1. Model Selection I: principles of model choice and designed experiments
Quantitative Methods
Model Selection I:
principles of model choice and designed experiments

2. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice

3. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice

4. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice
Varying a
Varying b
Y = a + bX

5. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice
Varying c
Y = a + bX + cX2

6. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice
Varying c
Varying d, Part I
Varying d, Part II
Y = a + bX + cX2
Y = a + bX + cX2 + dX3
Any continuous curve can be sufficiently well approximately by a polynomial of high enough order.

7. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice
Y1 = *X *X12

8. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice
Y1 = *X *X *X13

9. The problem of model choice
Model Selection I: principles of model choice
The problem of model choice
Linear
Quadratic
Cubic …
Y1 = X1
Y1 = X1|X1
Y1 = X1|X1|X1 …
Y1 = *X1
Y1 = *X *X12
Y1 = *X *X *X13 …

10. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice

11. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Economy of variables
Multiplicity of p-values
Marginality

12. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Economy of variables
Multiplicity of p-values
Marginality
Hierarchies must be respected in model formulae
Significance of interactions includes importance of main effects
Do not test main effects with a SS that has been adjusted for the interaction

13. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
What does marginal mean?
A is marginal to A*B, A*B*C, A*X*X
A is not marginal to B, B*C, B*C*X
X is marginal to X*X, A*X, A*B*X
X is not marginal to A, Z, Z*Z, A*B, A*B*Z

14. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Why marginal?

15. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Economy of variables
Multiplicity of p-values
Marginality
Hierarchies must be respected in model formulae
Significance of interactions includes importance of main effects
Do not test main effects with a SS that has been adjusted for the interaction

16. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Y=X
Y=X+X*X
Y=X+X*X+X*X*X
Hierarchical
Y=X*X
Y=X*X + X
Y=X*X*X + X
Not hierarchical
Lower order term missing
Lower order term after higher order term
Lower order term missing and wrong order

17. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Economy of variables
Multiplicity of p-values
Marginality
Hierarchies must be respected in model formulae
Significance of interactions includes importance of main effects
Do not test main effects with a SS that has been adjusted for the interaction

18. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
No main effect of A because the average value of Y at each level of A is the same. 1 2 3 A Y
B=1
B=2
No main effect of B because the average value of Y at each level of B is the same.
Yet there is an interaction, and this means A and B both affect Y.

19. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
No main effect of A because the average value of Y at each level of A is the same. 1 2 3 A Y
B=1
B=2
No main effect of B because the average value of Y at each level of B is the same.
Yet there is an interaction, and this means A and B both affect Y.
(i) a significant interaction A*B means that A affects the way B affects Y,
(ii) but then certainly B must affect Y.
So if A*B is significant, conclude that A and B affect Y as well as the direct inference that A affects the way B affects Y.

20. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice
Economy of variables
Multiplicity of p-values
Marginality
Hierarchies must be respected in model formulae
Significance of interactions includes importance of main effects
Do not test main effects with a SS that has been adjusted for the interaction

21. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice

22. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice

23. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice

24. Principles of model choice
Model Selection I: principles of model choice
Principles of model choice

25. Model Selection I: principles of model choice
Choosing a model

26. Choosing a model: polynomials
Model Selection I: principles of model choice
Choosing a model: polynomials

27. Choosing a model: polynomials
Model Selection I: principles of model choice
Choosing a model: polynomials

28. Choosing a model: polynomials
Model Selection I: principles of model choice
Choosing a model: polynomials
Y1 = *X *X12
s = square-root(6010) = 77.52

29. Choosing a model: orthogonal design
Model Selection I: principles of model choice
Choosing a model: orthogonal design

30. Choosing a model: orthogonal design
Model Selection I: principles of model choice
Choosing a model: orthogonal design
bottom up!
pooling?

31. Choosing a model: non-orthogonality
Model Selection I: principles of model choice
Choosing a model: non-orthogonality

32. Choosing a model: non-orthogonality
Model Selection I: principles of model choice
Choosing a model: non-orthogonality

33. Choosing a model: non-orthogonality
Model Selection I: principles of model choice
Choosing a model: non-orthogonality

34. Choosing a model: trends in a factor
Model Selection I: principles of model choice
Choosing a model: trends in a factor
- Shape
- Sensitivity to consistent effects

35. Choosing a model: trends in a factor
Model Selection I: principles of model choice
Choosing a model: trends in a factor

36. Choosing a model: trends in a factor
Model Selection I: principles of model choice
Choosing a model: trends in a factor

37. Choosing a model: trends in a factor
Model Selection I: principles of model choice
Choosing a model: trends in a factor

38. Choosing a model: trends in a factor
Model Selection I: principles of model choice
Choosing a model: trends in a factor
Sensitivity

39. Choosing a model: trends in a factor
Model Selection I: principles of model choice
Choosing a model: trends in a factor
Shape

40. Model Selection II: datasets with several explanatory variables
Model Selection I: principles of model choice
Last words…
Model choice represents a whole extra layer of sophistication to use of GLM
Very powerful extensions: polynomials
Very important principles: economy, multiplicity
Very important cautions: marginality
Model Selection II: datasets with several explanatory variables
Read Chapter 11