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Recently I came across a difficult situation on mediation using SEM for latent variables. My empirical results revealed that the predictor variable is not related to the ourcome variable. According to Kenny, Kashy, and Bolger (1998) it can still conduct mediation analysis. However, I find it difficult to interpret the results both logically and methodologically. Although the techniques conducting mediation analysis for latent variable is somewhat different, some puzzles still exist. £) L2 X* ]* Y1 x1 j) i+ V$ Q* v, C7 p) _
Hypothesis 1: X is positively related to Y (path c) £
& F$ [1 K* F8 ^7 F6 O& l9 WHypothesis 2: M mediates the relationship between X and Y (X->M, path a, M->Y, path b, X->Y, path c'). To test the two hypotheses, four steps are suggested by Baron and Kenny (1986): Step 1: estimate and test path c; Step 2: estimate and test path a; Step 3: estimate and test path b; Step 4: see path c' whether equals to zero. £
& m; C4 Q f5 ^9 ?- D) ZNow my research question is somewhat different: X, M, and Y are all latent variables. According to Kenny (2008), for latent variable models, the total effect estimated from a model without the mediator (that is path c) is usually not comparable to the direct effect estimated from a model in which the mediator is included. It is then inadvisable to test the relative fit of two structural models, one with the mediator and one without.
$ Y1 B% S5 u9 h# WRather c, the total effect, can be estimated using the formula of c' + a*b. " v/ G! B* C/ d4 A6 s* T" @
My question 1 is: if we only can use c' + a*b to see the total effect of X on Y for latent variables, how do we know the significance level of the effect (p value for c' + a*b) so we can determine whether the data support or reject Hypothesis 1. £
' V' T$ v/ M5 dThe second question is whether all of the steps have to be met for there to be mediation. Kenny, Kashy, and Bolger (1998) showed that Step 1 is not required. Recently, one of my research projects comes across such situation. Results from SEM are as following: | | | SEM Model without mediator (M1) | | | | | | SEM Model with mediator (M2) | | | | | | | | |
Note: X, M, and Y are all latent variables; the number in the bracket is t-value According to Kenny (2008), we cannot rely on M1 to test Hypothesis 1 and we must use the results of M2. So the total effect of X on Y = -.06 + .39*(-.17) R% X6 o7 Y# d# [& p% m m
≈ -.13. Then, as my Question 1, how can we know the effect (-.13) significant or not? If we suppose the effect (-.13) is insignificant, following Kenny, Kashy, and Bolger (1998), we can still conduct mediation analysis. Sobel test revealed that Z = -1.895 with p = .058. The percentage of indirect effect is .39*(-.17)/(-.13) = 51%. Thus, M partially mediated the effect of X on Y. : C) T/ z4 |( ]
My question 2 is: if we can not determine the significance level of -.13, does the percentage of indirect effect really have informative meanings? That is, if we fail to support H1, we cannot rule out the possibility that X and Y has null effect. Then, the result that 51% of total effect is mediated really makes sense? References [1] 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. [2] Kenny, D. A. (2008). Reflections on Mediation. Organizational Research Methods. 11(2), 353-358. [3] Kenny, D. A., Kashy, D. A., & Bolger, N. (1998). Data analysis in social psychology.
9 r# k) ` }( G3 t1 o* X: R7 pIn D. Gilbert, S. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 1, 4th ed., pp. 233-265).% }+ V' Z8 I' C8 t8 y4 M! n0 d* u* y8 |
Boston, MA: McGraw-Hill. | 
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发表于 2011-6-26 17:41:27
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