Regularized 2SLS Estimation of Structural Equation Model Parameters

References

• Arruda, E. H., & Bentler, P. M. (2017). A regularized GLS for structural equation modeling. Structural Equation Modeling, 24, 657–665. https://doi.org/10.1080/10705511.2017.1318392
   Web of Science ®Google Scholar
• Belloni, A., Chen, D., Chernozhukov, V., & Hansen, C. (2012). Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica, 80, 2369–2429.
   Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons.
   Google Scholar
• Bollen, K. A. (1996). An alternative two stage least square (2SLS) estimator for latent variables. Psychometrika, 61, 109–121. https://doi.org/10.1007/BF02296961
   Web of Science ®Google Scholar
• Bollen, K. A. (2001). Two-stage least squares and latent variable models: Simultaneous estimation and robustness to misspecifications. In R. Cudeck, S D. Toit, & D. Sorbom (Eds.), Structural equation modeling: Present and future, a festschrift in honor of Karl Jöreskog (pp. 125–152). Scientific Software.
   Google Scholar
• Bollen, K. A. (2019). Model implied instrumental variables (MIIVs): An alternative orientation to structural equation modeling. Multivariate Behavioral Research, 54, 31–46. https://doi.org/10.1080/00273171.2018.1483224
   PubMed Web of Science ®Google Scholar
• Bollen, K. A. (2020). When good loadings go bad: Robustness in factor analysis. Structural Equation Modeling, 27, 515–524. https://doi.org/10.1080/10705511.2019.1691005
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Bauer, D. J. (2004). Automating the selection of model-implied instrumental variables. Sociological Methods & Research, 32, 425–452. https://doi.org/10.1177/0049124103260341
   Web of Science ®Google Scholar
• Bollen, K. A., Kirby, J. B., Curran, P. J., Paxton, P. M., & Chen, F. (2007). Latent variable models under misspecification: Two stage least squares (2SLS) and maximum likelihood (ML) estimators. Sociological Methods and Research, 36, 46–86.
   Web of Science ®Google Scholar
• Bollen, K. A., Kolenikov, S., & Bauldry, S. (2014). Model-implied instrumental variables – generalized method of moments (MIIV-GMM) estimator of latent variable models. Psychometrika, 79, 20–50. https://doi.org/10.1007/s11336-013-9335-3
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Maydeu-Olivares, A. (2007). Polychoric instrumental variable (PIV) estimator for structural equations with categorical variables. Psychometrika, 3, 309–326.
   Web of Science ®Google Scholar
• Bollen, K. A., & Paxton, P. (1998). Two-stage least squares estimation of interaction effects. In R. E. Schumacker & G. A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 125–152). Lawrence Erlbaum Associates.
   Google Scholar
• Brandt, H., Umbach, N., Kelava, A., & Bollen, K. A. (2020). Comparing estimators for latent interaction models under structural and distributional misspecifications. Psychological Methods, 25, 321–345.
   PubMed Web of Science ®Google Scholar
• Breheny, P., & Huang, J. (2011). Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics, 5, 232–253.
   PubMed Web of Science ®Google Scholar
• Deisenroth, M. P., Faisal, A. A., & Ong, C. S. (2020). Mathematics FPR machine learning. Cambridge University Press.
   Google Scholar
• Fan, J., Li, R., Zhang, C.-H., & Zou, H. (2020). Statistical foundations of data science. CRC Press.
   Google Scholar
• Fan, Q., & Zhong, W. (2018). Variable selection for structural equation with endogeneity. Journal of Systems Science and Complexity, 31, 787–803. https://doi.org/10.1007/s11424-017-6195-4
   Web of Science ®Google Scholar
• Finch, W. H., & Miller, J. E. (2021). A comparison of regularized maximum-likelihood, regularized 2-stage least squares, and maximum-likelihood estimation with misspecified models, small samples, and weak factor structure. Multivariate Behavioral Research, 56, 608–626. https://doi.org/10.1080/00273171.2020.1753005
   PubMed Web of Science ®Google Scholar
• Fisher, Z. F., & Bollen, K. A. (2020). An instrumental variable estimator for mixed indicators: Analytic derivatives and alternative parameterizations. Psychometrika, 85, 660–683. https://doi.org/10.1007/s11336-020-09721-6
   PubMed Web of Science ®Google Scholar
• Fisher, Z. F., Bollen, K. A., & Gates, K. M. (2019). A limited information estimator for dynamic factor models. Multivariate Behavioral Research, 54, 246–263.
   PubMed Web of Science ®Google Scholar
• Fisher, Z. F., Bollen, K. A., Gates, K., & Rönkkö, M. (2021). Miivsem: Model implied instrumental variable (MIIV) estimation of structural equation models [Computer software manual]. https://CRAN.R-project.org/package=MIIVsem (R package version 0.5.8).
   Google Scholar
• Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1–22. https://www.jstatsoft.org/v33/i01/ https://doi.org/10.18637/jss.v033.i01
   PubMed Web of Science ®Google Scholar
• Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., et al. (2021). mvtnorm: Multivariate normal and t distributions [Computer software manual]. https://CRAN.R-project.org/package=mvtnorm (R package version 1.1-2)
   Google Scholar
• Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning. Springer.
   Google Scholar
• Hirose, K., & Yamamoto, M. (2014). Estimation of an oblique structure via penalized likelihood factor analysis. Computational Statistics & Data Analysis, 79, 120–132. https://doi.org/10.1016/j.csda.2014.05.011
   Web of Science ®Google Scholar
• Hirose, K., & Yamamoto, M. (2015). Sparse estimation via nonconcave penalized likelihood in factor analysis model. Statistics and Computing, 25, 863–875. https://doi.org/10.1007/s11222-014-9458-0
   Web of Science ®Google Scholar
• Holzinger, K. J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. Supplementary Educational Monographs, 48, xi + 91.
   Google Scholar
• Huang, P.-H. (2018). A penalized likelihood method for multi-group structural equation modelling. The British Journal of Mathematical and Statistical Psychology, 71, 499–522. https://doi.org/10.1111/bmsp.12130
   PubMed Web of Science ®Google Scholar
• Huang, P.-H. (2020). lslx: Semi-confirmatory structural equation modeling via penalized likelihood. Journal of Statistical Software, 93, 1–37. https://doi.org/10.18637/jss.v093.i07
   Web of Science ®Google Scholar
• Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A penalized likelihood method for structural equation modeling. Psychometrika, 82, 329–354. https://doi.org/10.1007/s11336-017-9566-9
   PubMed Web of Science ®Google Scholar
• Jacobucci, R., Brandmaier, A., & Kievit, R. (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, 55–76. https://doi.org/10.1177/2515245919826527
   PubMedGoogle Scholar
• Jacobucci, R., & Grimm, K. J. (2018). Comparison of frequentist and Bayesian regularization in structural equation modeling. Structural Equation Modeling, 25, 639–649. https://doi.org/10.1080/10705511.2017.1410822
   PubMed Web of Science ®Google Scholar
• Jacobucci, R., Grimm, K., & McArdle, J. (2016). Regularized structural equation modeling. Structural Equation Modeling, 23, 555–566. https://doi.org/10.1080/10705511.2016.1154793
   PubMed Web of Science ®Google Scholar
• Jin, S., Yang-Wallentin, F., & Bollen, K. (2021). A unified model-implied instrumental variable approach for structural equation modeling with mixed variables. Psychometrika, 86, 564–594.
   PubMed Web of Science ®Google Scholar
• Joreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183–202.
   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, 75–81. https://doi.org/10.3758/s13428-012-0206-0
   PubMed Web of Science ®Google Scholar
• Kline, R. B. (2016). Principles and practice of structural equation modeling. Guilford Press.
   Google Scholar
• Lauritzen, S. (1996). Graphical models. Oxford University Press.
   Google Scholar
• Lee, S. Y. (2007). Bayes structural equation models. Wiley.
   Google Scholar
• Lüdtke, O., Ulitzsch, E., & Robitzsch, A. (2021). A comparison of penalized maximum likelihood estimation and Markov chain Monte Carlo techniques for estimating confirmatory factor analysis models with small sample sizes. Frontiers in Psychology, 12, 615162. https://doi.org/10.3389/fpsyg.2021.615162
   PubMed Web of Science ®Google Scholar
• MacCallum, R. C. (2003). 2001 Presidential address: Working with imperfect models. Multivariate Behavioral Research, 38, 113–139. https://doi.org/10.1207/S15327906MBR3801_5
   PubMed Web of Science ®Google Scholar
• Murphy, K. (2012). Machine learning: A probabilistic perspective. MIT Press.
   Google Scholar
• Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557–585. https://doi.org/10.1007/BF02296397
   Web of Science ®Google Scholar
• Nestler, S. (2013). A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis. The British Journal of Mathematical and Statistical Psychology, 66, 127–143. https://doi.org/10.1111/j.2044-8317.2012.02044.x
   PubMed Web of Science ®Google Scholar
• Nestler, S. (2014). How the 2SLS/IV estimator can handle equality constraints in structural equation models: A system-of-equations approach. The British Journal of Mathematical and Statistical Psychology, 67, 353–369. https://doi.org/10.1111/bmsp.12023
   PubMed Web of Science ®Google Scholar
• Nestler, S. (2015a). A specification error test that uses instrumental variables to detect latent quadratic and latent interaction effects. Structural Equation Modeling, 22, 542–551. https://doi.org/10.1080/10705511.2014.994744
   Web of Science ®Google Scholar
• Nestler, S. (2015b). Using instrumental variables to estimate the parameters in unconditional and conditional second-order latent growth models. Structural Equation Modeling, 22, 461–473. https://doi.org/10.1080/10705511.2014.934948
   Web of Science ®Google Scholar
• Scharf, F., & Nestler, S. (2019). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling, 26, 576–590.
   Web of Science ®Google Scholar
• Scharf, F., Pförtner, J., & Nestler, S. (2021). Can ridge and elastic net structural equation modeling be used to stabilize parameter estimates when latent factors are correlated? Structural Equation Modeling, 28, 928–940. https://doi.org/10.1080/10705511.2021.1927736
   Web of Science ®Google Scholar
• Serang, S., Jacobucci, R., Brimhall, K. C., & Grimm, K. J. (2017). Exploratory mediation analysis via regularization. Structural Equation Modeling, 24, 733–744. https://doi.org/10.1080/10705511.2017.1311775
   PubMed Web of Science ®Google Scholar
• Trendafilov, N. (2014). From simple structure to sparse components: A review. Computational Statistics, 29, 431–454. https://doi.org/10.1007/s00180-013-0434-5
   Web of Science ®Google Scholar
• van Kesteren, E., & Oberski, D. L. (2022). Flexible extensions to structural equation models using computation graphs. Structural Equation Modeling, 29, 233–247. https://doi.org/10.1080/10705511.2021.1971527
   Web of Science ®Google Scholar
• Witten, D. M., & Tibshirani, R. (2009). Covariance-regularized regression and classification for high dimensional problems. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 71, 615–636.
   PubMed Web of Science ®Google Scholar
• Witten, D. M., & Tibshirani, R. (2015). scout: Implements the scout method for covariance-regularized regression [Computer software manual]. https://CRAN.R-project.org/package=scout (R package version 1.0.4)
   Google Scholar
• Wooldridge, J. M. (2002). Econometric analysis of cross section and panel data. MIT Press Books.
   Google Scholar
• Yamamoto, M., Hirose, K., & Nagata, H. (2017). Graphical tool of sparse factor analysis. Sociological Methodology, 44, 229–250.
   Google Scholar
• Yuan, K.-H., & Hayashi, K. (2006). Standard errors in covariance structure models: Asymptotics versus bootstrap. Sociological Methodology, 59, 397–417.
   Google Scholar
• Yuan, K.-H., Marshall, L. L., & Bentler, E. M. (2003). Assessing the effect of model misspecifications on parameter estimates in structural equation models. Sociological Methodology, 33, 241–265. https://doi.org/10.1111/j.0081-1750.2003.00132.x
   Web of Science ®Google Scholar