Understanding the Results of Multiple Linear Regression: Beyond Standardized Regression Coefficients

Organizational Research Methods

Volumn 16, Issue 4, 2013, Pages 650-674

  Nimon, Kim F ^a   Oswald, Frederick L ^b  

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b RICE UNIVERSITY   (United States)

Author keywords

exploratory; multiple regression; quantitative research; research design

Indexed keywords

EID: 84883407233     PISSN: 10944281     EISSN: 15527425     Source Type: Journal    
DOI: 10.1177/1094428113493929     Document Type: Review

References (55)

1. Algina J.,Keselman H. J.,Penfield R. D.Confidence intervals for squared semipartial correlation coefficients: The effect of nonnormality.Educational and Psychological Measurement. 2010;70:926-940.
2. Azen R.,Budescu D. V.The dominance analysis approach for comparing predictors in multiple regression.Psychological Methods. 2003;8:129-148.
3. Azen R.,Budescu D. V.Comparing predictors in multivariate regression models: An extension of dominance analysis.Journal of Educational and Behavioral Statistics. 2006;31:157-180.
4. Beckstead J. W.Isolation and examining source of suppression and multicollinearity in multiple linear regression.Multivariate Behavioral Research. 2012;47:224-246.
5. Braun M. T.,Oswald F. L.Exploratory regression analysis: A tool for selecting models and determining predictor importance.Behavioral Research Methods. 2011;43:331-339.
6. Budescu D. V.Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression.Psychological Bulletin. 1993;114:542-551.
7. Budescu D. V.,Azen R.Beyond global measures of relative importance: Some insights from dominance analysis.Organizational Research Methods. 2004;7:341-350.
8. CantyA.RipleyB. (2011). boot: Bootstrap R (S-Plus) functions (R package version 1.3-2) [Computer software].
9. Chevan A.,Sutherland M.Hierarchical partitioning.The American Statistician. 1991;45:90-96.
10. Courville T.,Thompson B.Use of structure coefficients in published multiple regression articles: β is not enough.Educational and Psychological Measurement. 2001;61:229-248.
11. Culpepper S. A.,Aguinis H.R is for revolution: A cutting-edge, free, open source statistical package.Organizational Research Methods. 2011;14:735-740.
12. Cumming G.,Finch S.A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions.Educational and Psychological Measurement. 2001;61:532-574.
13. Cumming G.,Finch S.Inference by eye: Confidence intervals and how to read pictures of data.American Psychologist. 2005;60:170-180.
14. Dalal D. K.,Zickar M. J.Some common myths about centering predictors in moderated multiple regression and polynomial regression.Organizational Research Methods. 2012;15:339-362.
15. Darlington R. B.Multiple regression in psychological research and practice.Psychological Bulletin. 1968;69:161-182.
16. Fabbris L.Measures of predictor variable importance in multiple regression: An additional suggestion.Quality & Quantity. 1980;4:787-792.
17. Genizi A.Decomposition of R2 in multiple regression with correlated regressors.Statistica Sinica. 1993;3:407-420.
18. Grömping U.Relative importance for linear regression in R: The package relaimpo.Journal of Statistical Software. 2006;17:1-27.
19. Hedges L. V.,Olkin I.The asymptotic distribution of commonality coefficients.Psychometrika. 1981;46:331-336.
20. Johnson J. W.A heuristic method for estimating the relative weight of predictor variables in multiple regression.Multivariate Behavioral Research. 2000;35:1-19.
21. Johnson J. W.Factors affecting relative weights: The influence of sampling and measurement error.Organizational Research Methods. 2004;7:283-299.
22. Johnson J. W.,LeBreton J. M.History and use of relative importance indices in organizational research.Organizational Research Methods. 2004;7:238-257.
23. Kraha A.,Turner H.,Nimon K.,Zientek L.,Henson R.The multifaceted concept of predictor importance: Tools to support interpreting multiple regression.Frontiers in Psychology. 2012;3 (44): 1-16.
24. Krasikova D.,LeBreton J. M.,Tonidandel S.International review of industrial and organizational psychology. Hodgkinson G. P.Ford J. K., ed. Indianapolis, IN: Wiley; 2011:119-141.
25. LeBreton J. M.,Ployhart R. E.,Ladd R. T.A Monte Carlo comparison of relative importance methodologies.Organizational Research Methods. 2004;7:258-282.
26. LeBreton J. M.,Tonidandel S.Multivariate relative importance: Relative weight analysis to multivariate criterion spaces.Journal of Applied Psychology. 2008;93:329-345.
27. Lindeman R. H.,Merenda P. F.,Gold R. Z.Introduction to bivariate and multivariate analysis. Glenview, IL: Scott, Foresman and Company; 1980:.
28. Lorenzo-Seva U.,Ferrando P. J.,Chico E.Two SPSS programs for interpreting multiple regression results.Behavior Research Methods. 2010;42:29-35.
29. Mayeske G. W.,Cohen W. M.,Wisler C. E.,Okada T.,Beaton A. E.,Proshek J. M.,Tabler K. A.A study of our nation's schools. Washington, DC: U.S. Department of Health, Education, and Welfare, Office of Education; 1969:.
30. Mitchell T. J.,Beauchamp J. J.Bayesian variable selection in linear regression.Journal of the American Statistical Association. 1988;83:1023-1032.
31. Mood A. M.Macro-analysis of the American educational system.Operations Research. 1969;17:770-784.
32. Mood A. M.Partitioning variance in multiple regression analyses as a tool for developing learning models.American Educational Research Journal. 1971;8:191-202.
33. Nathans L. L.,Oswald F. L.,Nimon K.Interpreting multiple regression: A guidebook of variable importance.Practical Assessment, Research & Evaluation. 2012;9:1-19.
34. Newton R. G.,Spurrell D. J.A development of multiple regression for the analysis of routine data.Applied Statistics. 1967;16:51-64.
35. Nimon K.,Gavrilova M.,Roberts J. K.Proceedings of the Human Resource Development 2010 International Conference. Graham C.Dirani K., ed. Knoxville, TN: AHRD; 2010:803-812.
36. Nimon K.,Henson R.,Gates M.Revisiting interpretation of canonical correlation analysis: A tutorial and software solution for canonical commonality analysis.Multivariate Behavioral Research. 2010;45:702-724.
37. Nimon K.,Reio T.Regression commonality analysis: A technique for quantitative theory building.Human Resource Development Review. 2011;10:329-340.
38. NimonK.RobertsJ. K. (2012). yhat: Interpreting regression effects (R package version 1.0-5) [Computer software]. Retrieved fromhttp://CRAN.R-project.org/package=yhat.
39. Nunnally J. C.,Bernstein I. H.Psychometric theory. 1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill.New York, NY: McGraw-Hill; 1994:.
40. OnwuegbuzieA. J.DanielL. G. (2003, February 19). Typology of analytical and interpretational errors in quantitative and qualitative educational research. Current Issues in Education, 6(2). Retrieved fromhttp://cie.asu.edu/volume6/number2/.
41. Podsakoff P. M.,Ahearne M.,MacKenzie S. B.Organizational citizenship behavior and the quantity and quality of work group performance.Journal of Applied Psychology. 1997;82:262-270.
42. Pratt J. W.Proceedings of the second international Tampere conference in statistics. Pukkila T.Puntanen S., ed. Tampere, Finland: University of Tampere; 1987:245-260.
43. Vienna, Austria: R Foundation for Statistical Computing; 2013:.
44. Raftery A. E.,Madigan D.,Hoeting J. A.Bayesian model averaging for linear regression models.Journal of the American Statistical Association. 1997;92:179-191.
45. Rowell R. K.Advances in social science methodology. Thompson B., ed. Greenwich, CT: JAI Press; 1996:33-43.
46. Schoen J. L.,DeSimone J. A.,James L. R.Exploring joint variance between independent variables and a criterion: Meaning, effect, and sizes.Organizational Research Methods. 2011;14:674-695.
47. Seibold D. R.,McPhee R. D.Commonality analysis: A method for decomposing explained variance in multiple regression analysis.Human Communication Research. 1979;5:355-363.
48. Thomas D. R.,Hughes E.,Zumbo B. D.On variable importance in linear regression.Social Indicators Research. 1998;45:253-275.
49. Thompson B.Foundations of behavioral statistics: An insight-based approach. New York, NY: Guilford Press; 2006:.
50. Tibshirani R.Regression shrinkage and selection via the lasso.Journal of the Royal Statistical Society B. 1996;51:267-288.
51. Tonidandel S.,LeBreton J. M.Relative importance analysis-A useful supplement to regression analyses.Journal of Business and Psychology. 2011;26:1-9.
52. Tonidandel S.,LeBreton J. M.,Johnson J. W.Statistical significance tests for relative weights.Psychological Methods. 2009;14:387-399.
53. Zientek L. R.,Capraro M. M.,Capraro R. M.Reporting practices in quantitative teacher education research: One look at the evidence cited in the AERA panel report.Educational Researcher. 2008;34:208-216.
54. Zientek L. R.,Thompson B.Commonality analysis: Partitioning variance to facilitate better understanding of data.Journal of Early Intervention. 2006;28:299-307.
55. Zientek L. R.,Yetkiner Z. E.,Thompson B.Characterizing the mathematics anxiety literature using confidence intervals as a literature review mechanism.The Journal of Educational Research. 2010;103:424-438.