Extracting the variance inflation factor and other multicollinearity diagnostics from typical regression results
Abstract
Multicollinearity is a potential problem in all regression analyses. However, the examination of multicollinearity is rarely reported in primary studies. In this article we discuss and show several post hoc methods for assessing multicollinearity. One such multicollinearity diagnostic is the variance inflation factor. We outline the post hoc variance inflation factor method, which computes the variance inflation factor from the standardized regression coefficient and semi-partial correlation, both of which can be calculated from commonly reported regression results. Three examples of computing multicollinearity diagnostics using data from published studies are shown. We conclude with a discussion and practical implications.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
There is no potential problem of multicollinearity among the independent variables in this study, as all VIF values were less than 10 and all tolerance values were greater than 0.1.
“By calculating the tolerance values and variance inflation factors (VIF), all VIF values were less than 10 and all tolerance values were greater than 0.1, indicating that there is no potential problem of multicollinearity among the independent variables in this study (Thompson et al., 2017).”
From A study on the influence of rural tourism’s perceived destination restorative qualities on loyalty based on SOR model (2025) · cites this paper as Thompson et al., 2017
Cites
Statistical power analysis for the behavioral sciences
Cohen, J. (1990) · Computers Environment and Urban Systems · doi:10.1016/0198-9715(90)90050-4 · Cited by 65,406 · see citing works
Statistical Power Analysis for the Behavioral Sciences
Cohen, J. (2013) · doi:10.4324/9780203771587 · Cited by 25,373 · see citing works
A Caution Regarding Rules of Thumb for Variance Inflation Factors
O’brien, R. M. (2007) · Quality & Quantity · doi:10.1007/s11135-006-9018-6 · Cited by 11,217 · see citing works
Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
Belsley, D. A., Kuh, E., & Welsch, R. E. (1980) · Wiley Series in Probability and Statistics · doi:10.1002/0471725153 · Cited by 7,297 · see citing works
Regression Diagnostics -- Identifying Influential Data and Sources of Collinearity
Beaumont, C. D., Belsley, D. A., Kuh, E., & Welsch, R. E. (1981) · Journal of the Operational Research Society · doi:10.2307/2581267 · Cited by 6,362 · see citing works
Applied Linear Regression Models
(1997) · Technometrics · doi:10.1080/00401706.1997.10485142 · Cited by 4,638 · see citing works
Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences.
Fong, G. T., Cohen, J., & Cohen, P. R. (1985) · Journal of the American Statistical Association · doi:10.2307/2287930 · Cited by 4,608 · see citing works
CONFRONTING MULTICOLLINEARITY IN ECOLOGICAL MULTIPLE REGRESSION
Graham, M. (2003) · Ecology · doi:10.1890/02-3114 · Cited by 2,583 · see citing works
Applied Regression Analysis and Generalized Linear Models
Fox, J. (2008) · Cited by 2,051 · see citing works
Applied Linear Regression Models
Lambrinos, J., Neter, J., Wasserman, W., & Kutner, M. (1984) · Technometrics · doi:10.2307/1269508 · Cited by 876 · see citing works
Regression Analysis by Example
Kanji, G. K., Chatterjee, S., & Price, B. (1993) · Biometrics · doi:10.2307/2532627 · Cited by 513 · see citing works
Kline, R. B. (2015) · Basic and Applied Social Psychology · doi:10.1080/01973533.2015.1049349 · Cited by 460 · see citing works
Statistical Confluence Analysis by means of Complete Regression Systems.
Allen, R. G. D., & Frisch, R. (1935) · The Economic Journal · doi:10.2307/2225583 · Cited by 316 · see citing works
Mela, C. F., & Kopalle, P. K. (2002) · Applied Economics · doi:10.1080/00036840110058482 · Cited by 282 · see citing works
Regression Analysis by Example (2nd ed.).
Short, T. H., Chatterjee, S., & Price, B. P. (1992) · Journal of the American Statistical Association · doi:10.2307/2290238 · Cited by 273 · see citing works
A primer of statistics for non-statisticians.
Franzblau, A. N. (1958) · Harcourt, Brace eBooks · Cited by 202 · see citing works
Applied regression analysis and generalized linear models, 2nd ed.
Fox, J. (2008) · Cited by 183 · see citing works
The Synthesis of Partial Effect Sizes
Aloe, A. M., & Thompson, C. G. (2013) · Journal of the Society for Social Work and Research · doi:10.5243/jsswr.2013.24 · Cited by 152 · see citing works
Self-citationPrescriptions for Working Statisticians
Madansky, A. (1988) · Springer texts in statistics · doi:10.1007/978-1-4612-3794-5 · Cited by 150 · see citing works
Prescriptions for Working Statisticians.
Wolf, F. L., & Madansky, A. (1990) · Journal of the American Statistical Association · doi:10.2307/2289570 · Cited by 132 · see citing works
An Effect Size for Regression Predictors in Meta-Analysis
Aloe, A. M., & Becker, B. J. (2011) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998610396901 · Cited by 131 · see citing works
Self-citationLife After NHST: How to Describe Your Data Without “p-ing” Everywhere
Valentine, J. C., Aloe, A. M., & Lau, T. S. (2015) · Basic and Applied Social Psychology · doi:10.1080/01973533.2015.1060240 · Cited by 103 · see citing works
Self-citationClark, L. M., DePiper, J. N., Frank, T. J., Nishio, M., Campbell, P. F., Smith, T., Griffin, M. J., Rust, A. H., Conant, D. L., & Choi, Y. (2014) · Journal for Research in Mathematics Education · doi:10.5951/jresematheduc.45.2.0246 · Cited by 91 · see citing works
Pay-for-performance dilemma revisited: Empirical example of the importance of group effects.
Markham, S. E. (1988) · Journal of Applied Psychology · doi:10.1037/0021-9010.73.2.172 · Cited by 83 · see citing works
Robust multicollinearity diagnostic measure in collinear data set
Midi, H., & Bagheri, A. (2010) · International Conference on Applied Mathematics · Cited by 39 · see citing works
Seethaler, P. M., Fuchs, L. S., Fuchs, D., & Compton, D. L. (2011) · Journal of Educational Psychology · doi:10.1037/a0024968 · Cited by 38 · see citing works
Ill-conditioning and multicollinearity
Öztürk, F., & Akdeniz, F. (2000) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00147-6 · Cited by 37 · see citing works
Toward a balanced assessment of collinearity diagnostics
Gunst, R. F. (1984) · The American Statistician · Cited by 13 · see citing works
Comment: Toward a Balanced Assessment of Collinearity Diagnostics
Gunst, R. F. (1984) · The American Statistician · doi:10.2307/2683238 · Cited by 12 · see citing works
Pay-for-performance dilemma revisited: Empirical example of the importance of group effects.
Markham, S. E. (1988) · Journal of Applied Psychology · doi:10.1037//0021-9010.73.2.172 · Cited by 5 · see citing works
Some Limits in the Theory of Multicollinearity
Sastry, M. V. R. (1970) · The American Statistician · doi:10.2307/2682295 · Cited by 4 · see citing works
Some Limits in the Theory of Multicollinearity
Sastry, M. V. R. (1970) · The American Statistician · doi:10.1080/00031305.1970.10477176 · Cited by 3 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Danopoulos, E., Twiddy, M., West, R., & Rotchell, J. M. (2022) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2021.127861 · Cited by 230 · see citing works
Tomczyk, S., Barth, S., Schmidt, S., & Muehlan, H. (2021) · Journal of Medical Internet Research · doi:10.2196/25447 · Cited by 69 · see citing works
Zhu, N., Xu, H., Zhang, X., & Chen, L. (2025) · Frontiers in Psychology · doi:10.3389/fpsyg.2025.1529686 · Cited by 25 · see citing works
Low, D. M., Rao, V., Randolph, G., Song, P. C., & Ghosh, S. S. (2024) · PLOS Digital Health · doi:10.1371/journal.pdig.0000516 · Cited by 16 · see citing works
Kimbley, C. T., Cox, D. W., Kahn, J. H., & Renshaw, K. D. (2023) · Journal of Traumatic Stress · doi:10.1002/jts.22930 · Cited by 9 · see citing works
Castro-Lopez, A., El Abed, M., Cervero, A., & Álvarez-Blanco, L. (2026) · European Journal of Higher Education · doi:10.1080/21568235.2026.2620686 · Cited by 3 · see citing works
- Authors
- Thompson, C. G., Kim, R. S., Aloe, A. M., & Becker, B. J.
- Affiliations
- Florida State University (US)
- American Institutes for Research (US)
- University of Iowa (US)
- Corresponding author
- Thompson, Christopher Glen
- Venue
- Basic and Applied Social Psychology
- Publisher
- Informa UK Limited
- Published
- 2017-02
- Volume
- 39
- Issue
- 2
- Pages
- 81-90
- ISSN
- 0197-3533 (ISSN-L)
- 1532-4834
- OpenAlex
- W2586047144
- Cited by
- 1,092
- References
- 32
- Citations by year
- 2026: 154 · 2025: 236 · 2024: 179 · 2023: 189 · 2022: 129 · 2021: 117 · 2020: 57 · 2019: 18 · 2018: 10 · 2017: 1 · 2013: 1
- FWCI
- 16.22
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Basic and Applied Social Psychology (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- multicollinearity, variance inflation factor, post hoc analysis, standardized regression coefficients
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
