Assumptions of multiple regression: Correcting two misconceptions

Practical Assessment, Research and Evaluation

Volumn 18, Issue 9, 2013, Pages 1-14

  Williams, Matt N ^a   Grajales, Carlos Alberto Gómez ^b   Kurkiewicz, Dason ^c  

^a MASSEY UNIVERSITY   (New Zealand)

^b UNIVERSIDAD VERACRUZANA   (Mexico)

^c IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84886306661     PISSN: None     EISSN: 15317714     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. Andrews, F. M. (1984). Construct validity and error components of survey measures: A structural modeling approach. Public Opinion Quarterly, 48(2), 409-442. doi:10.1086/268840
2. Baryla, E., Shelley, G., & Trainor, W. (2012). Transforming rubrics using factor analysis. Practical Assessment, Research & Evaluation, 17(4). Retrieved from http://www.pareonline.net/getvn.asp?v=17&n=4
3. Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. New York, NY: John Wiley & Sons.
4. Berk, R. A. (2004). Regression analysis: a constructive critique. Thousand Oaks, CA: SAGE.
5. Borsboom, D. (2005). Measuring the mind: Conceptual issues in contemporary psychometrics. Cambridge, United Kingdom: Cambridge University Press.
6. Borsboom, D., & Mellenbergh, G. J. (2002). True scores, latent variables, and constructs: A comment on Schmidt and Hunter. Intelligence, 30(6), 505-514. doi:10.1016/S0160-2896(02)00082-X
7. Chatterjee, S., & Hadi, A. S. (2012). Regression analysis by example (5th ed.). Hoboken, NJ: John Wiley & Sons.
8. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
9. Cryer, J. D., & Chan, K. (2008). Time series analysis: with applications in R (2nd ed.). New York, NY: Springer.
10. Dougherty, C. (2007). Introduction to Econometrics (3rd ed.). Oxford, United Kingdom: Oxford University Press.
11. Efron, B., & Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, 1(1), 54-75. doi:10.1214/ss/1177013815
12. Fox, J. (1997). Applied regression analysis, linear models, and related methods. Thousand Oaks, CA: SAGE.
13. Gaito, J. (1980). Measurement scales and statistics: Resurgence of an old misconception. Psychological Bulletin, 87(3), 564-567. doi:10.1037/0033-2909.87.3.564
14. Goldstein, H. (2011). Multilevel statistical models. Chichester, United Kingdom: John Wiley & Sons.
15. Hamilton, J. D. (1994). Time series analysis. Cambridge, United Kingdom: Cambridge University Press.
16. Han, K. T. (2012). Fixing the c parameter in the threeparameter logistic model. Practical Assessment, Research & Evaluation, 17(1). Retrieved from http://pareonline.net/pdf/v17n1.pdf
17. Hand, D. J. (1996). Statistics and the theory of measurement. Journal of the Royal Statistical Society. Series A (Statistics in Society), 159(3), 445-492. doi:10.2307/2983326
18. Hoekstra, R., Kiers, H. A. L., & Johnson, A. (2012). Are assumptions of well-known statistical techniques checked, and why (not)? Frontiers in Psychology, 3. doi:10.3389/fpsyg.2012.00137
19. Kline, R. B. (2005). Principles and practice of structural equation modeling (2nd ed.). New York, NY: The Guilford Press.
20. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
21. Michell, J. (1986). Measurement scales and statistics: A clash of paradigms. Psychological Bulletin, 100(3), 398-407. doi:10.1037/0033-2909.100.3.398
22. Michell, J. (1999). Measurement in psychology: A critical history of a methodological concept. Cambridge, United Kingdom: Cambridge University Press.
23. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2001). Introduction to linear regression analysis (3rd ed.). New York, NY: John Wiley & Sons.
24. Osborne, J. W., & Waters, E. (2002). Four assumptions of multiple regression that researchers should always test. Practical Assessment, Research & Evaluation, 8(2). Retrieved from http://pareonline.net/getvn.asp?v=8&n=2
25. Pedhazur, E. J. (1997). Multiple regression in behavioral research: Explanation and prediction (3rd ed.). Fort Worth, TX: Harcourt Brace College Publishers.
26. Raykov, T. (2004). Behavioral scale reliability and measurement invariance evaluation using latent variable modeling. Behavior Therapy, 35(2), 299-331. doi:10.1016/S0005-7894(04)80041-8
27. Raykov, T., & Marcoulides, G. A. (2011). Introduction to psychometric theory. New York, NY: Taylor & Francis.
28. Slinker, B. K., & Glantz, S. A. (1985). Multiple regression for physiological data analysis: the problem of multicollinearity. American Journal of Physiology - Regulatory, Integrative and Comparative Physiology, 249(1), R1-R12.
29. Snedecor, G. W., & Cochran, W. G. (1980). Statistical methods (7th ed.). Ames, IA: Iowa State University Press.
30. Stevens, J. P. (1984). Outliers and influential data points in regression analysis. Psychological Bulletin, 95(2), 334-344. doi:10.1037/0033-2909.95.2.334
31. Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677-680. doi:10.1126/science.103.2684.677
32. Tenopir, C., & King, D. W. (2000). Towards electronic journals: Realities for scientists, librarians, and publishers. Washington, DC: Special Libraries Association.
33. Thompson, N. A., & Weiss, D. J. (2011). A framework for the development of computerized adaptive tests. Practical Assessment, Research & Evaluation, 16(1). Retrieved from http://www.pareonline.net/pdf/v16n1.pdf
34. Weisberg, S. (2005). Applied linear regression. Hoboken, NJ: John Wiley & Sons.
35. Western, B. (1995). Concepts and suggestions for robust regression analysis. American Journal of Political Science, 39(3), 786-817. doi:10.2307/2111654
36. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica: Journal of the Econometric Society, 48(4), 817-838. doi:10.2307/1912934
37. White, H., & MacDonald, G. M. (1980). Some large-sample tests for nonnormality in the linear regression model. Journal of the American Statistical Association, 75(369), 16-28. doi:10.2307/2287373
38. Winship, C., & Radbill, L. (1994). Sampling weights and regression analysis. Sociological Methods & Research, 23(2), 230-257. doi:10.1177/0049124194023002004
39. Wooldridge, J. M. (2009). Introductory econometrics: A modern approach. Mason, OH: South-Western Cengage Learning.
40. Zand Scholten, A. (2011). Admissible statistics from a latent variable perspective (PhD dissertation). University of Amsterdam, Amsterdam, Netherlands. Retrieved from http://dare.uva.nl/record/366790
41. Zimmerman, D. W. (1998). How should classical test theory have defined validity? Social indicators research, 45(1-3), 233-251. doi:10.1023/A:1006949915525
42. Zimmerman, D. W., & Williams, R. H. (1977). The theory of test validity and correlated errors of measurement. Journal of Mathematical Psychology, 16(2), 135-152. doi:10.1016/0022-2496(77)90063-3