multiple linear regression with mediator. conceptual model iv1 iv2 iv3 iv4 iv5 indirect effect h1h1...

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


H1

Conceptual Model

IV2

IV3

IV4

Loyalty

IV5

H1

H2

H3

H4

H5

H7

H8

H9

H10

H11-15

H16

H17


IV1

SatisfactionPurchase Intention


H6

Conceptual Model

IV2

IV3

IV4

IV5

H1

H2

H3

H4

H5

H6

H7

H8

H9

H10

H16

H17


IV1

Purchase Intention

Satisfaction


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)


• 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)

• 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:


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


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


Segment 1 1 1 0

Segment 2 2

Segment 3 3



Dummy Variable


Segment 1 1 1 0

Segment 2 2 0 1

Segment 3 3 0 0



Dummy Variable

Overall Satisfaction Model with Gender

There is no gender effect on Overall Satisfaction with Advisor


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


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)



• 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


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


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)

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)



Final Model

Satisfaction

comm

avail

info

gender*info

gender


multiple linear regression with mediator. conceptual model iv1 iv2 iv3 iv4 iv5 indirect effect h1h1...

Documents

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