Download - Quantitative Methods
![Page 1: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/1.jpg)
Quantitative Methods
Model Selection II:datasets with several explanatory variables
![Page 2: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/2.jpg)
Model Selection II: several explanatory variables
The problem of model choice
![Page 3: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/3.jpg)
Model Selection II: several explanatory variables
The problem of model choice
![Page 4: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/4.jpg)
Model Selection II: several explanatory variables
The problem of model choice
With 5 x-variables, there are 25=32 possible models, not including interactions.
If we include two-way interactions without squared terms, there are1x1 + 5x1 + 10x2 + 10x8 + 5x64 + 1x1024 = 1450 models
If we do allow squared terms, there are1x1 + 5x2 + 10x8 + 10x64 + 5x1024 + 1x32768 = 38619 models.
With multiple models, there are many p-values and possible “right-leg/left-leg” and “poets’ dates” effects.
![Page 5: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/5.jpg)
Model Selection II: several explanatory variables
The problem of model choice
• Economy of variables• Multiplicity of p-values• Marginality
![Page 6: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/6.jpg)
Model Selection II: several explanatory variables
The problem of model choice
![Page 7: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/7.jpg)
Model Selection II: several explanatory variables
Economy of variables
![Page 8: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/8.jpg)
Model Selection II: several explanatory variables
Economy of variables
![Page 9: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/9.jpg)
Model Selection II: several explanatory variables
Economy of variables
all variables increase R2
F<1 - adding the variable decreased R2 adjF>1 - adding the variable increased R2 adj
![Page 10: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/10.jpg)
Model Selection II: several explanatory variables
Economy of variables
continuous
![Page 11: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/11.jpg)
Model Selection II: several explanatory variables
Economy of variables
![Page 12: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/12.jpg)
Model Selection II: several explanatory variables
Economy of variables
(Predictions for datapoint 39)
![Page 13: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/13.jpg)
Model Selection II: several explanatory variables
Multiplicity of p-values
![Page 14: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/14.jpg)
Model Selection II: several explanatory variables
Multiplicity of p-values
Multiple bites at the cherry
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Number of tests
![Page 15: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/15.jpg)
Model Selection II: several explanatory variables
Multiplicity of p-values
Focus, don’t fish
- reduce number of X-variables - use outside information to decide on inclusion - use outside information to decide on exclusion
Stringency
- reduce nominal p-value
Combine model terms
- for once, reverse the usual splitting
![Page 16: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/16.jpg)
Model Selection II: several explanatory variables
Multiplicity of p-values
![Page 17: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/17.jpg)
Model Selection II: several explanatory variables
Multiplicity of p-values
DF SeqSS1 366.91 42.71 14.7
3 424.3
MS=424.3/3=141.4
F = 141.4/108.9 = 1.30on 3 and 30 DF
Single p-value from Minitabusing CDF: p=0.293CDF 1.30 K1;
F 3 30.LET K2=1-K1
![Page 18: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/18.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 19: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/19.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 20: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/20.jpg)
Model Selection II: several explanatory variables
Stepwise regression
General Linear Model: LRGWHAL versus
Source DF Seq SS Adj SS Adj MS F PVIS 1 61.166 61.166 61.166 193.35 0.000Error 230 72.759 72.759 0.316Total 231 133.925
Term Coef SE Coef T PConstant -4.52464 0.06116 -73.98 0.000VIS 0.125222 0.009005 13.91 0.000
![Page 21: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/21.jpg)
Model Selection II: several explanatory variables
Stepwise regression
General Linear Model: LRGWHAL versus
Source DF Seq SS Adj SS Adj MS F PVIS 1 61.166 61.166 61.166 193.35 0.000Error 230 72.759 72.759 0.316Total 231 133.925
Term Coef SE Coef T PConstant -4.52464 0.06116 -73.98 0.000VIS 0.125222 0.009005 13.91 0.000
![Page 22: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/22.jpg)
Model Selection II: several explanatory variables
Stepwise regression
General Linear Model: LRGWHAL versus
Source DF Seq SS Adj SS Adj MS F PVIS 1 61.166 61.166 61.166 193.35 0.000Error 230 72.759 72.759 0.316Total 231 133.925
Term Coef SE Coef T PConstant -4.52464 0.06116 -73.98 0.000VIS 0.125222 0.009005 13.91 0.000
![Page 23: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/23.jpg)
General Linear Model: LRGWHAL versus
Source DF Seq SS Adj SS Adj MS F PVIS 1 61.166 61.166 61.166 193.35 0.000Error 230 72.759 72.759 0.316Total 231 133.925
Term Coef SE Coef T PConstant -4.52464 0.06116 -73.98 0.000VIS 0.125222 0.009005 13.91 0.000
Model Selection II: several explanatory variables
Stepwise regression
![Page 24: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/24.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 25: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/25.jpg)
Model Selection II: several explanatory variables
Stepwise regression
Forward = Backward
Forward ≠ Backward
![Page 26: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/26.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 27: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/27.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 28: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/28.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 29: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/29.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 30: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/30.jpg)
Model Selection II: several explanatory variables
Stepwise regression
![Page 31: Quantitative Methods](https://reader034.vdocument.in/reader034/viewer/2022042616/5681359c550346895d9d10b6/html5/thumbnails/31.jpg)
Last words…
• Economy of variables: prediction, adjusted R2
• Multiplicity: outside information, focussing, stringency, combining model terms
• Stepwise regressions not usually suitable -- but are for initial sifting of a large number of potential predictors in a preliminary study
Random Effects
Read Chapter 12
Model Selection II: several explanatory variables