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Multiple Linear Regression with Mediator

Multiple Linear Regression with Mediator. Conceptual Model. IV1. H 1. H 2. IV2. H 11. Satisfaction. Purchase Intention. H 3. IV3. H 4. IV4. H 5. IV5. Indirect Effect. Conceptual Model (direct and indirect effects). H 1. IV1. H 6. H 2. H 7. IV2. H 11. Satisfaction.

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Multiple Linear Regression with Mediator

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  1. Multiple Linear Regressionwith Mediator

  2. Conceptual Model IV1 H1 H2 IV2 H11 Satisfaction Purchase Intention H3 IV3 H4 IV4 H5 IV5 Indirect Effect

  3. Conceptual Model (direct and indirect effects) H1 IV1 H6 H2 H7 IV2 H11 Satisfaction Purchase Intention H3 H8 IV3 H9 H4 IV4 H5 H10 IV5 Indirect Effect Direct Effect

  4. Testing Mediator Effects Three regression equations should be estimated • Regressing the mediator on the IV--the IV must affect the mediator (Path A) • Regressing the DV on the IV--the IV must affect the DV (Path C) • Regressing the DV on both IV and on mediator--mediator must affect the DV, and the effect of the IV on DV must be less than the effect in the second equation

  5. Test Mediator Effect (Satisfaction) • Model 1: Mediator and IVs • Model 2: DV and IVs • Model 3: Full Model (with interactions) Regressing Satisfaction on IVs: Sat = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5) Regressing PI on IVs: PI = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5) Regressing PI on Satisfaction, Loyalty, and IVs: PI = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5) + + b6(IV1*Sat) + b7(IV2*Sat) + b8(IV3*Sat) + b9(IV4*Sat) + b10(IV5*Sat) + b11(Sat)

  6. Conceptual Model H1 IV1 H6 H17 H2 H7 IV2 H16 Satisfaction Purchase Intention H11 H3 H8 IV3 H9 H4 • For each IV, there are both direct effect and indirect • effect from the IV to DV • Considering the effects of IV1 on DV, the direct effect • is tested by H1; whereas, the indirect effects are • tested by H6 and H11 IV4 H5 H10 IV5

  7. Conceptual Model H1 Test alternative hypothesis that H1: b1 ≠ 0 Loyalty IV1 H6 H17 H11-15 H2 H7 IV2 H16 Satisfaction Purchase Intention H3 H8 IV3 H9 H4 IV4 Regressing PI on Satisfaction, Loyalty, and IVs: PI = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5) + + b6(IV1*Sat) + b7(IV2*Sat) + b8(IV3*Sat) + b9(IV4*Sat) + b10(IV5*Sat) + b11(Sat) H5 H10 IV5

  8. Conceptual Model H1 Test alternative hypothesis that H6: b6 ≠ 0 Loyalty IV1 H6 H17 H11-15 H2 H7 IV2 H16 Satisfaction Purchase Intention H3 H8 IV3 H9 H4 IV4 Regressing PI on Satisfaction, Loyalty, and IVs: PI = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5) + + b6(IV1*Sat) + b7(IV2*Sat) + b8(IV3*Sat) + b9(IV4*Sat) + b10(IV5*Sat) + b11(Sat) H5 H10 IV5

  9. Conceptual Model Test alternative hypothesis that H11: b11 ≠ 0 H1 IV1 H6 H17 H2 H7 IV2 H16 Satisfaction Purchase Intention H11 H3 H8 IV3 H9 H4 IV4 H5 H10 Regressing PI on Satisfaction, Loyalty, and IVs: PI = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5) + + b6(IV1*Sat) + b7(IV2*Sat) + b8(IV3*Sat) + b9(IV4*Sat) + b10(IV5*Sat) + b11(Sat) IV5

  10. Test Mediator Effect (Satisfaction) • Model 1: Mediator and IVs • check whether an IV effects mediator • at least one of the coefficients/parameter estimates is not equal to 0 (at least b1, b2, b3, b4, or b5 ≠ 0) Regressing Satisfaction on IVs: Sat = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5)

  11. Test Mediator Effect (Satisfaction) • Model 2: DV and IVs • check whether an IV effects DV • at least one of the coefficients/parameter estimates is not equal to 0 (at least b1,2, b2,2, b3,2, b4,2, or b5,2 ≠ 0) Regressing PI on IVs: PI = b0 + b1,2(IV1) + b2,2(IV2) + b3,2(IV3) + b4,2(IV4) + b5,2(IV5)

  12. Test Mediator Effect (Satisfaction) Regressing PI on Satisfaction, Loyalty, and IVs: PI = b0 + b1,3(IV1) + b2,3(IV2) + b3,3(IV3) + b4,3(IV4) + b5,3(IV5) + + b6(IV1*Sat) + b7(IV2*Sat) + b8(IV3*Sat) + b9(IV4*Sat) + b10(IV5*Sat) + b11(Sat) • Model 3: Full Model (with interactions) • check whether Mediator effects DV; therefore, b16 must not equal to 0 (b16 ≠ 0) • check whether the effect of the IV on DV must be less than the same effect in the second equation; therefore, one of these must be true: • b1,3 < b1,2 • b2,3 < b2,2 • b3,3 < b3,2 • b4,3 < b4,2 • b5,3 < b5,2

  13. Multiple Linear Regressionwith Moderator

  14. Model without moderator Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .088 + .198 (comm) + .184 (encou) + .237 (info) + .383 (avail) comm encou Satisfaction info avail

  15. Model Developing with Moderator Can we directly add gender into our regression model? Sat = b0 + b1(comm) + … + b7(avail) + b8(gender) The answer is NO; All variables in MLR must be interval, ratio scales, or dummy variable; ‘gender’ has only nominal scale (male and female)

  16. Model Developing with Moderator • We need to transform nominal-scale variable (gender) into dummy variable • Dummy variable has only 2 values (0 or 1; 0 means that category is not present; 1 mean it is present) • For nominal-scale variable with (n) values (# of categories), we need (n-1) dummy variables to represent them • Gender (male/female) has two values; therefore, we need 2-1 = 1 dummy variable

  17. Dummy Variable • Gender (male/female) is transformed to dummy variable, say female • female = 1 if a respondent is female = 0 if otherwise Model for Male is called the based model

  18. Dummy Variable Cluster membership (3 segments; 1, 2, and 3) is transformed to 2 dummy variables, say s1, and s2 s1 = 1 if a respondent belongs to segment 1 = 0 if otherwise s2 = 1 if a respondent belongs to segment 2 = 0 if otherwise Segment 3 is called the based segment here

  19. Dummy Variable Cluster membership (3 segments; 1, 2, and 3) is transformed to 2 dummy variables, say s1, and s2 s1 = 1 if a respondent belongs to segment 1 = 0 if otherwise s2 = 1 if a respondent belongs to segment 2 = 0 if otherwise Segment 3 is called the based segment here

  20. Dummy Variable Cluster membership (3 segments; 1, 2, and 3) is transformed to 2 dummy variables, say s1, and s2 s1 = 1 if a respondent belongs to segment 1 = 0 if otherwise s2 = 1 if a respondent belongs to segment 2 = 0 if otherwise Segment 3 is called the based segment here

  21. Overall Satisfaction Model with Gender

  22. Overall Satisfaction Model with Gender There is no gender effect on Overall Satisfaction with Advisor

  23. Overall Satisfaction Model with Gender Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .055 + .180(comm) + .117(encou) + .328(info) + .402(avail) - .082(female)

  24. Overall Satisfaction Model with Gender Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .055 + .180(comm) + .117(encou) + .328(info) + .402(avail) - .082(female) • Model for female (female = 1) • Model for male (female = 0) Regression Model for Predicting Overall Satisfaction with Advisor: Sat = (.055 - .082) + .180(comm) + .117(encou) + .328(info) + .402(avail) Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .055 + .180(comm) + .117(encou) + .328(info) + .402(avail) Coefficient of female dummy indicates the difference of Overall Satisfaction between female and based category (male (female=0), in this case)

  25. Model Developing with Moderator • Presenting only direct effect of gender is not enough • Moderator effect is also represented as crossover interaction between IVs and moderator (gender) • Interaction variables are created by directly multiple IVs with moderator (dummy variable/female) • For example, new interaction fcomm comes from female times comm (fcomm = female * comm)

  26. Creating Interaction Variable in SPSS From Menu: Transform >> Compute Variables

  27. Interaction Variables

  28. Overall Satisfaction Model with Gender Now we will run a regression model with: • ‘Overall Satisfaction with Advisor’ as DV • 15 variables as IVs • 7 original IVs • 1 female dummy variable, and • 7 interaction variables (interaction between IVs and female)

  29. Overall Satisfaction Model with Gender Final Model: Combined effect of gender and info on Satisf Direct effect of gender on Satisf

  30. Overall Satisfaction Model with Gender Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .336 + .218(comm) + .314(info) + .420(avail) - .597(female) + .135(finfo)

  31. Overall Satisfaction Model with Gender Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .336 + .218(comm) + .314(info) + .420(avail) - .597(female) + .135(finfo) • Model for female (female = 1) • Model for male (female = 0) Regression Model for Predicting Overall Satisfaction with Advisor: Sat = (.336 - .597) + .218(comm) + (.314 + .135)(info) + .420(avail) Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .336 + .218(comm) + .314(info) + .420(avail) Coefficient of female dummy indicates the difference of Overall Satisfaction between female and based category (male (female=0), in this case)

  32. Final Model Regression Model for Predicting Overall Satisfaction with Advisor: Sat = .336 + .218(comm) + .314(info) + .420(avail) - .597(female) + .135(finfo) comm avail Satisfaction info gender*info gender

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