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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: -allpossible- available on SSC |

Date |
Tue, 1 Oct 2002 19:30:36 +0100 |

Thanks to Kit Baum, an -allpossible- module is now available on SSC. Setting aside inappropriate and hubristic overtones of omnicompetence, the creation of this beast was driven by a particular need. An outside critic of a current project urged the merits of trying all possible subsets of predictors, given a response variable measured on the ground and reflectances measured by satellite in several spectral bands. We have many reservations about shotgun-assisted model building, but we need the evidence before we can discuss. That aside, -allpossible- is best understood by example, but not our data which you don't have: . use auto, clear (1978 Automobile Data) . gen gpm = 1 / mpg . allpossible reg gpm head-displ, s(r2_a rmse) ---------------------------------------------------- model | predictors r2_a rmse ----------+----------------------------------------- 1 | (none) 0.000 0.013 2 | 1 0.170 0.012 3 | 2 0.392 0.010 4 | 3 0.726 0.007 5 | 4 0.667 0.007 6 | 5 0.561 0.008 7 | 6 0.589 0.008 8 | 1 2 0.383 0.010 9 | 1 3 0.723 0.007 10 | 1 4 0.663 0.007 11 | 1 5 0.569 0.008 12 | 1 6 0.588 0.008 13 | 2 3 0.729 0.007 14 | 2 4 0.666 0.007 15 | 2 5 0.607 0.008 16 | 2 6 0.627 0.008 17 | 3 4 0.724 0.007 18 | 3 5 0.724 0.007 19 | 3 6 0.723 0.007 20 | 4 5 0.671 0.007 21 | 4 6 0.688 0.007 22 | 5 6 0.645 0.008 23 | 1 2 3 0.726 0.007 24 | 1 2 4 0.661 0.007 25 | 1 2 5 0.602 0.008 26 | 1 2 6 0.624 0.008 27 | 1 3 4 0.720 0.007 28 | 1 3 5 0.720 0.007 29 | 1 3 6 0.719 0.007 30 | 1 4 5 0.666 0.007 31 | 1 4 6 0.684 0.007 32 | 1 5 6 0.642 0.008 33 | 2 3 4 0.725 0.007 34 | 2 3 5 0.726 0.007 35 | 2 3 6 0.725 0.007 36 | 2 4 5 0.670 0.007 37 | 2 4 6 0.687 0.007 38 | 2 5 6 0.663 0.007 39 | 3 4 5 0.721 0.007 40 | 3 4 6 0.720 0.007 41 | 3 5 6 0.720 0.007 42 | 4 5 6 0.687 0.007 43 | 1 2 3 4 0.722 0.007 44 | 1 2 3 5 0.723 0.007 45 | 1 2 3 6 0.722 0.007 46 | 1 2 4 5 0.666 0.007 47 | 1 2 4 6 0.684 0.007 48 | 1 2 5 6 0.659 0.007 49 | 1 3 4 5 0.717 0.007 50 | 1 3 4 6 0.716 0.007 51 | 1 3 5 6 0.716 0.007 52 | 1 4 5 6 0.683 0.007 53 | 2 3 4 5 0.722 0.007 54 | 2 3 4 6 0.721 0.007 55 | 2 3 5 6 0.722 0.007 56 | 2 4 5 6 0.686 0.007 57 | 3 4 5 6 0.717 0.007 58 | 1 2 3 4 5 0.719 0.007 59 | 1 2 3 4 6 0.718 0.007 60 | 1 2 3 5 6 0.719 0.007 61 | 1 2 4 5 6 0.683 0.007 62 | 1 3 4 5 6 0.713 0.007 63 | 2 3 4 5 6 0.718 0.007 64 | 1 2 3 4 5 6 0.715 0.007 ---------------------------------------------------- 1 headroom 2 trunk 3 weight 4 length 5 turn 6 displacement More generally, -allpossible- by default (1) computes all possible models fitted by a model command to a response and subsets of up to 6 predictors and (2) tabulates a list of statistics for each model fitted. Alternatively, (1') the maximum number of predictors fitted may be specified as a number less than 6. The model command must be a command fitting a model to a single response variable. In the example above, it is -regress-; in our project, it is -glm-. The list of statistics must include one or more names of e-class results, as would be displayed by -estimates list- after fitting an individual model. Naturally, this command does not purport to replace the detailed scrutiny of individual models or to offer an unproblematic way of finding "best" models. Its main use may lie in demonstrating that several models exist within many projects possessing roughly equal merit as measured by omnibus statistics. In fact, I can see this featuring in my own teaching together with suitable homilies and injunctions. The magic number 6 does not reflect any principle; it is as far as I got given that we have 6 spectral bands in our specific satellite data. Having been brought up on the idea that with seven parameters you can fit an elephant, I have some inhibitions about going further. In any case, looking at all 2^7 = 128 fits with 7 predictors creates a longer table than might be wished. Let me stress that the restriction of 6 is to how many predictors are included in any one model; you can specify more candidate predictors if you like, so long as the total number of models fitted does not exceed the number of observations. Stata 7 required. In searching for earlier work in this direction, I was able to draw upon ideas in the -rsquare- program of Philip Ender and Rie von Eyben of UCLA, which has different but overlapping aims. It saved me a lot of time. Phil tells me there is something similar in SAS. Nick n.j.cox@durham.ac.uk * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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