Statistical Inference in Redundancy Analysis: A Direct Covariance Structure Modeling Approach

References

• Anderson, T. W. (1999). Asymptotic distribution of the reduced rank regression estimator under general conditions. The Annals of Statistics, 27(4), 1141–1154. https://doi.org/10.1214/aos/1017938918
   Web of Science ®Google Scholar
• Bagozzi, R. P., Fornell, C., & Larcker, D. F. (1981). Canonical correlation analysis as a special case of a structural relations model. Multivariate Behavioral Research, 16(4), 437–454. https://doi.org/10.1207/s15327906mbr1604_2
   PubMed Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. Wiley.
   Google Scholar
• Browne, M. W. (1984). Asymptotic distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37(1), 62–83. https://doi.org/10.1111/j.2044-8317.1984.tb00789.x
   PubMed Web of Science ®Google Scholar
• Burnham, A. J., Viveros, R., & MacGregor, J. F. (1996). Frameworks for latent variable multivariate regression. Journal of Chemometrics, 10(1), 31–45. https://doi.org/10.1002/(SICI)1099-128X(199601)10:1 < 31::AID-CEM398 > 3.0.CO;2-1
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1037/0033-2909.115.3.475
   PubMed Web of Science ®Google Scholar
• Davies, P. T., & Tso, M. K.-S. (1982). Procedures for reduced-rank regression. Journal of the Royal Statistical Society. Series C (Applied Statistics), 31, 244–255. https://doi.org/10.2307/2347998
   Web of Science ®Google Scholar
• de Jong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18(3), 251–263. https://doi.org/10.1016/0169-7439(93)85002-X
   Web of Science ®Google Scholar
• Fan, X. (1997). Canonical correlation analysis and structural equation modeling: What do they have in common? Structural Equation Modeling, 4(1), 65–79. https://doi.org/10.1080/10705519709540060
   Web of Science ®Google Scholar
• Fornell, C. (1979). External single-set components analysis of multiple criterion/multiple predictor variables. Multivariate Behavioral Research, 14(3), 323–338. https://doi.org/10.1207/s15327906mbr1403_3
   PubMed Web of Science ®Google Scholar
• Fortier, J. J. (1966). Simultaneous linear prediction. Psychometrika, 31(3), 369–381. https://doi.org/10.1007/BF02289469
   PubMed Web of Science ®Google Scholar
• Gu, F., & Wu, H. (2018). Simultaneous canonical correlation analysis with invariant canonical loadings. Behaviormetrika, 45, 111–132. https://doi.org/10.1007/s41237-017-0042-8
   Google Scholar
• Gu, F., Wu, H., Yung, Y.-F., & Wilkins, J. L. M. (2021). Standard error estimates for rotated estimates of canonical correlation analysis: An implementation of the infinitesimal jackknife method. Behaviormetrika, 48(1), 143–168. https://doi.org/10.1007/s41237-020-00123-7
   Google Scholar
• Höskuldsson, A. (1988). PLS regression methods. Journal of Chemometrics, 2(3), 211–228. https://doi.org/10.1002/cem.1180020306
   Google Scholar
• Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24(6), 417–441. https://doi.org/10.1037/h0071325
   Google Scholar
• Hotelling, H. (1935). The most predictable criterion. Journal of Educational Psychology, 26(2), 139–142. https://doi.org/10.1037/h0058165
   Google Scholar
• Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3–4), 321–377. https://doi.org/10.2307/2333955
   Google Scholar
• Hotelling, H. (1957). The relations of the newer multivariate statistical methods to factor analysis. British Journal of Statistical Psychology, 10(2), 69–79. https://doi.org/10.1111/j.2044-8317.1957.tb00179.x
   Web of Science ®Google Scholar
• Izenman, A. J. (1975). Reduced-rank regression for the multivariate linear model. Journal of Multivariate Analysis, 5(2), 248–264. https://doi.org/10.1016/0047-259X(75)90042-1
   Google Scholar
• Jackson, J. E. (1991). A user’s guide to principal components. John Wiley & Sons.
   Google Scholar
• Jennrich, R. I. (2008). Nonparametric estimation of standard errors in covariance analysis using the infinitesimal jackknife. Psychometrika, 73(4), 579–594. https://doi.org/10.1007/s11336-008-9083-y
   Web of Science ®Google Scholar
• Jöreskog, K. G., & Goldberger, A. S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 70, 631–639. https://doi.org/10.2307/2285946
   Web of Science ®Google Scholar
• Lambert, Z. V., Wildt, A. R., & Durand, R. M. (1988). Redundancy analysis: An alternative to canonical correlation and multivariate multiple regression in exploring interset associations. Psychological Bulletin, 104(2), 282–289. https://doi.org/10.1037/0033-2909.104.2.282
   Web of Science ®Google Scholar
• Legendre, P., & Legendre, L. (2012). Numerical ecology (3rd English Ed.). Elsevier.
   Google Scholar
• Muller, K. E. (1981). Relationships between redundancy analysis, canonical correlation, and multivariate regression. Psychometrika, 46(2), 139–142. https://doi.org/10.1007/BF02293894
   Web of Science ®Google Scholar
• Nimon, K., Zigarmi, D., Houson, D., Witt, D., & Diehl, J. (2011). The work cognition inventory: Initial evidence of construct validity. Human Resource Development Quarterly, 22(1), 7–35. https://doi.org/10.1002/hrdq.20064
   Web of Science ®Google Scholar
• Nimon, K., Joo, B.-K., & Bontrager, M. (2021). Work cognitions and work intentions: A canonical correlation study. Human Resource Development International, 24(1), 65–91. https://doi.org/10.1080/13678868.2020.1775038
   Web of Science ®Google Scholar
• Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2(11), 559–572. https://doi.org/10.1080/14786440109462720
   Google Scholar
• Qu, W., Liu, H., & Zhang, Z. (2020). A method of generating multivariate non-normal random numbers with desired multivariate skewness and kurtosis. Behavior Research Methods, 52(3), 939–946. https://doi.org/10.3758/s13428-019-01291-5
   PubMed Web of Science ®Google Scholar
• Raykov, T., & Marcoulides, G. A. (2014). Population proportion of explained variance in principal component analysis: A note on its evaluation via a large-sample approach. Structural Equation Modeling, 21(4), 588–595. https://doi.org/10.1080/10705511.2014.919826
   Web of Science ®Google Scholar
• Reinsel, G. C., & Velu, R. P. (1998). Multivariate reduced-rank regression. Springer.
   Google Scholar
• Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Sage Publications, Inc.
   Google Scholar
• Stewart, D., & Love, W. (1968). A general canonical correlation index. Psychological Bulletin, 70(3), 160–163. https://doi.org/10.1037/h0026143
   PubMed Web of Science ®Google Scholar
• Takane, Y., & Hwang, H. (2005). On a test of dimensionality in redundancy analysis. Psychometrika, 70(2), 271–281. https://doi.org/10.1007/s11336-003-1089-x
   Web of Science ®Google Scholar
• ten Berge, J. M. F. (1985). On the relationship between Fortier’s simultaneous linear prediction and Van Den Wollenberg’s redundancy analysis. Psychometrika, 50(1), 121–122. https://doi.org/10.1007/BF02294152
   Web of Science ®Google Scholar
• Tso, M. K.-S. (1981). Reduced-rank regression and canonical analysis. Journal of the Royal Statistical Society. Series B (Methodological), 43(2), 183–189. https://doi.org/10.1111/j.2517-6161.1981.tb01169.x
   Google Scholar
• Van Den Wollenberg, A. (1977). Redundancy analysis: An alternative for canonical correlation analysis. Psychometrika, 42(2), 207–219. https://doi.org/10.1007/BF02294050
   Web of Science ®Google Scholar
• Wold, H. (1985). Partial least squares. In S. Kotz and N. L. Johnson (Eds.), Encyclopedia of statistical sciences (Vol. 6, pp. 581–591). Wiley.
   Google Scholar
• Yuan, K.-H., Yang-Wallentin, F., & Bentler, P. M. (2012). ML versus MI for missing data with violation of distribution conditions. Sociological Methods & Research, 41(4), 598–629. https://doi.org/10.1177/0049124112460373
   PubMed Web of Science ®Google Scholar
• Yung, Y.-F., Browne, M. W., & Zhang, W. (2015). Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure. The British Journal of Mathematical and Statistical Psychology, 68(1), 178–193. https://doi.org/10.1111/bmsp.12034
   PubMed Web of Science ®Google Scholar