Multiple Linear Regression with Mediator

Conceptual Model IV1 IV2 IV3 IV4 IV5 Indirect Effect H1H1 H2H2 H3H3 H4H4 H5H5 H 11

Conceptual Model (direct and indirect effects) IV1 IV2 IV3 IV4 IV5 Indirect Effect Direct Effect H1H1 H2H2 H3H3 H4H4 H5H5 H6H6 H7H7 H8H8 H9H9 H 10 H 11

Testing Mediator Effects Three regression equations should be estimated 1.Regressing the mediator on the IV--the IV must affect the mediator (Path A) 2.Regressing the DV on the IV--the IV must affect the DV (Path C) 3.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

Model 1: Mediator and IVs Model 2: DV and IVs Model 3: Full Model (with interactions) Regressing Satisfaction on IVs: Sat = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) Test Mediator Effect (Satisfaction) Regressing PI on IVs: PI = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) Regressing PI on Satisfaction, Loyalty, and IVs: PI = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) + + b 6 (IV1*Sat) + b 7 (IV2*Sat) + b 8 (IV3*Sat) + b 9 (IV4*Sat) + b 10 (IV5*Sat) + b 11 (Sat)

Conceptual Model IV2 IV3 IV4 IV5 H2H2 H3H3 H4H4 H5H5 H7H7 H8H8 H9H9 H 10 H 16 H 17 H 11 H6H6 IV1 H1H1 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 H 1 ; whereas, the indirect effects are tested by H 6 and H 11

Conceptual Model IV2 IV3 IV4 IV5 H2H2 H3H3 H4H4 H5H5 H6H6 H7H7 H8H8 H9H9 H 10 H H 16 H 17 Test alternative hypothesis that H 1 : b 1 ≠ 0 IV1 Regressing PI on Satisfaction, Loyalty, and IVs: PI = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) + + b 6 (IV1*Sat) + b 7 (IV2*Sat) + b 8 (IV3*Sat) + b 9 (IV4*Sat) + b 10 (IV5*Sat) + b 11 (Sat) H1H1

Conceptual Model IV2 IV3 IV4 IV5 H1H1 H2H2 H3H3 H4H4 H5H5 H7H7 H8H8 H9H9 H 10 H H 16 H 17 Test alternative hypothesis that H 6 : b 6 ≠ 0 IV1 Regressing PI on Satisfaction, Loyalty, and IVs: PI = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) + + b 6 (IV1*Sat) + b 7 (IV2*Sat) + b 8 (IV3*Sat) + b 9 (IV4*Sat) + b 10 (IV5*Sat) + b 11 (Sat) H6H6

Conceptual Model IV2 IV3 IV4 IV5 H1H1 H2H2 H3H3 H4H4 H5H5 H6H6 H7H7 H8H8 H9H9 H 10 H 16 H 17 Test alternative hypothesis that H 11 : b 11 ≠ 0 IV1 Regressing PI on Satisfaction, Loyalty, and IVs: PI = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) + + b 6 (IV1*Sat) + b 7 (IV2*Sat) + b 8 (IV3*Sat) + b 9 (IV4*Sat) + b 10 (IV5*Sat) + b 11 (Sat) H 11

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 b 1, b 2, b 3, b 4, or b 5 ≠ 0) Regressing Satisfaction on IVs: Sat = b 0 + b 1 (IV1) + b 2 (IV2) + b 3 (IV3) + b 4 (IV4) + b 5 (IV5) 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 b 1,2, b 2,2, b 3,2, b 4,2, or b 5,2 ≠ 0) Test Mediator Effect (Satisfaction) Regressing PI on IVs: PI = b 0 + b 1,2 (IV1) + b 2,2 (IV2) + b 3,2 (IV3) + b 4,2 (IV4) + b 5,2 (IV5)

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: Test Mediator Effect (Satisfaction) Regressing PI on Satisfaction, Loyalty, and IVs: PI = b 0 + b 1,3 (IV1) + b 2,3 (IV2) + b 3,3 (IV3) + b 4,3 (IV4) + b 5,3 (IV5) + + b 6 (IV1*Sat) + b 7 (IV2*Sat) + b 8 (IV3*Sat) + b 9 (IV4*Sat) + b 10 (IV5*Sat) + b 11 (Sat) b 1,3 < b 1,2 b 2,3 < b 2,2 b 3,3 < b 3,2 b 4,3 < b 4,2 b 5,3 < b 5,2

Multiple Linear Regression with Moderator

Model without moderator comm encou info Regression Model for Predicting Overall Satisfaction with Advisor: Sat = (comm) (encou) (info) (avail) avail

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

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 Model Developing with Moderator

Dummy Variable genderfemale Male10 Female21 Model for Male is called the based model Gender (male/female) is transformed to dummy variable, say female female = 1 if a respondent is female = 0 if otherwise

Cluster Members1s2 Segment 11 Segment 22 Segment 33 Segment 3 is called the based segment here 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 Dummy Variable

Cluster Members1s2 Segment 1110 Segment 22 Segment 33 Segment 3 is called the based segment here 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 Dummy Variable

Cluster Members1s2 Segment 1110 Segment 2201 Segment 3300 Segment 3 is called the based segment here 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 Dummy Variable

Overall Satisfaction Model with Gender

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

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

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

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)

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

Interaction Variables

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)

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

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

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

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