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Biases and Standard Errors of Standardized Regression Coefficients

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan  and
Wai Chan
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Wai Chan
Affiliation:
The Chinese University of Hong Kong
*
Requests for reprints should be sent to Ke-Hai Yuan, University of Notre Dame, Notre Dame, IN 46556, USA. E-mail: kyuan@nd.edu
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Abstract

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.

Keywords

asymptoticsbiasconsistencyMonte Carlo
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 4 , October 2011 , pp. 670 - 690
Copyright
Copyright © 2011 The Psychometric Society

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Footnotes

This research was supported by Grants DA00017 and DA01070 from the National Institute on Drug Abuse.

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