Local influence and robust procedures for mediation analysis

Multivariate Behavioral Research

Volumn 45, Issue 1, 2010, Pages 1-44

  Zu, Jiyun ^a   Yuan, Ke Hai ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951161696     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1080/00273170903504695     Document Type: Article

References (56)

1. Barnett, V., & Lewis, T. (1994). Outliers in statistical data. New York: Wiley.
2. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychologicalresearch: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.
3. Beasley, W. H., DeShea, L., Toothaker, L. E., Mendoza, J. L., Bard, D. E., & Rodgers, J. L. (2007). Bootstrapping to test for nonzero population correlation coefficients using univariate sampling. Psychological Methods, 12, 414-433.
4. Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. New York: Wiley.
5. Bollen, K. A., & Stine, R. (1990). Direct and indirect effects: Classical and bootstrap estimates of variability. Sociological Methodology, 20, 115-140.
6. Cadigan, N. G. (1995). Local influence in structural equation models. Structural Equation Modeling, 2,13-30.
7. Casella, G., & Berger, R. L. (2001). Statistical inference (2nd ed.). Pacific Grove, CA: Duxbury Press.
8. Cook, R. D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society B, 48, 133-169.
9. Craig, C. C. (1936). On the frequency function of xy. Annals of Mathematical Statistics, 7, 1-15.
10. Davies, P. T., Forman, E. M., Rasi, J. A., & Stevens, K. I. (2002). Assessing children's emotional security in the interparental relationship: The security in the interparental subsystem scales. Child Development, 73, 544-562.
11. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Boca Raton, FL: Chapman & Hall/CRC.
12. Erceg-Hurn, D. M., & Mirosevich, V. M. (2008). Modern robust statistical methods: An easy way to maximize the accuracy and power of your research. American Psychologist, 63, 591-601.
13. Finch, J. F., West, S. G., & MacKinnon, D. P. (1997). Effects of sample size and nonnormality on the estimation of mediated effects in latent variable models. Structural Equation Modeling, 4, 87-107.
14. Fox, J. (1991). Regression diagnostics. Newbury Park, CA: Sage.
15. Hoaglin, D. C., Mosteller, F., & Tukey, J. W. (1983). Understanding robust and exploratory data analysis. New York: Wiley.
16. Huber, P. J. (1981). Robust statistics. New York: Wiley.
17. Huber, P. J. (1996). Robust statistical procedures (2nd ed.). Philadelphia: SIAM.
18. Keselman, H. J., Algina, J., Lix, L. M., Wilcox, R. R., & Deering, K. N. (2008). A generally robust approach for testing hypotheses and setting confidence intervals for effect sizes. Psychological Methods, 13, 110-129.
19. Kim Park, I. J. (2007). Enculturation of Korean American adolescents within familial and cultural contexts: The mediating role of ethnic identity. Family Relations, 56, 403-412.
20. Kouros, C. D., Merrilees, C. E., & Cummings, E. M. (2008). Marital conflict and children's emotional security in the context of parental depression. Journal of Marriage and Family, 70, 684-697.
21. Kovacs, M. (1985). The children's depression inventory (CDI). Psychopharmacology Bulletin, 21, 995-998.
22. Lee, S.-Y., & Tang, N.-S. (2004). Local influence analysis of nonlinear structural equation models. Psychometrika, 69, 573-592.
23. Lee, S.-Y., & Wang, S. J. (1996). Sensitivity analysis of structural equation models. Psychometrika, 61, 93-108.
24. Lee, S.-Y., & Xu, L. (2003). On local influence analysis of full information item factor models. Psychometrika, 68, 339-360.
25. Lee, W.-C., & Rodgers, J. L. (1998). Bootstrapping correlation coefficients using univariate and bivariate sampling. Psychological Methods, 3, 91-103.
26. Little, R. J. A. (1988). Robust estimation of the mean and covariance matrix from data with missing values. Applied Statistics, 37, 23-38.
27. Lockwood, C. M. (1999). Effects of nonnormality on tests of mediation. Unpublished master's thesis, Arizona State University, Tempe, AZ.
28. MacKinnon, D. P. (2000). Contrasts in multiple mediator models. In J. S. Rose, L. Chassin, C. C. Presson, & S. J. Sherman (Eds.), Multivariate applications in substance use research: New methods for new questions (pp. 141-160). Mahwah, NJ: Erlbaum.
29. MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83-104.
30. MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39,99-128.
31. Magnus, J. R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics (Rev. ed.). New York: Wiley.
32. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57,519-530.
33. Maronna, R. A. (1976). Robust M-estimators of multivariate location and scatter. Annals of Statistics, 4,51-67.
34. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
35. Pan, J.-X., & Fang, K.-T. (2002). Growth curve models with statistical diagnostics. New York: Springer.
36. Pituch, K. A., & Stapleton, L. M. (2008). The performance of methods to test upper-level mediation in the presence of nonnormal data. Multivariate Behavioral Research, 43, 237-267.
37. Poon, W.-Y., & Poon, Y. S. (1999). Conformal normal curvature and assessment of local influence. Journal of the Royal Statistical Society B, 61, 51-61.
38. Poon, W.-Y., & Poon, Y. S. (2002). Influential observations in the estimation of mean vector and covariance matrix. British Journal of Mathematical and Statistical Psychology, 55, 177-192.
39. Porter, B., & O'Leary, K. D. (1980). Marital discord and childhood behavior problems. Journal of Abnormal Child Psychology, 8, 287-295.
40. Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879-891.
41. Roth, P. L., & Switzer, F. S., III (2002). Outliers and influential cases: Handling those discordant contaminated maverick rogues. In S. G. Rogelberg (Ed.), Handbook of research methods in industrial and organizational psychology (pp. 297-309). New York: Blackwell.
42. Rousseeuw, P. J., & Leroy, A. M. (2003). Robust regression and outlier detection. New York: Wiley.
43. Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7, 422-445.
44. Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology, 13, 290-312.
45. Stoker, J. J. (1969). Differential geometry. New York: Wiley.
46. Stone, C. A., & Sobel, M. E. (1990). The robustness of estimate of total indirect effects in covariance structure models estimated by maximum likelihood. Psychometrika, 55, 337-352.
47. Tyler, D. E. (1983). Robustness and efficiency properties of scatter matrices. Biometrika, 70, 411-420.
48. Wilcox, R. R. (1998). How many discoveries have been lost by ignoring modern statistical methods? American Psychologist, 53, 300-314.
49. Wilcox, R. R. (2001). Fundamentals of modern statistical methods: Substantially improving power and accuracy. New York: Springer.
50. Wilcox, R. R. (2005). Introduction to robust estimation and hypothesis testing (2nd ed.). San Diego, CA: Academic.
51. Yuan, K.-H., & Bentler, P. M. (1998). Structural equation modeling with robust covariances. Sociological Methodology, 28, 363-396.
52. Yuan, K.-H., Bentler, P. M., & Zhang, W. (2005). The effect of skewness and kurtosis on mean and covariance structure analysis: The univariate case and its multivariate implication. Sociological Methods & Research, 34, 240-258.
53. Yuan, K.-H., Chan, W., & Bentler, P. M. (2000). Robust transformation with applications to structural equation modeling. British Journal of Mathematical and Statistical Psychology, 53, 31-50.
54. Yuan, K.-H., & Zhong, X. (2008). Outliers, leverage observations and influential cases in factor analysis: Minimizing their effect using robust procedures. Sociological Methodology, 38, 329-368.
55. Zhu, H.-T., & Lee, S.-Y. (2001). Local influence for incomplete-data models. Journal of the Royal Statistical Society B, 63, 111-126.
56. Zimmerman, D. W. (1998). Invalidation of parametric and nonparametric statistical tests by concurrent violation of two assumptions. Journal of Experimental Education, 67, 55-68