The Geometry of Enhancement in Multiple Regression

Psychometrika

Volumn 76, Issue 4, 2011, Pages 634-649

  Waller, Niels G ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

multiple regression; suppression; suppressor variable

Indexed keywords

EID: 80355144627     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-011-9220-x     Document Type: Article

References (49)

1. Bertrand, P. V. (1998). Constructing explained and explanatory variables with strange statistical analysis results. The Statistician, 47, 377-383.
2. Bertrand, P. V., & Holder, R. L. (1988). A quirk in multiple-regression: the whole regression can be greater than the sum of its parts. The Statistician, 37(4), 371-374.
3. Briel, J. B., O'Neill, K., & Scheunernan, J. D. (1993). GRE technical manual. Princeton: Educational Testing Service.
4. Bryant, P. (1982). Geometry, statistics, probability: variations on a common theme. The American Statistician, 38(1), 38-48.
5. Conger, A. J. (1974). A revised definition for suppressor variables: a guide to their identification and interpretation. Educational and Psychological Measurement, 34(1), 35-46.
6. Cox, D. R. (1968). Notes on some aspects of regression analysis. Journal of the Royal Statistical Society, Series A, 131, 265-279.
7. Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Holt, Rinehart, and Winston.
8. Cuadras, C. M. (1993). Interpreting an inequality in multiple regression. The American Statistician, 47(4), 256-258.
9. Currie, I., & Korabinski, A. (1984). Some comments on bivariate regression. The Statistician, 33(3), 283-292.
10. Dayton, C. M. (1972). A method for constructing data which illustrate a suppressor variable. The American Statistician, 26(5), 36.
11. Derksen, S., & Keselman, H. J. (1992). Backward, forward and stepwise automated subset selection algorithms: frequency of obtaining authentic and noise variables. British Journal of Mathematical and Statistical Psychology, 45(2), 265-282.
12. Dicken, C. (1963). Good impression, social desirability, and acquiescence as suppressor variables. Educational and Psychological Measurement, 23(4), 699-720.
13. Ferguson, C. C. (1979). Intersections of ellipsoids and planes of arbitrary orientation and position. Mathematical Geology, 11(3), 329-33.
14. yx2 (revisited). The American Statistician, 42(1), 89-90.
15. Friedman, L., & Wall, M. (2005). Graphical views of suppression and multicollinearity in multiple linear regression. The American Statistician, 59(2), 127-136.
16. Graybill, F. A. (1983). Matrices with applications in statistics (2nd ed.). London: Thomson Learning.
17. Gromping, U. (2007). Estimators of relative importance in linear regression based on variance decomposition. The American Statistician, 61(2), 139-147.
18. Hadi, A. S. (1996). Matrix algebra as a tool. Belmont: Duxbury Press.
19. yx2: correlated variables are not always redundant. The American Statistician, 41(2), 129-132.
20. Hamilton, D. (1988). Reply. The American Statistician, 42, 90-91.
21. Hawkins, D. M., & Fatti, L. P. (1984). Exploring multivariate data using the minor principal components. The Statistician, 33(4), 325-338.
22. Holling, H. (1983). Suppressor structures in the general linear model. Educational and Psychological Measurement, 43(1), 1-9.
23. Horst, P. (1941). The prediction of personal adjustment (Bulletin No. 48). New York: Social Science Research Council.
24. Hotelling, H. (1957). The relationship of the newer statistical multivariate statistical methods to factor analysis. British Journal of Statistical Psychology, 10(2), 69-79.
25. Kendall, M. G., & Stuart, A. (1973). The advanced theory of statistics (3rd edn.). London: Charles Griffin and Company.
26. Kuncel, N. R., Hezlett, S. A., & Ones, D. S. (2001). A comprehensive meta-analysis of the predictive validity of the graduate record examinations: implications for graduate student selection and performance. Psychological Bulletin, 127(1), 162-181.
27. Lewis, J. W., & Escobar, L. A. (1986). Suppression and enhancement in bivariate regression. The Statistician, 35(1), 17-26.
28. Lipovetsky, S., & Conklin, M. (2004). Enhance-synergism and suppression effects in multiple regression. International Journal of Mathematics Education in Science and Technology, 35(3), 391-402.
29. Magnus, J. R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics. New York: Wiley.
30. Marsaglia, G., & Olkin, I. (1984). Generating correlation-matrices. SIAM Journal on Scientific and Statistical Computing, 5(2), 470-475.
31. Maassen, G. H., & Bakker, A. B. (2001). Suppressor variables in path models: definitions and interpretations. Sociological Methods & Research, 30(2), 241-270.
32. Meehl, P. E. (1945). A simple algebraic development of Horst's suppressor variables. The American Journal of Psychology, 58(4), 550-554.
33. Mitra, S. (1988). The relationship between the multiple and the zero-order correlation coefficients. The American Statistician, 42(1), 89.
34. Nickerson, C. (2008). Mutual suppression: comment on Paulhus et al. (2004). Multivariate Behavioral Research, 43(4), 556-563.
35. Paulhus, D. L., Robins, R. W., Trzesniewski, K. H., & Tracy, J. L. (2004). Two replicable suppressor situations in personality research. Multivariate Behavioral Research, 39(2), 301-326.
36. R Development Core Team (2011). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. ISBN 3-900051-07-0, URL http://www. R-project. org/.
37. Rao, C., & Mitra, S. (1971). Generalized inverse of the matrix and its applications. New York: Wiley.
38. Routledge, R. D. (1990). When stepwise regression fails: correlated variables some of which are redundant. International Journal of Mathematical Education in Science and Technology, 21(3), 403-410.
39. Saville, D. J., & Wood, G. R. (1986). A method for teaching statistics using N-dimensional geometry. The American Statistician, 40, 205-214.
40. Schey, H. M. (1993). The relationship between the magnitude of SSR(x2) and SSR(x2{pipe}x1): a geometric description. The American Statistician, 47(1), 26-30.
41. Schmidt, F., & Hunter, J. E. (1996). Measurement error in psychological research: lessons from 26 research scenarios. Psychological Methods, 1(2), 199-223.
42. Sharpe, N., & Roberts, R. (1997). The relationship among sums of squares, correlation coefficients, and suppression. The American Statistician, 51(1), 46-48.
43. Shieh, G. (2001). The inequality between the coefficient of determination and the sum of squared simple correlation coefficients. The American Statistician, 55(2), 121-124.
44. Taleb, N. N. (2007). The black swan: the impact of the highly improbable. New York: Random House.
45. Tzelgov, J., & Henik, A. (1985). A definition of suppression situations for the general linear model: a regression weights approach. Educational and Psychological Measurement, 45(2), 281-284.
46. Tzelgov, J., & Henik, A. (1991). Suppression situations in psychological research: definitions, implications, and applications. Psychological Bulletin, 109(3), 524-536.
47. Waller, N., & Jones, J. (2010). Correlation weights in multiple regression. Psychometrika, 75(1), 58-69.
48. Wickens, T. (1995). The geometry of multivariate statistics. Mahwah: Lawrence Erlbaum Associates.
49. Wiggins, J. S. (1973). Personality and prediction: principles of personality assessment. New York: Addison-Wesley.