Multiple regression 2
Download
1 / 49

Multiple Regression #2 - PowerPoint PPT Presentation


  • 145 Views
  • Updated On :

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Multiple Regression #2' - jennica


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Multiple regression 2 l.jpg

Multiple Regression #2

Weight, Shape, and Body Images

Geller, Johnston, & Madsen, 1997


Major points l.jpg
Major Points

  • The SAWBS scale

  • Relationships among variables

  • Multiple regression analyses

    • Standard multiple regression

    • Hierarchical regression

    • Semi-partial correlation

    • Partial correlation

Cont.


Major points cont l.jpg
Major Points-cont.

  • Tolerance

  • Interaction models

    • Centering

  • Moderating and mediating effects


The sawbs scale l.jpg
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.


The data l.jpg
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.


Data cont l.jpg
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


  • Relationship among variables l.jpg
    Relationship Among Variables

    • SAWBS and

      • Physical characteristics

      • Perceptions

      • Eating disorders

      • Self-Esteem

    • See next slide for matrix


    Multiple regression analysis l.jpg
    Multiple Regression Analysis

    • Predict eating disorders from

      • BMI

      • Depression (BDI)

      • Self-esteem (RSES)


    Hierarchical regression l.jpg
    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.


    Results l.jpg
    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


    F test on increment in r 2 l.jpg
    F test on increment in R2


    Alternative test l.jpg
    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.


    Semi partial correlation l.jpg
    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


    Partial correlation l.jpg
    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.


    Venn diagram l.jpg
    Venn Diagram

    B

    C

    • Semi-partial squared = A/(A+B+C+D)

    • Partial squared = A/(A+D)

    A

    D


    Tolerance l.jpg
    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


    Slide20 l.jpg

    Predicting EDICOMP from BMI, BDI, RSES, and SAWBS

    Predicting BMI from other predictors


    Interaction effects l.jpg
    Interaction Effects

    • Analogous to Anova

    • Suppose SAWBS was highly correlated with depression for females, but not for males.

    • Dep = SAWBS + SEX + SAWBSSex


    Moderating effects l.jpg
    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.



    Procedure l.jpg
    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



    Centering l.jpg
    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.


    A different data set l.jpg
    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.





    Mediating effects l.jpg
    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


    Testing for mediation l.jpg
    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.


    Mediation in esther leerkes study l.jpg
    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


    Step 1 l.jpg
    Step 1

    • Direct path

    .27*

    Maternal

    Care

    Self-Efficacy

    Self-Esteem


    Step 2 a b l.jpg
    Step 2a&b

    • Indirect path

    Maternal

    Care

    Self-Efficacy

    .40*

    .38*

    Self-Esteem


    Step 3 l.jpg
    Step 3

    • Full model

    .14ns

    Maternal

    Care

    Self-Efficacy

    .32*

    .40*

    Self-Esteem



    Conclusion 1 l.jpg
    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.


    Indirect path coefficient l.jpg
    Indirect Path Coefficient

    • bcare-->se-->effic = b2*b3 = .403*.323=.130

    See http://w3.nai.net/~dkenny/mediate.htm


    Calculations l.jpg
    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.


    Mediated model l.jpg
    Mediated model

    Maternal Care

    Self-efficacy

    .130*

    Self-esteem


    T test l.jpg
    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


    Assumptions for testing mediation l.jpg
    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.


    Another interesting example l.jpg
    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.


    Data generation l.jpg
    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.