1. Weight, Shape, and Body Images Geller, Johnston, & Madsen, 1997
Multiple Regression #2
Weight, Shape, and Body Images
Geller, Johnston, & Madsen, 1997

2. Major Points The SAWBS scale Relationships among variables
Multiple regression analyses
Standard multiple regression
Hierarchical regression
Semi-partial correlation
Partial correlation
Cont.
12/3/2018

3. Major Points-cont. Tolerance Interaction models
Centering
Moderating and mediating effects
12/3/2018

4. The SAWBS Scale Shape and Weight Based Self-Esteem
Geller, Johnston, & Madsen, 1997
Measures degree to which self-esteem is based on shape and weight
Not a measure of self-esteem
Subjects created pie chart indicating role of S&W.
Angle of pie = dep. var.
12/3/2018

5. The Data N = 84 female subjects Variables SAWBS
Wt. Perception(7 points 1=overweight, 7 = underweight)
Shape Perception (7 points 1 = unattractive, 6 = very attractive)
HIQ (presence and severity of disturbed eating practices)
Cont.
12/3/2018

6. Data-cont. I created data to match theirs
EDIcomp (Eating Disorders Index)
RSES (Rosenberg Self-esteem Scale)
BDI (Beck Depression Inventory)
BMI (Body Mass Index)
SES (Socio-economic status)
SocDesir (a lie scale)
I created data to match theirs
12/3/2018

7. Relationship Among Variables
SAWBS and
Physical characteristics
Perceptions
Eating disorders
Self-Esteem
See next slide for matrix
12/3/2018

8. 12/3/2018

9. Multiple Regression Analysis
Predict eating disorders from
BMI
Depression (BDI)
Self-esteem (RSES)
12/3/2018

11. Hierarchical Regression
Not a new concept, just an “in” name.
Does the SAWBS add anything to prediction over and above other predictors?
Simply add SAWBS to preceding solution and look at increment.
12/3/2018

13. Results Notice change in R2 Note change in SSregression
from .575 to .671 = .096
Note change in SSregression
from 14,609 to 17,047 = 2,438
We have an F test on the increase
12/3/2018

14. F test on increment in R2
12/3/2018

15. Alternative Test
When we add only one predictor we have exactly the same test through the t on the slope.
From printout t = 4.797, which would square to F if I hadn’t rounded.
12/3/2018

16. Semi-partial Correlation
The increment in R2 when we add one or more predictors
For the example, this is =.096.
Increase in R2 over an above or controlling for the other predictors
Independent contribution of SAWBS
12/3/2018

17. Partial Correlation Semi-partial divided by (1-Rr2)
.096/(1-.575)=.226 = increment as a function of what was left to be explained.
See Venn Diagrams on next page.
12/3/2018

18. Venn Diagram Semi-partial squared = A/(A+B+C+D)
Partial squared = A/(A+D)
12/3/2018

19. Tolerance
(1- squared correlation) of one predictor from all other predictors.
Measure of what that predictor does not have in common with other predictors.
Use BMI versus BDI,RSES, & SAWBS =
12/3/2018

20. Predicting EDICOMP from BMI, BDI, RSES, and SAWBS
Predicting BMI from other predictors
12/3/2018

21. Interaction Effects Analogous to Anova
Suppose SAWBS was highly correlated with depression for females, but not for males.
Dep = SAWBS + SEX + SAWBSSex
12/3/2018

22. Moderating Effects This is basically what the interaction is.
In first example, there is a relationship between SAWBS and Depression for females, but not for males.
Sex moderates the relationship between SAWBS and depression.
12/3/2018

23. Depression and SAWBS-hypothetical data
12/3/2018

24. Procedure
Create a variable that is the product of the two supposedly interacting variables.
Add that variable to regression.
Look for significant effect for that interaction variable.
But there is a problem
multicollinearity
12/3/2018

25. The Problem
12/3/2018

26. Centering Subtract corresponding mean from each main effect variable.
Create product of two centered variables.
But, this will not change the interaction term, just the main effect terms.
Result on next slide for BDI from SAWBS and ShPer and Interaction.
12/3/2018

28. A Different Data Set Why generate new data set?
The idea was to predict Symp from Hassles at each of several levels of Support
Wanted to see that the slope of Symp on Hassles changed when support changed.
This would be an interaction.
12/3/2018

29. Italassi Representation-3D
12/3/2018

30. 2D with low support
12/3/2018

31. 2D with high support
12/3/2018

32. Mediating Effects Baron & Kenny (1986)
Important paper on this and moderating effects.
For B to mediate between A and C
A and B correlated
B and C correlated
PathAC reduced when B added to model B A C
12/3/2018

33. Testing for Mediation
Baron and Kenny talk about decrease in direct path when indirect added.
But how do we test decrease?
No good answer that I know of.
Baron and Kenny do give a test of the complete A-->B-->C path.
See slide #40.
12/3/2018

34. Mediation in Esther Leerkes’ Study
Does self-esteem mediate between maternal care (by mom’s mom) and maternal self-efficacy (of mom). b1
Maternal
Care
Self-Efficacy b2 b3
Self-Esteem
12/3/2018

35. Step 1 Direct path .27* Maternal Self-Efficacy Care Self-Esteem
12/3/2018

36. Step 2a&b Indirect path Maternal Self-Efficacy Care .40* .38*
Self-Esteem
12/3/2018

37. Step 3 Full model .14ns Maternal Self-Efficacy Care .32* .40*
Self-Esteem
12/3/2018

38. Step 3 printout
12/3/2018

39. Conclusion 1
Baron and Kenny argue that since the regression between maternal care and self-efficacy dropped out when self-esteem was entered, there was a mediating role of self-esteem.
Alternative approach would be to test the care-->self-esteem-->self-efficacy path.
12/3/2018

40. Indirect Path Coefficient
bcare-->se-->effic = b2*b3 = .403*.323=.130
See
12/3/2018

41. Calculations
In the previous slide note that we use beta and the standard error of beta. We could use b and its standard error, and it shouldn’t make any difference.
The subscripts refer to the paths as numbered on slide 34.
12/3/2018

42. Mediated model
Maternal Care
Self-efficacy
.130*
Self-esteem
12/3/2018

43. t test Just divide beta by its standard error
t = 0.130/.052 = 2.50, which is significant
Thus there is a significant indirect path from maternal care to daughter’s self esteem to daughter’s self-efficacy
12/3/2018

44. Assumptions for Testing Mediation
The dependent variable does not cause the mediator.
The mediator is measured without error.
This is virtually never true
When it is false, the test becomes conservative, in the sense that it is harder to show mediation.
12/3/2018

45. Another Interesting Example
Eron, Huesman, Lefkowitz, and Walder (1972) on TV violence and aggression.
They collected data on kids in 3rd grade and again when those kids were one year out of school (13th grade)
Recorded the amount of violent television they watched, and the amount of aggressive behavior.
The is called Cross-lagged Panel Analysis.
12/3/2018

46. Data Generation
I generated these data to match Eron’s correlations. I used standardized data for convenience, which explains why b and b are equal in printout that follows.
12/3/2018

47. Eron’s Results
12/3/2018

48. Regression Approach
12/3/2018

49. t Test on Mediation
12/3/2018