Multiple Linear Regression with Mediator
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Transcript of Multiple Linear Regression with Mediator
Multiple Linear Regressionwith Mediator
Conceptual Model
Satisfaction
IV1
IV2
IV3
IV4
IV5
Purchase Intention
Indirect Effect
H1
H2
H3
H4
H5
H11
Conceptual Model (direct and indirect effects)
Satisfaction
IV1
IV2
IV3
IV4
IV5
Purchase Intention
Indirect Effect
Direct Effect
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11
Testing Mediator EffectsThree regression equations should be estimated1. 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 = b0 + b1(IV1) + b2(IV2) + b3(IV3) + b4(IV4) + b5(IV5)
Test Mediator Effect (Satisfaction)
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)
Conceptual Model
IV2
IV3
IV4
IV5
H2
H3
H4
H5
H7
H8
H9
H10
H16
H17
Purchase Intention
SatisfactionH11
H6IV1
H1
• 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
Satisfaction
Conceptual Model
IV2
IV3
IV4
Loyalty
IV5
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11-15
H16
H17
Test alternative hypothesis thatH1: b1 ≠ 0
IV1
Purchase Intention
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)
H1
Conceptual Model
IV2
IV3
IV4
Loyalty
IV5
H1
H2
H3
H4
H5
H7
H8
H9
H10
H11-15
H16
H17
Test alternative hypothesis thatH6: b6 ≠ 0
IV1
SatisfactionPurchase Intention
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)
H6
Conceptual Model
IV2
IV3
IV4
IV5
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H16
H17
Test alternative hypothesis thatH11: b11 ≠ 0
IV1
Purchase Intention
Satisfaction
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)
H11
• 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)
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)
Test Mediator Effect (Satisfaction)
Regressing PI on IVs:PI = b0 + b1,2(IV1) + b2,2(IV2) + b3,2(IV3) + b4,2(IV4) + b5,2(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 = 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)
• b1,3 < b1,2
• b2,3 < b2,2
• b3,3 < b3,2
• b4,3 < b4,2
• b5,3 < b5,2
Multiple Linear Regressionwith Moderator
Model without moderator
Satisfaction
comm
encou
info
Regression Model for Predicting Overall Satisfaction with Advisor:Sat = .088 + .198 (comm) + .184 (encou) + .237 (info) + .383 (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
gender female
Male 1 0
Female 2 1
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 Member s1 s2
Segment 1 1
Segment 2 2
Segment 3 3
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 s2s1 = 1 if a respondent belongs to segment 1 = 0 if otherwises2 = 1 if a respondent belongs to segment 2 = 0 if otherwise
Dummy Variable
Cluster Member s1 s2
Segment 1 1 1 0
Segment 2 2
Segment 3 3
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 s2s1 = 1 if a respondent belongs to segment 1 = 0 if otherwises2 = 1 if a respondent belongs to segment 2 = 0 if otherwise
Dummy Variable
Cluster Member s1 s2
Segment 1 1 1 0
Segment 2 2 0 1
Segment 3 3 0 0
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 s2s1 = 1 if a respondent belongs to segment 1 = 0 if otherwises2 = 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 = .055 + .180(comm) + .117(encou) + .328(info) + .402(avail) - .082(female)
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)
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 = .336 + .218(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 = (.336 - .597) + .218(comm) + (.314 + .135)(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 = .336 + .218(comm) + .314(info) + .420(avail)
Regression Model for Predicting Overall Satisfaction with Advisor:Sat = .336 + .218(comm) + .314(info) + .420(avail) - .597(female) + .135(finfo)
Overall Satisfaction Model with Gender
Final Model
Satisfaction
comm
avail
info
gender*info
gender
Regression Model for Predicting Overall Satisfaction with Advisor:Sat = .336 + .218(comm) + .314(info) + .420(avail) - .597(female) + .135(finfo)