common applications of regression mediating models candy teaching evals happy

Common Applications of Regression

Common Applications of Regression

• Mediating Models

Candy Teaching Evals

Happy

Mediating Relationships

IVDV

Mediator

ab

c

Mediating Relationships

IV

Mediator

a

1. There is a relationship between the IV and the Mediator

Mediating Relationships

DV

Mediator

b

2. There is a relationship between the Mediator and the DV

Mediating Relationships

IVDV

c

3. There is a relationship between the IV and DV

Mediating Relationships

IVDV

Mediator

ab

c

4. When both the IV and mediator are used to predict the DV the importance of path c is greatly reduced

Common Applications of Regression

• Moderating Models

• Does the relationship between the IV and DV change as a function of the level of a third variable

• Interaction

Example

• Girls risk behavior– Cigarettes, alcohol, pot, kissing

• Openness to experience

• Pubertal Development

• How might pubertal development moderate the relationship between openness and participation in risk behaviors?– Note: pubertal development is the variable you think moderates

the relationship (mathematically this is irrelevant)

Example

• Data were collected from 20 girls

• Mother’s rating of openness

• Doctor’s rating of pubertal development

• One year later girls report of risk behaviors– Sum risk behavior

1.000 .143 .330

.143 1.000 .637**

.330 .637** 1.000

. .547 .156

.547 . .002

.156 .002 .

20 20 20

20 20 20

20 20 20

PUB

OPEN

RISK

PUB

OPEN

RISK

PUB

OPEN

RISK

PearsonCorrelation

Sig.(2-tailed)

N

PUB OPEN RISK

Correlations

Correlation is significant at the 0.01 level (2-tailed).**.

How do you examine an interaction?

• Multiply the two variables you think will interact with each other– Openness x puberty

• Should always center these variables BEFORE multiplying them– Reduces the relationship between them and

the resulting interaction term

1.000 .143 .330

.143 1.000 .637**

.330 .637** 1.000

. .547 .156

.547 . .002

.156 .002 .

20 20 20

20 20 20

20 20 20

PUB

OPEN

RISK

PUB

OPEN

RISK

PUB

OPEN

RISK

PearsonCorrelation

Sig.(2-tailed)

N

PUB OPEN RISK

Correlations

Correlation is significant at the 0.01 level (2-tailed).**.

1.000 .143 .330

.143 1.000 .637**

.330 .637** 1.000

. .547 .156

.547 . .002

.156 .002 .

20 20 20

20 20 20

20 20 20

CPUB

COPEN

RISK

CPUB

COPEN

RISK

CPUB

COPEN

RISK

PearsonCorrelation

Sig.(2-tailed)

N

CPUB COPEN RISK

Correlations

Correlation is significant at the 0.01 level (2-tailed).**.

1.000 .143 .000

.143 1.000 .278

.000 .278 1.000

. .547 1.000

.547 . .235

1.000 .235 .

20 20 20

20 20 20

20 20 20

CPUB

COPEN

CINTER

CPUB

COPEN

CINTER

CPUB

COPEN

CINTER

PearsonCorrelation

Sig.(2-tailed)

N

CPUB COPEN CINTER

Correlations

1.000 .143 .693**

.143 1.000 .766**

.693** .766** 1.000

. .547 .001

.547 . .000

.001 .000 .

20 20 20

20 20 20

20 20 20

PUB

OPEN

INTER

PUB

OPEN

INTER

PUB

OPEN

INTER

PearsonCorrelation

Sig.(2-tailed)

N

PUB OPEN INTER

Correlations

Correlation is significant at the 0.01 level (2-tailed).**.

How do you examine an interaction?

• Conduct a regression with:

• Centered IV1 (openness)

• Centered IV2 (puberty)

• Interaction of these (open x puberty)

• Predicting outcome (Sum Risk)

3.149 .091 34.569 .000

.161 .081 .265 1.971 .066

.246 .076 .454 3.245 .005

.257 .068 .525 3.792 .002

(Constant)

CPUB

COPEN

CINTER

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Coefficientsa

Dependent Variable: RISKa.

Graphing a Moderating Variable

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

Graphing a Moderating Variable

Using this information it is possible to predict what a girl’s risk behavior would for different levels of openness and puberty.

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

Graphing a Moderating Variable

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

Using this information it is possible to predict what a girl’s risk behavior would for different levels of openness and puberty.

For example -- Imagine 3 girls who have average development (i.e., cpuberty = 0).

One girl’s openness is 1 sd below the mean (copen = -1.14)

One girl’s opennes is at the mean (copen = 0)

One girl’s openness is 1 sd above the mean (copen = 1.14)

puberty Open o*p Pred Y

0 -1.14 0

0 0 0

0 1.14 0

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

puberty Open o*p Pred Y

0 -1.14 0 2.87

0 0 0 3.15

0 1.14 0 3.43

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

2

3

4

5

Openness

Ris

k B

ehav

ior

-1.14 0 1.14

puberty Open o*p Pred Y

0 -1.14 0 2.87

0 0 0 3.15

0 1.14 0 3.43

puberty Open o*p Pred Y

1.28 -1.14 -1.46

1.28 0 0

1.28 1.14 1.46

0 -1.14 0 2.87

0 0 0 3.15

0 1.14 0 3.43

More

Average

When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

puberty Open o*p Pred Y

1.28 -1.14 -1.46 2.70

1.28 0 0 3.36

1.28 1.14 1.46 4.02

0 -1.14 0 2.87

0 0 0 3.15

0 1.14 0 3.43

More

Average

When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

2

3

4

5

Openness

Ris

k B

ehav

ior

-1.14 0 1.14

puberty Open o*p Pred Y

1.28 -1.14 -1.46 2.70

1.28 0 0 3.36

1.28 1.14 1.46 4.02

puberty Open o*p Pred Y

1.28 -1.14 -1.46 2.70

1.28 0 0 3.36

1.28 1.14 1.46 4.02

0 -1.14 0 2.87

0 0 0 3.15

0 1.14 0 3.43

-1.28 -1.14 1.46

-1.28 0 0

-1.28 1.14 -1.46

More

Average

Less

When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

puberty Open o*p Pred Y

1.28 -1.14 -1.46 2.70

1.28 0 0 3.36

1.28 1.14 1.46 4.02

0 -1.14 0 2.87

0 0 0 3.15

0 1.14 0 3.43

-1.28 -1.14 1.46 3.09

-1.28 0 0 2.94

-1.28 1.14 -1.46 2.84

More

Average

Less

When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY

2

3

4

5

Openness

Ris

k B

ehav

ior

-1.14 0 1.14

puberty Open o*p Pred Y

-1.28 -1.14 1.46 3.09

-1.28 0 0 2.94

-1.28 1.14 -1.46 2.84

2

3

4

5

Openness

Ris

k B

ehav

ior

-1.14 0 1.14

More Dev.

Average Dev.

Less Dev.

Practice

• Based on past research you know that martial happiness is related unhealthy dieting habits in women.

• However, you think that women’s esteem might moderate this relationship– Specifically, you think a woman with high self esteem

will not be affected as greatly by a poor marriage as a woman with low self-esteem

Practice

• Date were collected from 172 women

• Martial Quality (M = 0; SD = 1)• Esteem (M = 0; SD = 1)• Unhealthy Dieting (Range 0 - 19)

• Determine if esteem moderated the relationship between marital quality and unhealthy dieting

2.528 .183 13.787 .000

-.681 .199 -.266 -3.431 .001

-.303 .187 -.118 -1.623 .107

.389 .151 .193 2.573 .011

(Constant)

ZESTEEM Zscore(ESTEEM)

ZMARQUAL Zscore(MARQUAL)

INTERAC

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Coefficientsa

Dependent Variable: UNDIETa.

)*(389.)(303.)(681.53.2ˆ esteemmarmarestY

2.528 .183 13.787 .000

-.681 .199 -.266 -3.431 .001

-.303 .187 -.118 -1.623 .107

.389 .151 .193 2.573 .011

(Constant)

ZESTEEM Zscore(ESTEEM)

ZMARQUAL Zscore(MARQUAL)

INTERAC

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Coefficientsa

Dependent Variable: UNDIETa.

Est Mar E*M Pred Y

-1 -1 1 3.90

-1 0 0 3.21

-1 1 -1 2.51

0 -1 0 2.83

0 0 0 2.53

0 1 0 2.23

1 -1 -1 1.76

1 0 0 1.85

1 1 1 1.93

Low

Mod

High

When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

)*(389.)(303.)(681.53.2ˆ esteemmarmarestY

1

1.5

2

2.5

3

3.5

4

Marital Quality

Un

hea

lth

y D

ieti

ng

-1 0 1

High SE

Average SE

Low SE

Handout

• DV = Risk Behavior (0 – 4)

• IV = Child’s perception of monitoring

• IV = Objective measure of monitoring

Handout Practice

• 1) Draw a causal model using the standardized regression coefficients.

• 2) Determine if the overall model significantly predicts risk behavior.

• 3) Compute the semipartial correlation for each IV

• 4) Determine if the unstandardized regression weights are significant.

• 5) Discuss in a few sentences what is the overall “story” being told by these data