Download presentation

Presentation is loading. Please wait.

Published byCody Blake Modified over 5 years ago

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

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

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

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

5
Model Selection I: principles of model choice The problem of model choice Varying c Y = a + bX + cX 2

6
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 + cX 2 + dX 3 Any continuous curve can be sufficiently well approximately by a polynomial of high enough order. Y = a + bX + cX 2

7
Model Selection I: principles of model choice The problem of model choice Y1 = -7.62 + 3.189*X1 + 0.825*X1 2

8
Model Selection I: principles of model choice The problem of model choice Y1 = -15.75 + 6.179*X1 + 0.6169*X1 2 + 0.00500*X1 3

9
Model Selection I: principles of model choice The problem of model choice Y1 = -128.08 + 29.473*X1 Y1 = -7.62 + 3.189*X1 + 0.825*X1 2 Y1 = -15.75 + 6.179*X1 + 0.6169*X1 2 + 0.00500*X1 3 … Y1 = X1 Y1 = X1|X1 Y1 = X1|X1|X1 … Linear Quadratic Cubic …

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

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

12
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 Model Selection I: principles of model choice Principles of model choice Economy of variables Multiplicity of p-values Marginality

13
Model Selection I: principles of model choice Principles of model choice 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 What does marginal mean?

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

15
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
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
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
Model Selection I: principles of model choice Principles of model choice 123 A Y B=1 B=2 No main effect of A because the average value of Y at each level of A is the same. 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
(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. Model Selection I: principles of model choice Principles of model choice 123 A Y B=1 B=2 No main effect of A because the average value of Y at each level of A is the same. 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.

20
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
Model Selection I: principles of model choice Principles of model choice

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

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

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

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

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

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

28
Model Selection I: principles of model choice Choosing a model: polynomials Y1 = -7.62 + 3.189*X1 + 0.825*X1 2 s = square-root(6010) = 77.52

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

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

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

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

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

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

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

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

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

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

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

40
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 Model Selection I: principles of model choice

Similar presentations

OK

7 - 1 8 - 1 Chapter 8: Regression Analysis PowerPoint Slides Prepared By: Alan Olinsky Bryant University Management Science: The Art of Modeling with Spreadsheets,

7 - 1 8 - 1 Chapter 8: Regression Analysis PowerPoint Slides Prepared By: Alan Olinsky Bryant University Management Science: The Art of Modeling with Spreadsheets,

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google