1. Remaining Classes
Class 25 (Dec. 5): Moderated Multiple Regression Quiz 3 postponed to Dec. 7.
Class 26 (Dec. 7): Quiz 3; Designing Questions
Class 27 (Dec. 12): Writing Up Research
FINAL: Tuesday, Dec. 19, 11:30-1:00+
Room 371—Computer Lab
TAKE Home Exercise: Start of Final, Dec. 19

2. Dummy Variables and Moderated Multiple Regression
Class 24

3. Dummy Variables Continuous Predictor: Does age predict willingness
to be seen as angry?
Categorical Predictor: Does gender predict willingness to be seen as angry?
Gender is coded as a “dummy variable”
Values are always 0 and 1
e.g., Males = 0 Females = 1

4. Syntax (command) for Regression with Dummy Variable
IF (gender = 1) gender.dummy = 0.
EXECUTE.
IF (gender = 2) gender.dummy = 1.
[NOTE: Did this b/c “gender” was originally coded 1 = male, 2 = female.]
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT angerseen
/METHOD=ENTER age
/METHOD=ENTER gender.dummy.

6. Coefficient Outcomes With Dummy Variable

7. Dummy Coding for Categorical Variables with Multiple Values
Birth Order: First Born (oldest)
Middle Child
Last Born (youngest)
Only Child
Select one cond. as comparison, e.g. First Born. Select due to hyp. (Firsts diff. from all others) or Select because comp. group is largest
Comparison condition will ALWAYS have value of 0
First Born Middle Last Born Only Child
Birth.dummy
Birth.dummy
Birth.dummy

8. Syntax Dummy Variable with Multiple Values
Birth: 1 = oldest 2 = Middle 3 = Youngest 4 = Only Child
IF (birth = 1) birth.dummy1 = 0.
EXECUTE.
IF (birth = 2) birth.dummy1 = 1.
IF (birth = 3 | birth = 4) birth.dummy1 = 0
Birth.dummy1: Compares Oldest to Middle
“|” = “OR”
IF (birth = 1) birth.dummy2 = 0.
EXECUTE.
IF (birth = 3) birth.dummy2 = 1.
IF (birth = 2 | birth = 4) birth.dummy2= 0
Birth.dummy2: Compares Oldest to Youngest
IF (birth = 1) birth.dummy3 = 0.
EXECUTE.
IF (birth = 4) birth.dummy3 = 1.
IF (birth = 2 | birth = 3) birth.dummy3= 0
Birth.dummy3: Compares Oldest to Only Child

9. Syntax Dummy Variable with Multiple Values
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT angerseen
/METHOD=ENTER age
/METHOD = birth.dummy1 birth.dummy2 birth.dummy3.

11. Coefficients Summary with Multiple Dummy Variables
Oldest vs. Middle
Oldest vs. Youngest
Oldest vs. Only Child

12. Why Use Dummy Variables? Why Not Just Use ANOVA?
Need to use dummy variables if:
a. Study uses both categorical and continuous predictors
Gender and Age
b. You wish to examine interaction of categorical and continuous predictors
Gender X Age
OR neither a. or b. are true, but
c. You like to make things difficult for yourself

13. Moderated Multiple Regression
Class 24

14. VERY HELPFUL TEXTS ON MMR

15. Regression Models Basic Linear Model
Basic Linear Model
Features: Intercept, one predictor
Y = b0 + b1 + Error (residual)
Do bullies aggress more after being reprimanded? 
Multiple Linear Model
Features: Intercept, two or more predictors
Y = b0 + b1 + b2 + Error (residual)
  Do bullies aggress after reprimand and after family stress?
Moderated Multiple Linear Model
Features: Intercept, two or more predictors, and interaction term(s)
Y = b0 + b1 + b2 + b1b2 + Error (residual)
Aggress after reprimand, family stress, and (reprimand * stress)

16. Does Self Esteem Moderate the Use of Emotion as Information?
Harber, 2004, Personality and Social Psychology Bulletin, 31,
People use their emotions as information, especially when objective info.
is lacking.
Emotions are therefore persuasive messages from the self to the self.
Are all people equally persuaded by their own emotions?
Perhaps feeling good about oneself will affect whether to "believe" one's
own emotions.
Therefore, self-esteem should determine how much emotions affect judgment.
Thus, when self-esteem is high, emotions should influence judgment more,
when self-esteem is low, emotions should influence judgments less.

17. Self Esteem and Emotions as Info: Method
1. Collect self-esteem scores several weeks before experiment.
2. Subjects listen to series of 12 disturbing baby cries.
3. Subjects rate how much the baby is conveying distress
through his cries, for each cry.
4. After rating all 12 cries, subjects indicate how upsetting it was for them to listen to the cries.

18. Upset That Subjects Felt
Predictions
 Overall positive relation between personal upset and cry ratings
(more upset subjects feel, more extremely they'll rate baby cries), BUT:
The relation between own upset and baby cries will be
moderated by self-esteem
* For people w’ high esteem, the relation will be strongest
* For people w’ low esteem, the relation will be weakest.
Upset That Subjects Felt

19. Developing Predictor and Outcome Variables
PREDICTORS
Upset = single item "How upset did
baby cries make you feel?"
COMPUTE upsteem = upset*esteem .
EXECUTE .
OUTCOME
COMPUTE crytotl = (cry1 + cry2 + cry3 + cry4 + cry5 +
cry6 + cry7 + cry8 + cry9 + cry10 + cry11 + cry12) / 12 .
EXECUTE . 
Primary Predictor
Esteem = esteem1R + esteem2R + esteem3 + esteem4R + esteem5 + esteem6R + esttem7r + esteem8 + esteem9 + esteem10) / 10 .
Moderator
Interaction Term

20. SPSS Syntax for MMR _____ Stepwise _____ Hierarchical
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS BCOV R ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT crytotl
/METHOD=ENTER upset esteem
/METHOD=ENTER upset esteem upsteem .
_____ Stepwise
_____ Hierarchical
_____ Forced entry
What regression method used here? X
Why upset and esteem entered in Model 1, and upsteem in Model 2?
To test the unique contribution of interaction term (upsteem).

21. Interpreting SPSS Regression Output (a)
Regression
page A1

22. page A2

23. page B1 “Residual” = random error, NOT interaction R =
Adj. R2 =
R sq. change =
Power of regression
Amount var. explained
Sig. F Change =
Corrects for multiple predictors
Does new model explain signif. amount added variance
Impact of each added model
“Residual” = random error, NOT interaction

24. SPSS Regression Output: Predictor Effects
Constant refers to what?
Intercept; Value of DV when ALL IVs = 0
Slope; influence of IV on DV
B refers to what?
Variance around the slope
Std. Error refers to what?
Beta refers to what?
Standardization of B
t refers to what?
B / Std. Error
Sig. refers to what?
Significance of effect of IV on DV, sig. of slope

25. Understanding the Interaction in MMR
Pos. B for upsteem means pos. relation between (upset * esteem) and cry ratings;
Joe: High upset (5) and low esteem (1) Upsteem = 5*1 = 5 * b3 =
Lisa: Low upset (1) and low esteem (1) Upsteem = 1*1 = 1 * b3 = 0.18
Tim: Low upset (1) and high esteem (4) Upsteem = 1*4 = 4 * b3 = 0.73
Jane: High upset (5) and high esteem (5) Upsteem = 5*5 = 25 * b3 = 4.58
NOTES: b3 = 0.183; Graphs below do not include constant (intercept)
High Esteem People
Low Esteem People
Upset
Cry Ratings
Joe
.92
Lisa
.18
Jane
4.58
Cry Ratings
Tim
.73
Upset

26. Esteem and Affect as Information
Regression Model for
Esteem and Affect as Information
Model Y = b0 + b1X + b2Z + b3XZ
Where Y = cry rating
X = upset score
Z = esteem score
XZ = esteem*upset score
And b0 = X.XX = MEANING?
b1 = = X.XX = MEANING?
b2 = = X.XX = MEANING?
b3 = =X.XX = MEANING?

27. Esteem and Affect as Information
Regression Model for
Esteem and Affect as Information
Model: Y = b0 + b1X + b2Z + b3XZ
Where Y = cry rating
X = upset score
Z = esteem score
XZ = esteem*upset score
And b0 = = intercept (average score when
upset, esteem, upsetXexteem = 0)
b1 = = slope (influence) of upset
b2 = = slope (influence) of esteem
b3 = = slope (influence) of upset X
esteem interaction

28. DV? Moderator? Predictor?
Plotting Outcome: How Does Personal Upset Affect Baby Cry Ratings as a Function of One’s Self Esteem
DV?
Self Esteem
Moderator?
cry rating
Upset
Predictor?

29. PLOTTING INTERACTIONS: THREE PHASES
Develop three slopes, for three levels of the moderator
(e.g., Low Esteem, Average Esteem, High Esteem)
For each moderator slope, identify three points of the primary IV on which to draw the slope line.
Use moderator slopes and IV points to plot the interaction.

30. Phase 1: Develop Slopes for Three Levels of Moderator.
Y = b0 + b1X + b2Z + b3XZ
equals
Y = (b1 + b3Z)X + (b2Z + b0)
Y = (b1 + b3Z)X is simple slope of Y on X at Z.
Means “The effect Predictor X has on Outcome Y, conditioned
by the Moderator Z."
Means “The effect Upset has on Cry Ratings, conditioned by Self-Esteem.”
Thus, when Z (Esteem) is one value, the slope of X (Upset)
takes one shape, when Z (Esteem) is another value, the slope
of Upset takes other shape.

31. Transforming Regression Formula to Develop Moderator Slopes
Compute regression to obtain values of
Y = b0 + b1X + b2Z + b3XZ See Handout, last page.
2. Transform Y = b0 + b1X + b2Z + b3XZ into
Y = (b1 + b3Z)X + (b2Z + b0) and insert values
Y = (? + ?Z)X + (?Z + ?)
3. Select 3 values of Z that display the simple slopes of
X (upset) when Z (esteem) is low, average, and high.
Standard practice:
Z at one SD above the mean = ZH
Z at the mean = ZM
Z at one SD below the mean = ZL
Y = ( Z)X + (-.48Z )

32. Transforming Regression
(continued)
Insert values for all the regression coefficients (i.e., b1, b2, b3) and the intercept (i.e., b0), from computation (i.e., SPSS print-out).
Insert ZH into (b1 + b3Z)X + (b2Z + b0) to get slope when Z is high
Insert ZM into (b1 + b3Z)X + (b2Z + b0) to get slope when Z is moderate
Insert ZL into (b1 + b3Z)X + (b2Z + b0) to get slope when Z is low

33. Using Moderator Values to Derive Simple Slopes
Y (cry rating) = b (cry rating when all predictors = zero)
+ b1X (effect of upset) + b2Z (effect of esteem)
+ b3XZ (effect of upset X esteem interaction).
Y = X -.48Z + .18XZ.
Y = (b1 + b3Z)X + (b2Z + b0) [conversion for simple slopes]
Y = ( Z)X + (-.48Z )
Compute ZH, ZM, ZL via “Frequencies" for esteem, 3.95 = mean, .76 = SD
ZH, = ( ) = 4.71
ZM = ( ) = 3.95
ZL = (3.95― .76) = 3.19
Slope at ZH = ( * 4.71)X + ([-.48 * 4.71] ) = .32X
Slope at ZM = ( * 3.95)X + ([-.48 * 3.95] ) = .18X
Slope at ZL = ( * 3.19)X + ([-.48 * 3.19] ) = .04X

34. Phase 2: Selecting Values of Principal IV to Derive Slope Coordinates
1. Compute mean and SD of principal IV ("X") i.e., Upset
Upset mean = 2.94, SD = This is supplied in SPSS Descriptives
Select values on the X axis displaying main predictor, e.g. upset at:
Low upset = 1 SD below mean = 2.94 – 1.21 = 1.73
Medium upset = mean = 2.94 – 0.00 = 2.94
High upset = 1SD above mean = = 4.15
Plug these values into the ZH, ZM, ZL simple slope equations to compute coordinates
Simple
Slope
Formula
Low Upset
(X = 1.73)
Medium Upset
(X = 2.94)
High Upset
(X = 4.15) ZH
.32X
4.83
5.22
5.61 ZM
.18X
4.95
5.17
5.38 ZL
.04X
5.06
5.11
5.16

35. Plot Simple Slope Coordinates to Graph Interaction

36. Are the Simple Slopes Significant?
Question: Do the slopes of each of the simple effects lines
(ZH, ZM, ZL) significantly differ from zero?
Procedure to test, using as an example ZH (the slope when esteem is high):
1. Transform Z to Zcvh (cvh = conditional value / high) by subtracting ZH from Z.
Zcvh = Z - ZH = Z – 4.71
Conduct this transformation in SPSS as:
COMPUTE esthigh = esteem
Create new interaction term specific to Zcvh, i.e., (X* Zcvh)
  COMPUTE upesthi = upset*esthigh .
3. Run regression, using same X as before, but substituting
Zcvh for Z, and X* Zcvh for XZ

37. Are the Simple Slopes Significant?--Programming
COMMENT SIMPLE SLOPES FOR CLASS DEMO
COMPUTE esthigh = esteem
COMPUTE estmed = esteem
COMPUTE estlow = esteem
COMPUTE upesthi = esthigh*upset .
COMPUTE upestmed = estmed*upset .
COMPUTE upestlow = estlow*upset .
REGRESSION [for the simple effect of high esteem (esthigh)]
/MISSING LISTWISE
/STATISTICS COEFF OUTS BCOV R ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT crytotl
/METHOD=ENTER upset esthigh
/METHOD=ENTER upset esthigh upesthi .

38. Simple Slopes Significant?—Results
Regression
NOTE: Key outcome is B of "upset", Model 2. If significant, then the simple effect of upset for the high esteem slope is signif.

39. Moderated Multiple Regression with
Continuous Predictor and Categorical Moderator
(Aguinis, 2004)
Problem: Does performance affect faculty salary for tenured versus untenured professors?   
Criterion: Salary increase Continuous Var. $ $2148
Predictor: Performance Continuous Var
Moderator: Tenure Categorical Var (yes) 1 (no)

40. Regression Models to Test Moderating Effect of Tenure on Salary Increase
Without Interaction
Salary increase = b0 (ave. salary) + b1 (perf.) + b2 (tenure)
With Interaction
Salary increase = b0 (ave. salary) + b1 (perf.) + b2 (tenure) + b3 (perf. * tenure)
Tenure is categorical, therefore a "dummy variable", values = 0 or 1
These values are markers, do not convey quantity
Interaction term = Predictor * moderator, = perf. * tenure. That simple.
Conduct regression, plotting, simple slopes analyses same as when
predictor and moderator are both continuous variables.

41. Centering Data Centering data is done to standardize it.
Centering data is done to standardize it.
Aiken and West recommend doing it in all cases.
* Makes zero score meaningful
* Has other benefits
Aguinas recommends doing it in some cases.
* Sometimes uncentered scores are meaningful
Procedure
upset M = 2.94, SD = 1.19; esteem M = 3.94, SD = 0.75
COMPUTE upcntr = upset – 2.94.
COMPUTE estcntr = esteem = 3.94
upcntr: M = 0, SD = 1.19; estcntr: M = 0, SD = 0.75
Centering may affect the slopes of predictor and moderator, BUT
it does not affect the interaction term.

42. THE KENT AND HERMAN DIALOGUE
A Moderated Multiple Regression Drama
With A Satisfactory Conclusion
Appropriate for All Audiences

43. Overall model IS NOT significant
Interaction term IS marginally significant

44. Thank you for your response, Kent Harber
Act 1, Scene 1: Kent contacts Herman regarding this vexing conundrum.
Dear Dr. Aguinis, I am using your text in my graduate methods course. It is very clear and straightforward, which both my students and I appreciate.
A question came up that I thought you might be able to answer. If an MMR model produces a significant interaction, but the ANOVA F is not itself significant, is the significant interaction still a valid result? My impression is that the F of the overall model (as indicated by the ANOVA F and/or by the R-sqr. change) must be significant.
Thank you for your response, Kent Harber

45. Act 1, scene 2: Herman replies!
Kent, I believe you are referring to a test of a targeted interaction effect without looking at the overall (omnibus) effect. Please see pp of the book. Let me know if this does not answer your question and I will be delighted to follow up with you. Thanks for your kind words about my book! All the best, --Herman.

46. Act 1, scene 3: Are simple effects doomed???
Herman, thanks for getting back to me on this. Based on those pages of your text, it appears that the answer to my question is as follows:
If the omnibus F is itself not significant, then a significant interaction term within this non-significant model will itself not be interpretable.
Sadly (for some rather appealing interaction effects) this makes sense.
Again, very good of you to get back to me on this question. Best regards, Kent

47. Act 1, scene 4: Herman sustains the dramatic tension.
Kent, Before I give you an answer and to make sure I understand the question. What do you mean precisely by "the ANOVA F test"? Regards, --Herman.

48. Act 1, scene 4: Herman drops the Big Clue
Kent, Thanks for the clarification.
Now, I understand your question perfectly.
An article by Bedeian and Mossholder (1994), J. of Management, addresses this question directly. The full citation is on page 177 of my book.
All the best, --Herman.

49. Finale: Simple effects are redeemed!!! [enter marching band, stage right]

50. Overall model IS NOT significant
IF I predict this effect ahead of time (a priori), I can claim it, even if overall F is not significant.
Analogous to “planned contrast” in ANOVA.