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Multiple Regression #2

Multiple Regression #2. Weight, Shape, and Body Images Geller, Johnston, & Madsen, 1997. Major Points . The SAWBS scale Relationships among variables Multiple regression analyses Standard multiple regression Hierarchical regression Semi-partial correlation Partial correlation. Cont.

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Multiple Regression #2

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  1. 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.

  3. Major Points-cont. • Tolerance • Interaction models • Centering • Moderating and mediating effects

  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.

  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.

  6. Data-cont. • 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

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

  8. Multiple Regression Analysis • Predict eating disorders from • BMI • Depression (BDI) • Self-esteem (RSES)

  9. 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.

  10. Results • Notice change in R2 • 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

  11. F test on increment in R2

  12. 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.

  13. Semi-partial Correlation • The increment in R2 when we add one or more predictors • For the example, this is .671-.575=.096. • Increase in R2over an above or controlling for the other predictors • Independent contribution of SAWBS

  14. 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.

  15. Venn Diagram B C • Semi-partial squared = A/(A+B+C+D) • Partial squared = A/(A+D) A D

  16. 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 • 1 - .02825 = .97175

  17. Predicting EDICOMP from BMI, BDI, RSES, and SAWBS Predicting BMI from other predictors

  18. Interaction Effects • Analogous to Anova • Suppose SAWBS was highly correlated with depression for females, but not for males. • Dep = SAWBS + SEX + SAWBSSex

  19. 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.

  20. Depression and SAWBS-hypothetical data

  21. 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

  22. The Problem

  23. 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.

  24. 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.

  25. Italassi Representation-3D

  26. 2D with low support

  27. 2D with high support

  28. 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

  29. 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.

  30. 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

  31. Step 1 • Direct path .27* Maternal Care Self-Efficacy Self-Esteem

  32. Step 2a&b • Indirect path Maternal Care Self-Efficacy .40* .38* Self-Esteem

  33. Step 3 • Full model .14ns Maternal Care Self-Efficacy .32* .40* Self-Esteem

  34. Step 3 printout

  35. 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.

  36. Indirect Path Coefficient • bcare-->se-->effic = b2*b3 = .403*.323=.130 See http://w3.nai.net/~dkenny/mediate.htm

  37. 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.

  38. Mediated model Maternal Care Self-efficacy .130* Self-esteem

  39. ttest • 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

  40. 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.

  41. 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.

  42. 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.

  43. Eron’s Results

  44. Regression Approach

  45. t Test on Mediation

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