Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 1,432

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation

Open access
Hayes, Andrew F., Cai, Li·2007·Behavior Research Methods
DOI 10.3758/bf03192961
Open this paper in CoChat — free account

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3758/bf03192961

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 1 references

Research works printed but not linked: 45

  1. Bera, A. K., Suprayitno, T., &Premaratne, G. (2002). On some heteroskedasticity-robust estimators of variance-covariance matrix of the least-squares estimators.Journal of Statistical Planning & Inference,108, 121–136. · DOI
  2. Berry, W. D. (1993).Understanding regression assumptions. Newbury Park, CA: Sage. · DOI · Paper page
  3. Box, G. E. P., &Cox, D. R. (1964). An analysis of transformations.Journal of the Royal Statistical Society B,26, 211–243. · DOI · Paper page
  4. Cai, L., & Hayes, A. F. (in press). A new test of linear hypotheses in OLS regression under heteroskedasticity of unknown form.Journal of Educational & Behavioral Statistics.
  5. Carroll, R. J. (2003). Variances are not always nuisance parameters.Biometrics,59, 211–220. · DOI
  6. Carroll, R. J., &Ruppert, D. (1988).Transformation and weighting in regression. New York: Chapman and Hall. · DOI · Paper page
  7. Chesher, A., &Jewitt, I. (1987). The bias of a heteroskedasticity consistent covariance matrix estimator.Econometrica,55, 1217–1222. · DOI
  8. Cook, R. D., &Weisberg, S. (1983). Diagnostics for heteroskedasticity in regression.Biometrika,70, 1–10. · DOI
  9. Cook, R. D., &Weisberg, S. (1999).Applied regression including computing and graphics. New York: Wiley. · DOI · Paper page
  10. Cribari-Neto, F. (2004). Asymptotic inference under heteroskedasticity of unknown form.Computational Statistics & Data Analysis,45, 215–233. · DOI
  11. Cribari-Neto, F., Ferrari, S. L. P., &Cordeiro, G. M. (2000). Improved heteroskedasticity-consistent covariance matrix estimators.Biometrika,87, 907–918. · DOI
  12. Cribari-Neto, F., Ferrari, S. L. P., &Oliveira, W. A. S. C. (2005). Numerical evaluation of tests based on different heteroskedasticity-consistent covariance matrix estimators.Journal of Statistical Computation & Simulation,75, 611–628. · DOI
  13. Cribari-Neto, F., &Zarkos, S. G. (2001). Heteroskedasticity-consistent covariance matrix estimation: White’s estimator and the bootstrap.Journal of Statistical Computation & Simulation,68, 391–411. · DOI
  14. Darlington, R. B. (1990).Regression and linear models. New York: McGraw-Hill.
  15. Davidson, R., &MacKinnon, J. G. (1993).Estimation and inference in econometrics. Oxford: Oxford University Press.
  16. Downs, G. W., &Rocke, D. M. (1979). Interpreting heteroskedasticity.American Journal of Political Science,23, 816–828. · DOI
  17. Draper, N. R., &Smith, H. (1981).Applied regression analysis (2nd ed.). New York: Wiley.
  18. Duncan, G. T., &Layard, W. M. J. (1973). A Monte-Carlo study of asymptotically robust tests for correlation coefficients.Biometrika,60, 551–558. · DOI
  19. Edgell, S. E., &Noon, S. M. (1984). Effect of violation of normality on the t test of the correlation coefficient.Psychological Bulletin,95, 576–583. · DOI
  20. Eicker, F. (1963). Asymptotic normality and consistency of the least squares estimator for families of linear regression.Annals of Mathematical Statistics,34, 447–456. · DOI
  21. Eicker, F. (1967). Limit theorems for regression with unequal and dependent errors. In L. M. Le Cam & J. Neyman (Eds.),Proceedings of the fifth Berkeley symposium on mathematical statistics and probability. Berkeley, CA: University of California Press.
  22. Furno, M. (1996). Small sample behavior of a robust heteroskedasticity consistent covariance matrix estimator.Journal of Statistical Computation & Simulation,54, 115–128. · DOI
  23. Godfrey, L. G. (2006). Tests for regression models with heteroskedasticity of unknown form.Computational Statistics & Data Analysis,50, 2715–2733. · DOI
  24. Godfrey, L. G., &Orne, C. D. (2004). Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients.Economics Letters,82, 281–287. · DOI
  25. Goldfeld, S. M., &Quandt, R. E. (1965). Some tests for homoskedasticity.Journal of the American Statistical Association,60, 539–547. · DOI
  26. Hayes, A. F. (1996). Permutation test is not distribution-free: TestingH o: π=0.Psychological Methods,1, 184–198. · DOI · Paper page
  27. Hinkley, D. V. (1977). Jackknifing in unbalanced situations.Technometrics,19, 285–292. · DOI
  28. Huber, P. J. (1967). The behavior of maximum likelihood estimation under nonstandard conditions. In L. M. Le Cam & J. Neyman (Eds.),Proceedings of the fifth Berkeley symposium on mathematical statistics and probability. Berkeley, CA: University of California Press.
  29. Kauermann, G., &Carroll, R. J. (2001). A note on the efficiency of sandwich covariance matrix estimation.Journal of the American Statistical Association,96, 1387–1396. · DOI · Paper page
  30. Kowalski, C. J. (1973). On the effects of non-normality on the distribution of the sample product-moment correlation coefficient.Applied Statistics,21, 1–12. · DOI
  31. Long, J. S., &Ervin, L. H. (2000). Using heteroskedasticity consistent standard errors in the linear regression model.American Statistician,54, 217–224. · DOI
  32. MacCallum, R. C. (2003). Working with imperfect models.Multivariate Behavioral Research,38, 113–139. · DOI
  33. MacKinnon, J. G., &White, H. (1985). Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties.Journal of Econometrics,29, 305–325. · DOI · Paper page
  34. Mardia, K. V., Kent, J. T., &Bibby, J. M. (1979).Multivariate analysis. New York: Academic Press.
  35. Moore, D. S., &McCabe, G. P. (2003).Introduction to the practice of statistics (4th ed.). New York: Freeman.
  36. Olejnik, S. F. (1988). Variance heterogeneity: An outcome to explain or a nuisance factor to control?Journal of Experimental Education,56, 193–197. · DOI
  37. Perry, D. K. (1986). Looking for heteroskedasticity: A means of searching for neglected conditional relationships. In M. L. McLaughlin (Ed.),Communication yearbook 9 (pp. 658–670). Beverly Hills, CA: Sage.
  38. Rasmussen, J. L. (1989). Computer-intensive correlational analysis: Bootstrap and approximate randomization techniques.British Journal of Mathematical & Statistical Psychology,42, 103–111. · DOI
  39. Sudmant, W., &Kennedy, P. (1990). On inference in the presence of heteroskedasticity without replicated observations.Communication in Statistics-Simulation & Computation,19, 491–504. · DOI
  40. Weisberg, S. (1980).Applied linear regression. New York: Wiley.
  41. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.Econometrica,48, 817–838. · DOI · Paper page
  42. Wilcox, R. R. (2001). Comment.The American Statistician,55, 374–375.
  43. Wilcox, R. R. (2005).Introduction to robust estimation and hypothesis testing. New York: Academic Press.
  44. Wooldridge, J. M. (2000).Introductory econometrics: A modern approach. Cincinnati, OH: South-Western College Publishing.
  45. Wu, C. F. J. (1986). Jackknife bootstrap and other resampling methods in regression analysis.Annals of Statistics,14, 1261–1295. · DOI · Paper page

Cited by

See all 1,432

Metadata

Authors
Hayes, A. F., & Cai, L.
Venue
Behavior Research Methods
Publisher
Springer Science and Business Media LLC
Published
2007-11
Volume
39
Issue
4
Pages
709-722
ISSN
  • 1554-351X (ISSN-L)
  • 1554-3528
DOI
10.3758/bf03192961
OpenAlex
W2032167823
Cited by
1,432
References
1
FWCI
9.91
Type
journal article
Language
en
Open access
bronze
Licence
www.springer.com/tdm (tdm)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation. https://app.cochat.ai/papers/10.3758/bf03192961
The paper
Hayes, A. F., & Cai, L. (2007). Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation. Behavior Research Methods. https://doi.org/10.3758/bf03192961

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.