Quantitative Methods

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Quantitative Methods

• Model Selection II
• datasets with several explanatory variables

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Model Selection II several explanatory variables
The problem of model choice
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Model Selection II several explanatory variables
The problem of model choice
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Model Selection II several explanatory variables
The problem of model choice
With 5 x-variables, there are 2532 possible
models, not including interactions. If we
include two-way interactions without squared
terms, there are 1x1 5x1 10x2 10x8 5x64
1x1024 1450 models If we do allow squared
terms, there are 1x1 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.
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Model Selection II several explanatory variables
The problem of model choice

• Economy of variables
• Multiplicity of p-values
• Marginality

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Model Selection II several explanatory variables
The problem of model choice
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Model Selection II several explanatory variables
Economy of variables
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Model Selection II several explanatory variables
Economy of variables
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Model Selection II several explanatory variables
Economy of variables
all variables increase R2 Flt1 - adding the
variable decreased R2 adj Fgt1 - adding the
variable increased R2 adj
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Model Selection II several explanatory variables
Economy of variables
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Model Selection II several explanatory variables
Economy of variables
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Model Selection II several explanatory variables
Economy of variables
(Predictions for datapoint 39)
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Model Selection II several explanatory variables
Multiplicity of p-values
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Model Selection II several explanatory variables
Multiplicity of p-values
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Model Selection II several explanatory variables
Multiplicity of p-values
Focus, dont 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
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Model Selection II several explanatory variables
Multiplicity of p-values
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Model Selection II several explanatory variables
Multiplicity of p-values
DF SeqSS 1 366.9 1 42.7 1 14.7
3 424.3 MS424.3/3141.4 F 141.4/108.9
1.30 on 3 and 30 DF Single p-value from
Minitab using CDF p0.293
CDF 1.30 K1 F 3 30. LET K21-K1
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
General Linear Model LRGWHAL versus Source DF
Seq SS Adj SS Adj MS F P VIS 1
61.166 61.166 61.166 193.35 0.000 Error 230
72.759 72.759 0.316 Total 231 133.925 Term
Coef SE Coef T P Constant
-4.52464 0.06116 -73.98 0.000 VIS
0.125222 0.009005 13.91 0.000
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Model Selection II several explanatory variables
Stepwise regression
General Linear Model LRGWHAL versus Source DF
Seq SS Adj SS Adj MS F P VIS 1
61.166 61.166 61.166 193.35 0.000 Error 230
72.759 72.759 0.316 Total 231 133.925 Term
Coef SE Coef T P Constant
-4.52464 0.06116 -73.98 0.000 VIS
0.125222 0.009005 13.91 0.000
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Model Selection II several explanatory variables
Stepwise regression
General Linear Model LRGWHAL versus Source DF
Seq SS Adj SS Adj MS F P VIS 1
61.166 61.166 61.166 193.35 0.000 Error 230
72.759 72.759 0.316 Total 231 133.925 Term
Coef SE Coef T P Constant
-4.52464 0.06116 -73.98 0.000 VIS
0.125222 0.009005 13.91 0.000
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Model Selection II several explanatory variables
Stepwise regression
General Linear Model LRGWHAL versus Source DF
Seq SS Adj SS Adj MS F P VIS 1
61.166 61.166 61.166 193.35 0.000 Error 230
72.759 72.759 0.316 Total 231 133.925 Term
Coef SE Coef T P Constant
-4.52464 0.06116 -73.98 0.000 VIS
0.125222 0.009005 13.91 0.000
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
Forward Backward
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
Stepwise regression
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Model Selection II several explanatory variables
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