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Biases and Standard Errors of Standardized Regression Coefficients


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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Author information

Correspondence to Ke-Hai Yuan.

Additional information

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

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  • asymptotics
  • bias
  • consistency
  • Monte Carlo