Regression Analysis with Latent Variables by Partial Least Squares and Four Other Composite Scores: Consistency, Bias and Correction

References

• Allen, M. J., & Yen, W. M. (1979). Introduction to measurement theory. Monterey, CA: Brooks-Cole.
   Google Scholar
• Areskoug, B. (1982). The first canonical correlation: Theoretical PLS analysis and simulation experiments. In K. G. Jöreskog & H. Wold (Eds.), Systems under indirect observations: Causality, structure, prediction (Part 2, pp. 95–118). Amsterdam, Netherlands: North-Holland.
   Google Scholar
• Bentler, P. M. (1968). Alpha-maximized factor analysis (Alphamax): Its relation to alpha and canonical factor analysis. Psychometrika, 33, 335–345. doi:10.1007/BF02289328
   PubMed Web of Science ®Google Scholar
• Bentler, P. M. (2006). EQS 6 structural equations program manual. Encino, CA: Multivariate Software.
   Google Scholar
• Bentler, P. M., & Huang, W. (2014). On components, latent variables, PLS and simple methods: Reactions to Rigdon’s rethinking of PLS. Long Range Planning, 47, 138–145. doi:10.1016/j.lrp.2014.02.005
   PubMed Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
   Google Scholar
• Chin, W. W. (1998). The partial least squares approach for structural equation modeling. In G. A. Marcoulides (Ed.), Modern methods for business research (pp. 295–336). Mahwah, NJ: Lawrence Erlbaum Associates.
   Google Scholar
• Croon, M. (2002). Using predicted latent scores in general latent structure models. In G. Marcoulides & I. Moustaki (Eds.), Latent variable and latent structure modeling (pp. 195–223). Mahwah, NJ: Lawrence Erblbaum Associates, Inc.
   Google Scholar
• Devlieger, I., Mayer, A., & Rosseel, Y. (2016). Hypothesis testing using factor score regression: A comparison of four methods. Educational and Psychological Measurement, 76, 741–770. doi:10.1177/0013164415607618
   PubMed Web of Science ®Google Scholar
• Devlieger, I., & Rosseel, Y. (2017). Factor score path analysis: An alternative for SEM? Methodology, 13, 31–38. doi:10.1027/1614-2241/a000130
   Web of Science ®Google Scholar
• Dijkstra, T. K. (1981). Latent variables in linear stochastic models: Reflections on “maximum likelihood” and “partial least squares” methods (Ph.D. thesis). Groningen University, Groningen. a second edition was published in 1985 by Sociometric Research Foundation,  Groningen, Netherlands.
   Google Scholar
• Dijkstra, T. K. (1983). Some comments on maximum likelihood and partial least squares methods. Journal of Econometrics, 22, 67–90. doi:10.1016/0304-4076(83)90094-5
   Web of Science ®Google Scholar
• Dijkstra, T. K., & Henseler, J. (2015). Consistent and asymptotically normal PLS estimators for linear structural equations. Computational Statistics and Data Analysis, 81, 10–23. doi:10.1016/j.csda.2014.07.008
   Web of Science ®Google Scholar
• Goodhue, D., Lewis, W., & Thompson, R. (2012). Comparing PLS to regression and LISREL: A response to Marcoulides, Chin, and Saunders. MIS Quarterly, 36, 703–716. doi:10.2307/41703476
   Web of Science ®Google Scholar
• Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). A primer on partial least squares structural equation modeling (PLS-SEM) (2nd ed). Thousand Oaks, CA: Sage. ISBN 9781483377445.
   Google Scholar
• Hair, J. F., Ringle, C. M., & Sarstedt, M. (2011). PLS-SEM: Indeed a silver bullet. Journal of Marketing Theory and Practice, 19, 139–152. doi:10.2753/MTP1069-6679190202
   Google Scholar
• Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning (2nd ed.). New York, NY: Springer.
   Google Scholar
• Jöreskog, K. G., & Sörbom, D. (1993). LISREL 8. Chicago, IL: Scientific Software International, Inc.
   Google Scholar
• Li, H. (1997). A unifying expression for the maximal reliability of a linear composite. Psychometrika, 62, 245–249. doi:10.1007/BF02295278
   Web of Science ®Google Scholar
• Loehlin, J. C. (2004). Latent variable models: An introduction to factor, path, and structural equation analysis (4th ed.). Mahwah, NJ: Lawrence Erlbaum.
   Google Scholar
• Lohmöller, J. (1989). Latent variable path modeling with partial least squares. Heildelberg, Germany: Physica-Verlag.
   Google Scholar
• Marcoulides, G. A., Chin, W., & Saunders, C. (2012). When imprecise statistical statements become problematic: A response to Goodhue, Lewis, and Thompson. MIS Quarterly, 36, 1–12. doi:10.2307/41703477
   Web of Science ®Google Scholar
• Marcoulides, G. A., Chin, W. W., & Saunders, C. (2009). A critical look at partial least squares modeling. MIS Quarterly, 33, 171–175. doi:10.2307/20650283
   Web of Science ®Google Scholar
• Marcoulides, G. A., & Saunders, C. (2006). PLS: A silver bullet? MIS Quarterly, 30, iv–viii. doi:10.2307/25148727
   Web of Science ®Google Scholar
• Marcoulides, K. M., & Yuan, K.-H. (2017). New ways to evaluate goodness of fit: A note on using equivalence testing to assess structural equation models. Structural Equation Modeling, 24, 148–153. doi:10.1080/10705511.2016.1225260
   Web of Science ®Google Scholar
• Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. New York, NY: Academic Press.
   Google Scholar
• McDonald, R. P. (1996). Path analysis with composite variables. Multivariate Behavioral Research, 31, 239–270. doi:10.1207/s15327906mbr3102_5
   PubMed Web of Science ®Google Scholar
• Meredith, W. (1964). Canonical correlations with fallible data. Psychometrika, 29, 55–65. doi:10.1007/BF02289567
   Web of Science ®Google Scholar
• Monecke, A., & Leisch, F. (2012). semPLS: Structural equation modeling using partial least squares. Journal of Statistical Software, 48, 1–32. doi:10.18637/jss.v048.i03
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus users guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill.
   Google Scholar
• Ringle, C. M., Wende, S., & Will, A. (2015). SmartPLS 3. Retrieved from https://www.smartpls.com/
   Google Scholar
• Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. doi:10.18637/jss.v048.i02
   Web of Science ®Google Scholar
• Schneeweiss, H. (1991). Models with latent variables: LISREL versus PLS. Statistica Neer- Landica, 45, 145–155. doi:10.1111/j.1467-9574.1991.tb01300.x
   Google Scholar
• Schneeweiss, H. (1993). Consistency at large in models with latent variables. In K. Haagen, D. J. Bartholomew, & M. Deistler (Eds.), Statistical modelling and latent variables (pp. 299–320). Amsterdam,  Netherlands: Elsevier.
   Google Scholar
• Tanaka, Y., Watadani, S., & Moon, S. H. (1991). Influence in covariance structure analysis: With an application to confirmatory factor analysis. Communication in Statistics-Theory and Method, 20, 3805–3821. doi:10.1080/03610929108830742
   Web of Science ®Google Scholar
• Treiblmaier, H., Bentler, P. M., & Mair, P. (2010). Formative constructs implemented via common factors. Structural Equation Modeling, 18, 1–17. doi:10.1080/10705511.2011.532693
   Web of Science ®Google Scholar
• Vinzi, V. E., Trinchera, L., & Amato, S. (2010). PLS path modeling: From foundations to recent developments and open issues for model assessment and improvement. In V. E. Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of partial least squares: Concepts, methods and applications (pp. 47–82). Berlin, Germany: Springer.
   Google Scholar
• Wold, H. (1966). Estimation of principal components and related models by iterative least squares. In P. R. Krishnaiah (Ed.), Multivariate analysis (pp. 391–420). New York, NY: Academic Press.
   Google Scholar
• Wold, H. (1980). Model construction and evaluation when theoretical knowledge is scarce. In J. Kmenta & J. B. Ramsey (Eds.), Evaluation of econometric models (pp. 47–74). New York, NY: Academic Press.
   Google Scholar
• Wold, H. (1985). Partial least squares. In S. Kotz & N. L. Johnson (Eds.), Encyclopedia of statistical sciences (Vol. 6, pp. 581–591). New York, NY: Wiley.
   Google Scholar
• Yang, M. (2018). Optimizing ridge generalized least squares for structural equation modeling (Unpublished dissertation). Indiana, IN: University of Notre Dame.
   Google Scholar
• Yuan, K.-H., & Bentler, P. M. (2002). On robustness of the normal-theory based asymptotic distributions of three reliability coefficient estimates. Psychometrika, 67, 251–259. doi:10.1007/BF02294845
   Web of Science ®Google Scholar
• Yuan, K.-H., & Chan, W. (2008). Structural equation modeling with near singular covariance matrices. Computational Statistics & Data Analysis, 52, 4842–4858. doi:10.1016/j.csda.2008.03.030
   Web of Science ®Google Scholar
• Yuan, K.-H., Chan, W., Marcoulides, G. A., & Bentler, P. M. (2016). Assessing structural equation models by equivalence testing with adjusted fit indices. Structural Equation Modeling, 23, 319–330. doi:10.1080/10705511.2015.1065414
   Web of Science ®Google Scholar
• Yuan, K.-H., & Hayashi, K. (2010). Fitting data to model: Structural equation modeling diagnosis using two scatter plots. Psychological Methods, 15, 335–351. doi:10.1037/a0020140
   PubMed Web of Science ®Google Scholar
• Yuan, K.-H., Marshall, L. L., & Bentler, P. M. (2003). Assessing the effect of model misspecifications on parameter estimates in structural equation models. Sociological Methodology, 33, 241–265. doi:10.1111/j.0081-1750.2003.00132.x
   Web of Science ®Google Scholar