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Quantitative Methods

Quantitative Methods. Model Selection II: datasets with several explanatory variables. Model Selection II: several explanatory variables. The problem of model choice. Model Selection II: several explanatory variables. The problem of model choice.

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Quantitative Methods

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  1. Quantitative Methods Model Selection II: datasets with several explanatory variables

  2. Model Selection II: several explanatory variables The problem of model choice

  3. Model Selection II: several explanatory variables The problem of model choice

  4. 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 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.

  5. Model Selection II: several explanatory variables The problem of model choice • Economy of variables • Multiplicity of p-values • Marginality

  6. Model Selection II: several explanatory variables The problem of model choice

  7. Model Selection II: several explanatory variables Economy of variables

  8. Model Selection II: several explanatory variables Economy of variables

  9. Model Selection II: several explanatory variables Economy of variables all variables increase R2 F<1 - adding the variable decreased R2 adj F>1 - adding the variable increased R2 adj

  10. continuous Model Selection II: several explanatory variables Economy of variables

  11. Model Selection II: several explanatory variables Economy of variables

  12. Model Selection II: several explanatory variables Economy of variables (Predictions for datapoint 39)

  13. Model Selection II: several explanatory variables Multiplicity of p-values

  14. Model Selection II: several explanatory variables Multiplicity of p-values

  15. 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

  16. Model Selection II: several explanatory variables Multiplicity of p-values

  17. Model Selection II: several explanatory variables Multiplicity of p-values DF SeqSS 1 366.9 1 42.7 1 14.7 3 424.3 MS=424.3/3=141.4 F = 141.4/108.9 = 1.30 on 3 and 30 DF Single p-value from Minitab using CDF: p=0.293 CDF 1.30 K1; F 3 30. LET K2=1-K1

  18. Model Selection II: several explanatory variables Stepwise regression

  19. Model Selection II: several explanatory variables Stepwise regression

  20. 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

  21. 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

  22. 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

  23. 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

  24. Model Selection II: several explanatory variables Stepwise regression

  25. Forward ≠ Backward Model Selection II: several explanatory variables Stepwise regression Forward = Backward

  26. Model Selection II: several explanatory variables Stepwise regression

  27. Model Selection II: several explanatory variables Stepwise regression

  28. Model Selection II: several explanatory variables Stepwise regression

  29. Model Selection II: several explanatory variables Stepwise regression

  30. Model Selection II: several explanatory variables Stepwise regression

  31. 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

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