1. SFB stats workshop
Bodo Winter

2. Today
Correlation, linear models intro Linear models with categorical predictors and interactions Wrap-up & recommendations

3. Multiple regression / linear model awesomeness
y ~ A + B + C + D + ...
can be of any form
has to be continuous

4. Regression with categorical predictors

5. Regression with categorical predictors

6. Regression with categorical predictors

7. Regression with categorical predictors

8. Regression with categorical predictors

9. Regression with categorical predictors

10. Regression with categorical predictors

11. Regression with categorical predictors

12. Regression with categorical predictors

13. Demo set.seed(666) pred = c(rep(0,20),rep(1,20))
resp = c(rnorm(20,mean=2,sd=1),
rnorm(20,mean=2,sd=1))
for(i in 1:10){
resp = c(resp[1:20],resp[21:40]+1)
plot(resp~pred,
xlim=c(-1,2),ylim=c(0,14),xaxt="n",xlab="")
axis(side=1,at=c(0,1),labels=c("A","B"))
text(paste("mean of B\nequals:",i,sep="\n"),
x=-0.5,y=10,cex=1.5,font=2)
abline(lm(resp~pred))
Sys.sleep(1.25) }

14. Output for categorical predictors
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) <2e-16 *** genderFemale <2e-16 ***
The males are in the intercept (=109)
The slope for “female” is the change with respect to the male group

15. Default: Treatment coding

16. Default: Treatment coding
pitch gender male male male male female female female female

17. Default: Treatment coding
pitch gender gender male male male male female female female female 1
these are called dummy codes
by default, R does “treatment coding” and assumes that the alphanumerically first element is the reference level

18. Changing the reference level
xdata$myfac = relevel(xdata$myfac,ref=“male”)
Before releveling:
Estimate Std. Error t value Pr(>|t|)
(Intercept) <2e-16 ***
genderFemale <2e-16 ***
After releveling:
(Intercept) <2e-16 ***
myfactor.revmale <2e-16 ***

19. Other coding schemes

20. Other coding schemes

21. the intercept is now the mean of all pitch values (ignoring gender)
Other coding schemes
the intercept is now the mean of all pitch values (ignoring gender)

22. this is now the difference from the mean (=55)
Other coding schemes
This is called
sum coding
this is now the difference from the mean (=55)

23. Other coding schemes
This is called
deviation coding

24. Female = 0, Male = 1 (Treatment coding) Estimate Std
Female = 0, Male = 1 (Treatment coding) Estimate Std. Error t value Pr(>|t|) (Intercept) e-09 *** gender e-06 *** Female = -1, Male = 1 (Sum coding) (Intercept) e-09 *** gender e-06 *** Female = -0.5, Male = 0.5 (Deviation coding) gender e-06 ***

25. An extended linear Model
Y ~ b b1*X b2*X error
coefficients
predictors can be continuous or categorical and there can be (in principle) infinitely many

26. Interactions

27. Continuous * categorical interaction

28. Continuous * categorical interaction

29. Continuous * categorical interaction
RT ~ Noise + Gender

30. Continuous * categorical interaction
RT ~ Noise + Gender + Noise:Gender
RT ~ Noise * Gender

31. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
Y ~ b b1*X b2*X b3*(X1*X2)
interaction term

32. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
say you wanted the prediction for noise = 10 for females
Y ~ b b1*X b2*X b3*(X1*X2)

33. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
say you wanted the prediction for noise = 10 for females
Y ~ b1*X b2*X b3*(X1*X2)

34. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
say you wanted the prediction for noise = 10 for females
Y ~ * b2*X b3*(X1*X2)

35. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
say you wanted the prediction for noise = 10 for females
Y ~ * (-150)* b3*(X1*X2)

36. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
say you wanted the prediction for noise = 10 for females
Y ~ * (-150)* *(10*1)
“1” for female and “10” for the noise value we wanted

37. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
What about the men?
Y ~ * (-150)* *(1*10)

38. Interpreting cont * cat interactions
Example: Intercept 500 Noise 2 GenderF -150 Noise:GenderF 5
What about the men?
Y ~ * (-150)* *(0*10)

39. Interactions between continuous variables
No interaction
Interaction

40. Interactions between continuous variables
No interaction
Interaction

41. Interactions between continuous variables
No interaction
Interaction

42. Interactions between continuous variables
No interaction
Interaction

43. Interpreting continuous interactions
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ** word_frequency CD <2e-16 *** word_frequency:CD <2e-16 ***
Y ~ b b1*X b2*X b3*(X1*X2)

44. Interpreting continuous interactions
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ** word_frequency CD <2e-16 *** word_frequency:CD <2e-16 ***
Y ~ (-1.6)*X *X *(X1*X2)
Predictions for word frequency 3 and CD 50
Y = (-1.6)* * *(3*50)

45. Interpreting continuous interactions
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ** word_frequency CD <2e-16 *** word_frequency:CD <2e-16 ***
Y ~ (-1.6)*X *X *(X1*X2)
Predictions for word frequency 3 and CD 50
Y = 801

46. Sign of the interaction
Coefficients: Estimate (Intercept) 10 A +1 B +1 A:B +1

47. Sign of the interaction
Coefficients: Estimate (Intercept) 10 A +1 B +1 A:B -1

48. Sign of the interaction
Coefficients: Estimate (Intercept) 10 A -1 B -1 A:B +1

49. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
male

50. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
male

51. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
male

52. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
male

53. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
260-30
male

54. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
260-30
male

55. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
260-30
male

56. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
260-30
male

57. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
260-30
male

58. Categorical interactions: 2 X 2 example output with treatment coding
attitude = “inf” or “pol”
gender = “F” or “M”
Opposite sign means that the effect of politeness is smaller for males
Estimate
(Intercept)
attitudepol
genderM
attitudepol:genderM
informal
polite
female
260
230
male
140
125

59. Today
Correlation, linear models intro Linear models with categorical predictors and interactions Wrap-up & recommendations

60. … or, as Uncle Ben would say

61. “A world of subjectivity”
Sarah Depaoli (UC Merced)
“IF YOU BEAT THE DATA, AT SOME TIME IT WILL SPEAK”
data loss
- illustrate how proportions loose data by 2/4 … and 30/60 ….etc.

63. Your regression equation = Your experiment = Your theory
My philosophy
Your regression equation = Your experiment = Your theory

64. design
analysis

65. Open, reproducible research
“BE HONEST…”
“NOT PURE”
John McArdle

67. Stay in touch (+ upcoming book)
Newsletter on my webpage: bodowinter.com

68. Reading list
(1) Will send R tutorial for recap (2) Read my linear models tutorial (3) Buy
(4) Datacamp ggplot2 tutorial
+ Coursera “data specialization”

69. Bedtime reading

70. “What we observe is not nature itself but nature exposed to our method of questioning.”
Werner Heisenberg

71. THANK YOU