The paper obtains consistent standard errors (SE) and biases of order O(1/n) for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample standardized regression coefficients are also biased in general, although it should not be a concern in practice when the sample size is not too small. Monte Carlo results imply that, for both standardized and unstandardized sample regression coefficients, SE estimates based on asymptotics tend to under-predict the empirical ones at smaller sample sizes.
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Bentler, P.M. (2007). Can scientifically useful hypotheses be tested with correlations? American Psychologist, 62, 772–782.
Bentler, P.M. (2008). EQS 6 Structural equations program manual. Encino: Multivariate Software.
Browne, M.W. (1982). Covariance structure analysis. In D.M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72–141). Cambridge: Cambridge University Press.
Cheung, M.W.L. (2009). Constructing approximate confidence intervals for parameters with structural equation models. Structural Equation Modeling, 16, 267–294.
Cohen, J., Cohen, P., West, S.G., & Aiken, L.S. (2003). Multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah: LEA.
Cudeck, R. (1989). Analysis of correlation matrices using covariance structure models. Psychological Bulletin, 105, 317–327.
Efron, B., & Tibshirani, R.J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.
Ferguson, T.S. (1996). A course in large sample theory. London: Chapman & Hall.
Gonzalez, R., & Griffin, D. (2001). Testing parameters in structural equation modeling: Every “one” matters. Psychological Methods, 6, 258–269.
Harris, R.J. (2001). A primer of multivariate statistics (3rd ed.). Mahwah: LEA.
Hays, W.L. (1994). Statistics (5th ed.). Belmont: Wadsworth.
Jamshidian, M., & Bentler, P.M. (2000). Improved standard errors of standardized parameters in covariance structure models: implications for construct explication. In R.D. Goffin, & E. Helmes (Eds.), Problems and solutions in human assessment (pp. 73–94). Dordrecht: Kluwer Academic.
Jennrich, R.I. (1974). Simplified formulae for SEs in maximum likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 27, 122–131.
Jöreskog, K.G., & Sörbom, D. (1996). LISREL 8 users’s reference guide. Chicago: Scientific Software International.
Kelley, K., & Maxwell, S.E. (2003). Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8, 305–321.
Lee, S.-Y. (1985). Analysis of covariance and correlation structures. Computational Statistics & Data Analysis, 2, 279–295.
Magnus, J.R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics (2nd edn.). New York: Wiley.
Mayer, L.S., & Younger, M.S. (1976). Estimation of standardized regression coefficients. Journal of the American Statistical Association, 71, 154–157.
Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156–166.
Muthén, L.K., & Muthén, B.O. (2007). Mplus user’s guide (5th ed.). Los Angeles: Muthén & Muthén.
Nakagawa, S., & Cuthill, I.C. (2007). Effect size, confidence interval and statistical significance: a practical guide for biologists. Biological Reviews, 82, 591–605.
Olkin, I., & Finn, J.D. (1995). Correlations redux. Psychological Bulletin, 118, 155–164.
Stevens, J. (1996). Applied multivariate statistics for the social sciences (3rd ed.). Mahwah: LEA.
Thompson, B. (Ed.) (2001). Confidence intervals around effect sizes [Special issue]. Educational and Psychological Measurement, 61(4).
Wilkinson, L. & The American Psychological Association Task Force on Statistical Inference (1999). Statistical methods in psychology journals: guidelines and explanations. American Psychologist, 54, 594–604.
Yuan, K.-H., & Bentler, P.M. (2000). Inferences on correlation coefficients in some classes of nonnormal distributions. Journal of Multivariate Analysis, 72, 230–248.
This research was supported by Grants DA00017 and DA01070 from the National Institute on Drug Abuse.
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Yuan, K., Chan, W. Biases and Standard Errors of Standardized Regression Coefficients. Psychometrika 76, 670–690 (2011). https://doi.org/10.1007/s11336-011-9224-6
- Monte Carlo