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1、http:/203.208.35.101/search?q=cache:IERvvryqTfQJ: partial+mediation rather statistics can be used to evaluate a presumed mediational model. The reader should consult the section below on Specification Error. There is a long history in the study of mediation (Hyman, 1955; MacCorquodale the mediator a
2、nd the outcome may be correlated because they are both caused by the initial variable X. Thus, the initial variable must be controlled in establishing the effect of the mediator on the outcome. Step 4: To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for
3、 M (path c)should be zero (see discussion on significance testing). The effects in both Steps 3 and 4 are estimated in the same equation. If all four of these steps are met, then the data are consistent with the hypothesis that variable M completely mediates the X-Y relationship, and if the first th
4、ree steps are met but the Step 4 is not, then partial mediation is indicated. Meeting these steps does not, however, conclusively establish that mediation has occurred because there are other (perhaps less plausible) models that are consistent with the data. Some of these models are considered later
5、 in the Specification Error section. Note that the steps are stated in terms of zero and nonzero coefficients, not in terms of statistical significance, as they were in Baron and Kenny (1986). Because trivially small coefficients can be statistically significant with large sample sizes and very larg
6、e coefficients can be nonsignificant with small sample sizes, the steps should not be defined in terms of statistical significance. Statistical significance is informative, but other information should be part of statistical decision making. For instance, consider the case in which a is large, b is
7、zero, and so c = c. It is very possible that the statistical test of c is not significant (due to the collinearity of X and M) whereas c is significant. It would then appear that there is complete mediation when if fact there is no mediation at all. Following, Kenny, Kashy, and Bolger (1998), one mi
8、ght ask whether all of the steps have to be met for there to be mediation. Certainly, Step 4 does not have to be met unless the expectation is for complete mediation. In the opinion of most though not all analysts, Step 1 is not required. However, note that a path from the initial variable to the ou
9、tcome is implied if Steps 2 and 3 are met. If c were opposite in sign to ab something that MacKinnon, Fairchild, and Fritz (2007) refer to as “inconsistent mediation,“ then it could be the case that Step 1 would not be met, but there is still mediation. In this case the mediator acts like a suppress
10、or variable. Most analysts believe that the essential steps in establishing mediation are Steps 2 and 3. James and Brett (1984) have argued that Step 3 should be modified by not controlling for the initial variable. Their rationale is that if there is complete mediation, there would be no need to co
11、ntrol for the initial variable. However, because complete mediation does not always occur, it would seem sensible to control for X in Step 3. Measuring Mediation or the Indirect Effect The amount of mediation, which is called the indirect effect, is defined as the reduction of the effect of the init
12、ial variable on the outcome or c - c. This difference in coefficients is theoretically exactly the same as the product of the effect of X on M times the effect of M on Y or ab; thus it holds that ab c - c. The two are exactly equal when a) multiple regression (or structural equation modeling without
13、 latent variables) is used, b) there are no missing data, c) and the same covariates are in the equation. However, the two are only approximately equal for multilevel models, logistic analysis and structural equation model with latent variables. For such models, it is probably inadvisable to compute
14、 c from Step 1, but rather c should be inferred to be c + ab and not directly computed. Note that the amount of reduction in the effect of X on Y is not equivalent to either the change in variance explained or the change in an inferential statistic such as F or a p value. It is possible for the F fr
15、om the initial variable to the outcome to decrease dramatically even when the mediator has no effect on the outcome! It is also not equivalent to a change in partial correlations. If Step 2 (the test of a) and Step 3 (the test of b) are met, it follows that there necessarily is a reduction in the ef
16、fect of X on Y. One way to test the null hypothesis that ab = 0 is to test that both a and b are zero (Steps 2 and 3). If such a strategy were used and one wanted a .05 probability of the combined test that a = 0 and b = 0, then alpha for the tests of a and b should lowered to .0253 so that the Type
17、 I error protection rate is correct. Much more commonly, a single test is used and is highly recommended (MacKinnon, Lockwood, Hoffman, West, these variables are commonly called covariates . They would generally included in each equation and would not be trimmed from equations unless they are droppe
18、d from all of the equations. Dichotomous Variables In this case either the mediator or the outcome is a dichotomy. Having the initial variable be a dichotomy is not problematic. In this case the analysis would likely be conducted using logistic regression when the criterion measure is dichotomous. O
19、ne can still use the Baron and Kenny steps and the Sobel test. The one complication is the computation of indirect effect the degree of mediation, but coefficients need to be transformed. (To read about the computation of indirect effects click here.) Multilevel Modeling Estimation of mediation with
20、in multilevel models can be very complicated, especially when the mediation occurs at level one and when that mediation is allowed to be random, i.e., vary across level two units. The reader is referred to Krull and MacKinnon (1999), Kenny, Korchmaros, and Bolger (2003), and Bauer and Preacher (2006
21、) for a discussion of this topic. Links to Other Sites The mediation site of Dave MacKinnon. To find out why computing partial correlations to test mediation is wrong. A web-based Sobel test of the indirect effect or abby Preacher and Leonardelli. Go to my moderation page. A paper I have written cal
22、led “Reflections on Mediation .“ References Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182. Bauer, D. J., Preacher, K.
23、 J., & Gil, K. M. (2006). Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: New procedures and recommendations. Psychological Methods, 11, 142-163. Edwards, J. R., & Lambert L. S. (2007). Methods for integrating moderation and mediation: A general anal
24、ytical framework using moderated path analysis. Psychological Methods, 12, 1-22. Hoyle, R. H., & Kenny, D. A. (1999). Statistical power and tests of mediation. In R. H. Hoyle (Ed.), Statistical strategies for small sample research . Newbury Park: Sage. Hyman, H. H. (1955). Survey design and analysis
25、. New York: Glencoe, IL: The Free Press. James, L. R., & Brett, J. M. (1984). Mediators, moderators and tests for mediation. Journal of Applied Psychology, 69, 307-321. Judd, C. M., & Kenny, D. A. (1981). Process analysis: Estimating mediation in treatment evaluations. Evaluation Review, 5, 602-619.
26、 Kenny, D. A., Kashy, D. A., & Bolger, N. (1998). Data analysis in social psychology. In D. Gilbert, S. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 1, 4th ed., pp. 233-265). Boston, MA: McGraw-Hill. Kenny, D. A., Korchmaros, J. D., & Bolger, N. (2003). Lower level mediation i
27、n multilevel models. Psychological Methods, 8, 115-128. Kraemer H. C., Wilson G. T., Fairburn C. G., & Agras W. S. (2002). Mediators and moderators of treatment effects in randomized clinical trials. Archives of General Psychiatry, 59, 877-883. Krull, J. L. & MacKinnon, D. P. (1999). Multilevel medi
28、ation modeling in group-based intervention studies. Evaluation Review, 23, 418-444. MacCorquodale, K., & Meehl, P. E. (1948). On a distinction between hypothetical constructs and intervening variables. Psychological Review, 55, 95-107. MacKinnon, D. P., Fairchild, A. J., & Fritz, M. S. (2007). Media
29、tion analysis. Annual Review of Psychology, 58, 593-614. MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test the significance of the mediated effect. Psychological Methods, 7, 83-104. MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995).
30、 A simulation study of mediated effect measures. Multivariate Behavioral Research, 30, 41-62. Muller, D., Judd, C. M., & Yzerbyt, V. Y. (2005). When moderation is mediated and mediation is moderated. Journal of Personality and Social Psychology, 89, 852-863. Shrout, P. E., & Bolger, N. (2002). Media
31、tion in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7, 422-445. Smith, E. (1982). Beliefs, attributions, and evaluations: Nonhierarchical models of mediation in social cognition. Journal of Personality and Social Psychology, 43,248-259. Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhardt (Ed.), Sociological Methodology 1982 (pp. 290-312). Washington DC: American Sociological Association.