1. DCAL Stats Workshop
Bodo Winter

2. Plan for today Generalized linear models Smileys Mixed models
Homework Q & A
Model selection
Handout
Extensive Q & A
Interaction theory
“Showreel”

3. Your smileys!
Jana Willer-Gold

4. Your smileys!
Sannah Gulamani

5. Your smileys!
Victoria Mousley

6. Your smileys!
Lindsay Ferrara

7. Your smileys!
Nicholas Barrie Palfreyman

8. Heidi’s smiley ;-)
m <-(x^2)/20 plot(x,m,col="red") points(0,10,col="pink",) points(-7,17,col="brown",) points(7,17,col="brown",)

9. An easy fix: xlab = ‘’ & ylab = ‘’

10. Plan for today
Smileys
Homework Q & A
Handout
Interaction theory

11. Plan for today
Smileys
Homework Q & A
Handout
Interaction theory

12. Plan for today
Smileys
Homework Q & A
Handout
Interaction theory

14. Plan for today
Smileys
Homework Q & A
Handout
Interaction theory

15. Mixing continuous and categorical predictors

16. Mixing continuous and categorical predictors

17. No interaction
RT ~ Noise + Gender

18. RT ~ Noise + Gender + Noise:Gender
With interaction
RT ~ Noise + Gender + Noise:Gender
RT ~ Noise * Gender

19. Mixing continuous and categorical predictors with interaction term
“non-parallel lines”
conditioning one predictor on another
‘the whole is more than the sum of its parts’

20. With interaction can be thought of a slope adjustment term
RT ~ Noise + Gender + Noise:Gender
RT ~ Noise * Gender

21. Continuous * categorical interaction output example
lm(RT ~ gender * noise, data = mydata)
(...)
Coefficients:
Estimate
(Intercept)
genderM
noise
genderM:noise -6
intercept: all other predictors = 0
= RT of women for
a noise of 0

22. Continuous * categorical interaction output example
lm(RT ~ gender * noise, data = mydata)
(...)
Coefficients:
Estimate
(Intercept)
genderM
noise
genderM:noise -6
female-male difference for
noise = 0

23. Continuous * categorical interaction output example
lm(RT ~ gender * noise, data = mydata)
(...)
Coefficients:
Estimate
(Intercept)
genderM
noise
genderM:noise -6
noise slope for women only

24. Continuous * categorical interaction output example
lm(RT ~ gender * noise, data = mydata)
(...)
Coefficients:
Estimate
(Intercept)
genderM
noise
genderM:noise -6
adjustment of noise slope for men

25. Continuous * categorical interaction output example
lm(RT ~ gender * noise, data = mydata)
(...)
Coefficients:
Estimate
(Intercept)
genderM
noise
genderM:noise -6
because these variables are conditioned on each other, they cannot be interpreted independently anymore

26. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
verb

27. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
verb

28. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

29. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

30. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

31. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

32. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

33. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

34. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
0.5
verb

35. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
sensory
abstract
noun
1.7
0.5
verb
2.9
1.5

36. Categorical * categorical interaction
N versus V
Yes versus No
lm(iconicity ~ part-of-speech * sensory_word, data = mydata) Estimate (Intercept) 0.5 part-of-speechV 1.0 sensoryYes 1.2 sensoryYes:part-of-speechV 0.2
beware of
conditioning!

37. Continuous * continuous interaction
No interaction
Interaction

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

39. Exercise
Linear model with interaction term