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1 21 12 23 . ( mediation analysis) Figure 1 . X Y M (mediator) . mediation model .. Baron and Kenny (1986) .. 1 .. 1) mediated moderation ( moderated mediation ) 2). (multilevel mediation model) .. M. a b X Y. c (c'). 1: . 1 .. Baron and Kenny (1986) .. a b c c a b . supressor variable model 2 . , e-mail: .. 1 Baron and Kenny (1986) 2009 12 10000 . 2 Maassen & Bakker (2001) . 1. (X) (Y ) . Y = intercept + c X + e (1). e c . c . M = intercept + aX + e (2). a .. Y = intercept + cX + bM + e (3). (1) X c . c c . (3) b X. M Y (indirect e ect) a b .. 1 c c . X Y M . X Y c M . c c .. c c = a b (4). c M .. c 1 X Y . X Y M . (complete mediation model) .. c . (partial mediation model) Kenny Judd & Kenny (1981) . Baron & Kenny (1986) .. X Y . , mediation e ect.

2 MacKinnon, Lockwood, Ho man, West, and Sheets (2002) MacKinnon (2008) . 2.. 1 a b ab . a b z= (5). ab 5% . MacKinnon et al. (2002) Sobel's test . Aroian (1944) a b (4) . c c a b c c . (Clogg et al., 1992 ) .. Sobel's test Sobel (1982) . a b .. ab = a2 b2 + b2 a2 (6). a , b a b (delta method) . X f (X) . f (X) 2. V ar(f (X)) = ( ) (V ar(X)) (7). X. X f (X) . V ar(f (X)) = d V d (8). V X f (X) X . d Mplus model constraint .. f (a, b) = a b a b b a . d = (b, a) X . ( ). a2 0. V = (9). 0 b2. (6) (8) 1 . 0 a b 0 1 . (MacKinnon et al., 1995) . Aroian (1944)'s test 1 2 . Aroian (1944) a b .. ab = a2 b2 + b2 a2 + a2 b2 (10). 3. Sobel's test Sobel's test . Distribution of a product method PRODCLIN . critical value .. (con dence interval) 3 95% 0 .. a b Dis- tribution of a product method Springer & Thompson (1966).

3 Table MacKinnon, Fritz, Williams, &. Lockwood (2007) PROD- CLIN (distribution of the PRODuct Con dence Limits for INdirect e ects) . davidpm/ripl/Prodclin/ . a, b, a , b .. a b . 0 0 X M .. t . 2. t critical value Table MacKinnon . Website 4 MacKinnon et al. (2004) Empirical-M method . 2 critical value Table MacKinnon Website 5 .. Bootstrapping method 1 .. a b . 3 . 4 davidpm/ 5 davidpm/ 4.. 95% 6 0 . nonparametric bootstrapping . SAS R . N N . a b a b a b . 7 parametric bootstrapping (Efron & Tibshirani, 1993) . a b a b 95% . bootstrap . a b Efron &. Tibshirani, 1993 bias-corrected bootstrapping method . MacKinnon et al. (2004) bootstrapping method . bias-corrected bootstrap . distribution of a product method . parametric bootstrapping . AMOS, EQS, Mplus SEM.

4 8 distribution of a product method bias-corrected bootstrapping . PRODCLIN . bootstrapping 2 . (X M1 M2 Y . bootstrapping .. (SEM) . (structural equation modeling; SEM) Baron and Kenny (1986) Figure 1 c . bootstrapping SEM . Baron and Kenny (1986) SEM 9 . Figure 1 . X Y .. SEM 1 (full infor- mation maximum likelihood method) . 6 . 7N N . 1 . 8 SEM Figure 1 bootstrapping .. 9 SEM t z .. 5. Baron and Kenny (1986) SEM .. SEM (multiple mediator model) .. a b a b . c . MacKinnon et al. (2002) . Baron and Kenny (1986) a b c .. Baron and Kenny (1986) . a, b, c .. H0 : a b = 0 vs. H1 : a b = 0 (11).. H0 : a = 0 OR b=0 (12). a b . a = 0 b = 0.. 2 Moderated mediation model mediation moderation mediation X Y M . moderation X Y Z. (moderator, moderator variable) X Z.)

5 (Baron and Kenny, 1986) .. Y = intercept + c X X + c Z Z + c XZ XZ + e (13). 6. X Z 10 X Z . XZ X Z . (Cronbach, 1987) . Y = intercept + (c X + cXZ Z)X + c Z Z + e (14). X Z.. moderated mediation model . 2 moderated mediation . Figure 1 a, b, c Z . Z a b . Z a b . moderated mediation Z . Figure 1 SEM. Z . mediated moderation Muller, Judd, and Yzerbyt (2005) Edwards and Lambert (2007) .. moderated mediation model Figure 2 . moderation e ect Z . mediated moderation cXZ . Edwards and Lambert (2007) Figure 2 moderated path analysis . M. aX + aXZ Z bM + bMZ Z. X Y. cX + cXZ Z. (c'X + c'XZ Z). 2: moderated mediation model . M . M = intercept + aX X + aZ Z + aXZ XZ + e (15). 10 Z X .. 7. (2) aXZ X M . Z Y . Y = intercept + cX X + cXZ XZ + bM M + bM Z M Z + dZ Z + e (16).

6 (3) . Z .. moderator +1SD -1SD . moderator . bootstrap Edwards and Lambert (2007) SPSS.. mediated moderation ? mediated moderation mediated moderation mediated moderation . Z . mediated moderation Muller et al. (2005) Edwards and Lambert (2007) mediated moderation moderated path analysis (Figure 2) moderation . mediated moderation Figure ?? . aXZ Figure ?? (moderated path model) moderated mediation mediated moderation .. 3 .. (multilevel mediation model, multilevel mediation analysis) . (Hierarchical linear model; HLM) (multilevel structural equation modeling; ML-SEM) . Krull and MacKinnon (1999, 2001) . ( , Bauer, Preacher, & Gil, 2006; Kenny, Bolger, & Korchmaros, 2003) .. Preacher 11 HLM (Zhang, Zyphur, & Preacher, 2009) ML-SEM (Preacher, Zhphur, & Zhang, in press).

7 11 . 8.. 1 . 2 1 . 1-1-1 2 . 2-1-1 . 2 2 2 = 8 1-1-2 .. Krull and MacKinnon (1999, 2001) 2-1-1. 2 1 1 .. 2 1 (Kreft & De Leeuw, 1998) . 2 1 . Preacher . 2 1 . 2.. 2 1 .. 2 1 . 1 2 . 1 2 .. 2 . 1 2-1-1 . 2 1 . 1 . 1-1 1 2 . X M Y 1 M Y . Figure 3 2-2-1 2 . 2 1 . 2 1-1-1 . 1 1 . 1 2 . 2 1-1-1 X M Y . 1 2 . 9. HLM . HLM ML-SEM . 1 . 2 2-1-1 . HLM Xj . Yij X 2 1 i .. (1) (1). Level 1 : Yij = 0j + rij (17). (1) (1) (1) (1). Level 2 : 0j = 00 + 01 Xj + u0j (18).. (2) (2). Level 1 : Mij = 0j + rij (19). (2) (2) (2) (2). Level 2 : 0j = 00 + 01 Xj + u0j (20).. (3) (3) (3). Level 1 : Yij = 0j + 1j Mij + rij (21). (3) (3) (3) (3). Level 2 : 0j = 00 + 01 Xj + u0j (22). (3) (3). 1j = 10. (21) Mij 1 . 1 2 . (3). 10 1 2 . 1 2 .. Mij 2 aggregate . 1 2. grand-mean centering 2.

8 Group-mean centering 12 (21) . 12 Enders and To ghi (2007) Y. ij Xij . grand-mean centering 2 . grand-mean centering . (a) (a) (a). Level 1 : Yij = 0j + 1j Xij + rij (23). (a) (a) (a) (a). Level 2 : 0j = 00 + 01 + u0j (24). (a) (a). 1j = 10 (25). (a). 01 1 Xij . 2 1 Xij (over and above) . contextual e ect compositional e ect . 10. (22) . (4) (4) (4). Level 1 : Yij = 0j + 1j (Mij ) + rij (30). (4) (4) (4) (4) (4). Level 2 : 0j = 00 + 01 Xj + 02 + u0j (31). (4) (4). 1j = 10. 1 group-mean centering 2 . 1 2 aggregation . 1 2. 2-1-1 . Figure 3 Preacher et al. (in press) . M .j 02( 4). 01( 2).. X j Y. 01( 4 ). ( ). (1). 01. M.. X Y. M ij 10( 4).. Y. 3: 2-1-1 Multilevel mediation model . 2-2-1 1-1-1 . 1 . group-mean centering . group-mean centering.

9 (b) (b) (b). Level 1 : Yij = 0j + 1j (Xij ) + rij (26). (b) (b) (b) (b). Level 2 : 0j = 00 + 01 + u0j (27). (b) (b). 1j = 10 (28). 2 1 . 2 group-mean centering . (Enders & To ghi, 2007) 2 1 . (b) (b). 2 01 10 contextual e ect . 2 contextual e ect . (a) (b) (b). 01 = 01 10 (29). (Ludtke et al., 2009) 1 2 group-mean centering . 11. Zhang et al. (2009) .. ML-SEM . ML-SEM 1 2 . HLM 1 . Xij ML-SEM.. Xij = + uj + rij (32). 1 uj 2 rij 2 . ML-SEM 1 2 . 13. ML-SEM . straightforward 2 .. ML-SEM Mplus . Preacher HP 14 2 between . 2 1 between/within . 1 2 .. (4) . 2 2. Sobel test . 15. Preacher et al. (in press) nonparametric bootstrapping parametric bootstrapping Mplus .. 2 .. moderated mediation model . multilevel mediation model Bauer et al. (2006) HLM.

10 13 2 . HLM ML-SEM . (Ludtke et al., 2009) socio-economic status (SES) aggregation Ludtke et al. (2009) . Marsh et al. (in press) . 14 preacher/syntax appendix 15 Mplus model constraint Sobel's test . 12. 4 References Aroian, L. A. (1944). The probability function of the product of two normally distributed variables. Annals of Mathematical Statistics, 18, 265-271. Baron, R. M. & Kenny, D. A. (1986). The moderator?mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Person- ality and Social Psychology, 51, 1173-1182. Bauer, D. J., Preacher, K. J., & Gil, K. M. (2006). Conceptualizing and testing random indirect e ects and moderated mediation in multilevel models: New procedures and recommendations.