Transcription of Variable Selection - Biostatistics
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Example: bachelor of science
Variable Selection - Biostatistics
Chapter10 VariableSelectionVariableselectionis intendedtoselectthe best wanttoexplainthedatainthesimplestway 's Razorstatesthatamongseveralplausibleexpl anationsfora phenomenon,thesimplestis ,thisimpliesthatthesmallestmodelthat tsthedatais causedbyhavingtoomany :if themodelistobeusedforprediction,wecansav e timeand/ormoney uentialpoints- maybeexcludethemat a naturalhierarchy. Forexample,inpolynomialmodels,x2is a ,it is importanttorespectthehierarchy. commonsituationswherethissituationarises : b0 b1x b2x2 eSupposewe tthismodeland ndthattheregressionsummaryshowsthatthete rminxis wethenremovedthexterm,ourreducedmodelwou ldthenbecomey b0 b2x2 scalechangex x a, thenthemodelwouldbecomey b0 b2a2 2b2ax b2x2 e The any rstordertermherecorrespondstothehypothes isthatthepredictedresponseis symmetricaboutandhasanoptimumatx ofthelowerorderterm. :y b0 b1x1 b2x2 b11x21 b22x22 b12x1x2We wouldnotnormallyconsiderremovingthex1x2i nteractiontermwithoutsimultaneouslyconsi d-eringtheremoval jointremoval wouldcorrespondtotheclearlymeaningfulcom parisonofa surfacethatis rotationofthepredictorspacewouldreintrod ucetheinteractiontermand,aswiththepolyno mials, a complex hierarchy, sometimescalledthe p-to-remove anddoesnothave tobe5%.
from the model before higher order terms in the same variable. There two common situations where this situation arises: Polynomials models. Consider the model y b0 b1x b2x 2 e Suppose we t this model and nd that the regression summary shows that the term in x is not signif-icant but the term in x2 is.
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