OJS> Vol.3 No.6A, December 2013

Could Sequential Residual Centering Resolve Low Sensitivity in Moderated Regression? Simulations and Cancer Symptom Clusters

DownloadDownload as PDF (Size:310KB)  HTML    PP. 24-44  

ABSTRACT

Multicollinearity constitutes shared variation among predictors that inflates standard errors of regression coefficients. Several years ago, it was proven that the common practice of mean centering in moderated regression cannot alleviate multicollinearity among variables comprising an interaction, but merely masks it. Residual centering (orthogonalizing) is unacceptable because it biases parameters for predictors from which the interaction derives, thus precluding interpretation of moderator effects. I propose and validate residual centering in sequential re-estimations of a moderated regression—sequential residual centering (SRC)—by revealing unbiased multicollinearity conditioning across the interaction and its related terms. Across simulations, SRC reduces variance inflation factors (VIF) regardless of distribution shape or pattern of regression coefficients across predictors. For any predictor, the reduced VIF is used to derive a lower standard error of its regression coefficient. A cancer sample illustrates SRC, which allows unbiased interpretations of symptom clusters. SRC can be applied efficiently to alleviate multicollinearity after data collection and shows promise for advancing synergistic frontiers of research.

Cite this paper

R. Francoeur, "Could Sequential Residual Centering Resolve Low Sensitivity in Moderated Regression? Simulations and Cancer Symptom Clusters," Open Journal of Statistics, Vol. 3 No. 6A, 2013, pp. 24-44. doi: 10.4236/ojs.2013.36A004.

References

[1] R. Echambadi, I. Arroniz, W. Reinartz and J. Lee, “Empirical Generalizations from Brand Extension Research: How Sure Are We?” International Journal of Research in Marketing, Vol. 23, No. 3, 2006, pp. 253-261.
http://dx.doi.org/10.1016/j.ijresmar.2006.02.002
[2] R. Echambadi and J. D. Hess, “Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Regression Models,” Marketing Science, Vol. 26, No. 3, 2007, pp. 438-445.
http://dx.doi.org/10.1287/mksc.1060.0263
[3] L. S. Aiken and S. G. West, “Multiple Regression: Testing and Interpreting Interactions,” Sage Publications, Newbury Park, 1991.
[4] L. J. Cronbach, “Statistical Tests for Moderator Variables: Flaws in Analyses Recently Proposed,” Psychological Bulletin, Vol. 102, No. 3, 1987, pp. 414-417.
http://dx.doi.org/10.1037/0033-2909.102.3.414
[5] J. R. Jaccard, R. Turrisi and C. K. Wan, “Interaction Effects in Multiple Regression,” Sage Publications, Newbury Park, 1990.
[6] D. A. Belsley, “Demeaning Conditioning Diagnostics through Centering,” The American Statistician, Vol. 38, No. 2, 1984, pp. 73-77.
[7] G. Coenders and M. Saez, “Collinearity, Heteroscedasticity, and Outlier Diagnostics in Regression: Do They Always Offer What They Claim?” In: A. Ferligoj and A. Mrvar, Eds., New Approaches in Applied Statistics, Metodoloski Zvezki, Faculty of Social Sciences, Ljubljana, Slovenia, 2000, pp. 17-94.
[8] D. A. Belsley, “Conditional Diagnostics: Collinearity and Weak Data in Regression,” John Wiley & Sons, New York, 1991.
[9] C. E. Lance, “Residual Centering, Exploratory and Confirmatory Moderator Analysis, and Decomposition of Effects in Path Models Containing Interactions,” Applied Psychological Measurement, Vol. 12, No. 2, 1988, pp. 163-175. http://dx.doi.org/10.1177/014662168801200205
[10] J. E. Champoux and W. S. Peters, “Form, Effect Size, and Power in Moderated Regression,” Journal of Occupational Psychology, Vol. 17, 1987, pp. 585-605.
[11] J. Cohen, J., P. Cohen, S. G. West and L. S. Aiken, “Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences,” 3rd Edition, Lawrence Erlbaum Associates, Mahwah, 2003.
[12] R. B. Francoeur, “Interpreting Interactions of Ordinal or Continuous Variables in Moderated Regression Using the Zero Slope Comparison: Tutorial, New Extensions and Cancer Symptom Applications,” Special Issue on Assessment Methods in Social Systems Science, International Journal of Society Systems Science, Vol. 3, No. 1/2, 2011, pp. 137-158.
http://dx.doi.org/10.1504/IJSSS.2011.038937
[13] L. G. Nye and L. A. Witt, “Interpreting Moderator Effects: Substitute for the Signed Coefficient Rule,” Educational and Psychological Measurement, Vol. 55, No. 1, 1995, pp. 27-31.
http://dx.doi.org/10.1177/0013164495055001002
[14] F. Guoqun and J. Saunders, “Consumer Evaluations of Brand Extensions: Empirical Evidence from China,” Asia Pacific Advances in Consumer Research, Vol. 5, 2002, pp. 395-399.
[15] A. Tiwana and M. Keil, “Does Peripheral Knowledge Complement Control? An Empirical Test in Technology Outsourcing Alliances,” Strategic Management Journal, Vol. 28, No. 6, 2007, pp. 623-634.
http://dx.doi.org/10.1002/smj.623
[16] A. Tiwana, “Does Technological Modularity Substitute for Control? A Study of Alliance Performance in Software Outsourcing,” Strategic Management Journal, Vol. 29, No. 7, 2008, pp. 769-780.
http://dx.doi.org/10.1002/smj.673
[17] A. Martìnez-Sánchez, M. J. Vela-Jiménez, M. PérezPérez and P. de-Luis-Carnicer, “Workplace Flexibility and Innovation: The Moderator Effect of Inter-Organizational Cooperation,” Personnel Review, Vol. 37, No. 6, 2008, pp. 647-665.
http://dx.doi.org/10.1108/00483480810906883
[18] H. Aguinis, “Regression Analysis for Categorical Moderators,” Guilford Press, New York, 2004.
[19] R. J. Friedrich, “In Defense of Multiplicative Terms in Multiple Regression Equations,” American Journal of Political Science, Vol. 26, No. 4, 1982, pp. 797-833.
http://dx.doi.org/10.2307/2110973
[20] R. Baron and D. Kenny, “The Moderator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations,” Journal of Personality and Social Psychology, Vol. 51, No. 6, 1986, pp. 1173-1182.
http://dx.doi.org/10.1037/0022-3514.51.6.1173
[21] R. B. Francoeur, “Fever and Depressive Affect Clarify a Common Cancer Cluster (Pain-Sleep Problems-Fatigue/ Weakness) in an Outpatient Survey: A New Method for Moderated Regression Improves Detection of Interactions and Synergistic Relationships,” Under Review.
[22] P. Kennedy, “A Guide to Econometrics,” 4th Edition, MIT Press, Cambridge, 1998.
[23] G. Shieh, “Clarifying the Role of Mean Centring in Multicollinearity of Interaction Effects,” British Journal of Mathematical and Statistical Psychology, Vol. 64, No. 3, 2011, pp. 462-477.
http://dx.doi.org/10.1111/j.2044-8317.2010.02002.x
[24] G. J. Geldhof, S. Pornprasertmanit, A. M. Schoemann and T. D. Little, “Orthogonalizing through Residual Centering: Extended Applications and Caveats,” Educational and Psychological Measurement, Vol. 73, No. 1, 2013, pp. 27-46. http://dx.doi.org/10.1177/0013164412445473
[25] R. Schulz R., G. M. Williamson, J. E. Knapp, J. Bookwala, J. Lave and M. Fello, “The Psychological Social, and Economic Impact of Illness among Patients with Recurrent Cancer,” Journal of Psychosocial Oncology, Vol. 13, No. 3, 1995, pp. 21-45.
http://dx.doi.org/10.1300/J077V13N03_02
[26] R. B. Francoeur, “The Relationship of Cancer Symptom Clusters to Depressive Affect in the Initial Phase of Palliative Radiation,” Journal of Pain and Symptom Management, Vol. 29, No. 2, 2005, pp. 130-155.
http://dx.doi.org/10.1016/j.jpainsymman.2004.04.014
[27] D. A. Belsley, E. Kuh and R. E. Welsch, “Regression Diagnostics: Identifying Influential Data and Sources of Collinearity,” John Wiley & Sons, Ltd., New York, 1980.
http://dx.doi.org/10.1002/0471725153
[28] S. Chatterjee, A. S. Hadi and B. Price, “Regression Analysis by Example,” John Wiley & Sons, New York, 2000.
[29] T. D. Little, J. A. Bovaird and K. F. Widaman, “On the Merits of Orthogonalizing Powered and Product Terms: Implications for Modeling Interactions among Latent Variables.” Structural Equation Modeling, Vol. 13, No. 4, 2006, pp. 497-519.
http://dx.doi.org/10.1207/s15328007sem1304_1
[30] J. Mullington, C. Korth, D. M. Hermann, A. Orth, C. Galanos, F. Holsboer and T. Pollmacher, “Dose-Dependent Effects of Endotoxin on Human Sleep,” American Journal of Physiology: Regulatory, Integrative, and Comparative Physiology, Vol. 278, No. 4, 2000, pp. R947R955.
[31] Y. Ganzach, “Misleading Interaction and Curvilinear Terms,” Psychological Methods, Vol. 2, No. 3, 1997, pp. 235-247. http://dx.doi.org/10.1037/1082-989X.2.3.235
[32] Y. Ganzach, “Nonlinearity, Multicollinearity and the Probability of Type II Error in Detecting Interactions,” Journal of Management, Vol. 24, No. 5, 1998, pp. 615622.

  
comments powered by Disqus

Copyright © 2014 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.