67.
   Web of Science ®Google Scholar
• Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3(4), 424–453.
   Web of Science ®Google Scholar
• Huang, P. H., Chen, H., & Weng, L. J. (2017). A penalized likelihood method for structural equation modeling. Psychometrika, 82(2), 329–354.
   PubMed Web of Science ®Google Scholar
• Jacobucci, R., Brandmaier, A. M., & Kievit, R. (2018). Variable selection in structural equation models with regularized MIMIC models. PsyArXiv. 10.31234/osf.io/bxzjf
   Google Scholar
• Jacobucci, R., Kievit, R., & Brandmaier, A. (2019). A practical guide to variable selection in structural equation modeling by using regularized multiple-indicators, multiple-causes models. Advances in Methods and Practices in Psychological Science, 2(1), 55–76.
   PubMedGoogle Scholar
• Jacobucci, R. (2017). regsem: Regularized structural equation modeling. arXiv Preprint arXiv. https://arxiv.org/abs/1703.08489
   Google Scholar
• Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 555–566.
   PubMed Web of Science ®Google Scholar
• Jung, S. (2013). Structural equation modeling with small sample sizes using two-stage ridge least-squares estimation. Behavior Research Methods, 45(1), 75–81. 10.3758/s13428-012-0206-0
   PubMed Web of Science ®Google Scholar
• Kaplan, D. (1988). The impact of specification error on the estimation, testing, and improvement of structural equation models. Multivariate Behavioral Research, 23(1), 69–86.
   PubMed Web of Science ®Google Scholar
• Kelcey, B. (2019). A robust alternative estimator for small to moderate sample SEM: Bias-corrected factor score path analysis. Addictive Behaviors, 94, 83–98.
   PubMed Web of Science ®Google Scholar
• Kline, R. B. (2016). Methodology in the social sciences. Principles and practice of structural equation modeling (4th ed.). Guilford Press.
   Google Scholar
• Liang, X., & Jacobucci, R. (2019, December 12). Regularized structural equation modeling to detect measurement bias in complex SEM models [Paper presentation]. American Educational Resource Conference, Toronto, ON, Canada.
   Google Scholar
• Molinaro, A. M., Simon, R., & Pfeiffer, R. M. (2005). Prediction error estimation: A comparison of resampling methods. Bioinformatics, 21(15), 3301–3307. doi:10.1093/bioinformatics/bti499
   PubMed Web of Science ®Google Scholar
• Muthèn, L. K., & Muthèn, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9(4), 599–620. 10.1207/S15328007SEM0904_8
   Web of Science ®Google Scholar
• R Core Team. (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
   Google Scholar
• Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/http://hdl.handle.net/1854/LU-3099674
   Web of Science ®Google Scholar
• Seo, D. G., & Jung, S. (2017). A study on the performance of three methods of estimation in SEM under conditions of misspecification and small sample sizes. Journal of the Korean Data and Information Science Society, 28(5), 1153–1165. 10.7465/jkdi.2017.28.5.1153
   Google Scholar
• Serang, S., Jacobucci, R., Brimhall, K. C., & Grimm, K. J. (2017). HHS Public Access. Structural Equation Modeling: A Multidisciplinary Journal, 24(5), 733–744. 10.1186/s40945-017-0033-9
   PubMed Web of Science ®Google Scholar
• Shaunessy, E., & Suldo, S. M. (2010). Strategies used by intellectually gifted students to cope with stress during their participation in a high school International Baccalaureate program. Gifted Child Quarterly, 54(2), 127–137.
   Web of Science ®Google Scholar
• Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288. 10.1111/j.2571-6161.1996.tb02080.x
   Google Scholar
• Tibshirani, R., Wainwright, M., & Hastie, T. (2015). Statistical learning with sparsity: The lasso and generalizations. Chapman and Hall/CRC.
   Google Scholar
• VandeWalle, D., Cron, W. L., & Slocum, J. W. (2001). The role of goal orientation following performance feedback. Journal of Applied Psychology, 86(4), 629–640.
   PubMed Web of Science ®Google Scholar
• Voineskos, A. N., Rajji, T. K., Lobaugh, N. J., Miranda, D., Shenton, M. E., Kennedy, J. L., Pollock, B. G., & Mulsant, B. H. (2012). Age-related decline in white matter tract integrity and cognitive performance: A DTI tractography and structural equation modeling study. Neurobiology of Aging, 33(1), 21–34. doi:10.1016/j.neurobiolaging.2010.02.009
   PubMed Web of Science ®Google Scholar
• Willaby, H. W., Costa, D. S. J., Burns, B. D., MacCann, C., & Roberts, R. D. (2015). Testing complex models with small sample sizes: A historical overview and empirical demonstration of what partial least squares (PLS) can offer differential psychology. Personality and Individual Differences, 84, 73–78.
   Web of Science ®Google Scholar
• Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. Annals of Statistics, 38(2), 894–942.
   Web of Science ®Google Scholar