Exploration of the variability of variable selection based on distances between bootstrap sample results

Transcription

1 Explortion of th vriility of vril sltion s on istns twn ootstrp smpl rsults Christin Hnnig Willi Surri Univrsity Collg Lonon Univrsität Friurg

2 Rgrssion vril sltion n vry unstl. Diffrnt mols my yil vry similr fits; n miguous tst my llow multipl quit iffrnt fits. y i = β + β x i + β x i β p x ip + i, i = i,..., n, i N (, σ ) ii. Vril sltion: hoos V {,..., p} : j V β j =.

3 Vril sltion n usful, ut it n lso prolmti n is sily misintrprt. Exploring its stility n vrity of mols givs mor omprhnsiv pitur of how th vrils ollort.

4 Hr: Us LS linr rgrssion, kwr sltion with AIC or BIC stopping ritrion.

5 Hr: Us LS linr rgrssion, kwr sltion with AIC or BIC stopping ritrion. But our thniqus r muh mor gnrl, oul us with GLMs, roust rgrssion, Lsso, forwr sltion, trs n forsts...

6 Dtst : (Colmn t l. ) Dt on n = shools, y: vrl mn tst sor, x : stff slry pr pupil, x : prntg of whit ollr fthrs, x : soioonomi sttus omposition initor, x : mn thr s vrl tst sor, x : mn mothr s utionl lvl.

7 slryp.. fthrw ssttus thrs mothrlv Y

8 Dtst Stuy on ozon ffts on shool hilrns lung growth, n = hilrn, p =. Ihorst t l. (), Buhholz t l. (). Surri t l. () invstigt stility of vril sltion using nonprmtri ootstrp.

9 Rspons: FFVC - for vitl pity (l) in utumn Explntory vrils: ALTER g (yrs) t -- ADHEU llrgi rhinitis ignos y physiin SEX ml, fml HOCHOZON ptint livs in villg with high ozon vlus AMATOP mtrnl topy (sthm, llrgi rhinitis, zm) AVATOP ptrnl topy (sthm, llrgi rhinitis, zm) ADEKZ zm ignos y physiin ARAUCH Too smok xposur t hom (no/ys) AGEBGEW wight (g) t irth FSNIGHT ough t night or in th morning FLGROSS hight (m) t pulmonry funtion tsting FMILB snsitiztion to ust mit llrgns FNOH mximl NO vlu of lst h for pulmonry funtion tsting (µg/m) FTIER snsitiztion to niml (og n t) nrs FPOLL snsitiztion to pollns (hzl, irh, grss) FLTOTMED totl numr of mitions t pulmonry funtion tsting FOH mx. O vlu of lst h for pulmonry funtion tsting (µg/m) FSPT snsitiztion to ny of pollns, og n t nrs or ust mits FTEH mx. tmprtur of lst h for pulmonry funtion tsting (Cl.) FSATEM shortnss of rth FSAUGE ithy or wtry ys FLGEW wight (kg) t pulmonry funtion tsting FSPFEI whzing or whistling in th hst FSHLAUF ough following xris

10 Distns Multiimnsionl Sling Clustr nlysis Anlysis uss B ootstrp mols (slt vrils) V,..., V B. Shools t: B = fins mols (kwr/aic). Ozon t: B = h kwr/aic n kwr/bic fins mols.. Distns Us istn-s mthos: Multiimnsionl sling, lustr nlysis.

11 Distns Multiimnsionl Sling Clustr nlysis Distns twn mols () Vril-s istn (Kulzynski ) ( V V V (V, V ) = + V ) V V V Cn lso pply s istn twn vrils oring to prsn in mols.

12 Distns Multiimnsionl Sling Clustr nlysis Distns twn mols () Vril-s istn (Kulzynski ) ( V V V (V, V ) = + V ) V V V Cn lso pply s istn twn vrils oring to prsn in mols.... ut mor rlvnt how mols trt points.

13 Distns Multiimnsionl Sling Clustr nlysis Distns twn mols () Vril-s istn (Kulzynski ) ( V V V (V, V ) = + V ) V V V () Fit-s istn Cn lso pply s istn twn vrils oring to prsn in mols.... ut mor rlvnt how mols trt points. F (V, V ) = n f V (x i ) f V (x i ) i= (Mnhttn-istn givs vry fit iffrn sm wight.)

14 Distns Multiimnsionl Sling Clustr nlysis. Multiimnsionl Sling Kruskl s () nonmtri MDS mps istns on Eulin sp with istns ˆ, optimising Strss = i,j [f ((z i, z j )) ˆ ij ], ˆ ij f monotoni trnsformtion. i,j

15 Distns Multiimnsionl Sling Clustr nlysis. Suitl lustring mthos E.g., hirrhil (singl, omplt, vrg linkg). Us vrg linkg (AL) hr. SL llows lrg within-lustr istns too sily, CL too oftn ivis wht is not sprt.

16 Shools t Ozon t. Shools t MDS on fit istn (with lustring) priso$points[molin, ][,] priso$points[molin, ][,]

17 Shools t Ozon t Whr r st mols? priso$points[,] priso$points[,]

18 Shools t Ozon t Mols n squr rsiuls

19 Shools t Ozon t Mols n vrils fthrw mothrlv slryp ssttus thrs

20 Shools t Ozon t Mols n vrils (y ootstrp run) fthrw mothrlv slryp ssttus thrs

21 Shools t Ozon t. Ozon t MDS on fit istn with lustrs priso$points[,] priso$points[,]

22 Shools t Ozon t Mols foun y AIC, BIC priso$points[,] priso$points[,] A B

23 Shools t Ozon t Bst AIC priso$points[,] priso$points[,] AIC top AIC top AIC top AIC top AIC wors

24 Shools t Ozon t Bst BIC priso$points[,] priso$points[,] BIC top BIC top BIC top BIC top BIC wors

25 Shools t Ozon t Siz of mols g g g g i h g f h h g g g g f f f f h g g f f g g f g f g g g h f f f f priso$points[,] priso$points[,]

26 Shools t Ozon t Vril-s istn (with lustrs from for) kuliso$points[,] kuliso$points[,]

27 Shools t Ozon t Mols n fits BIC mol R R R AIC mol

28 Shools t Ozon t Mols n squr rsiuls BIC mol R R R AIC mol

29 Shools t Ozon t Mols n squr rsiuls (olumn stnris) BIC mol R R R AIC mol

30 Shools t Ozon t Mols n vrils BIC mol AIC mol FSAUGE ARAUCH FSHLAUF AMATOP ADEKZ FSNIGHT FTIER AVATOP ADHEU FSPT AGEBGEW ALTER FOH FTEH FMILB FPOLL FLTOTMED FSATEM HOCHOZON FNOH FSPFEI FLGEW SEX FLGROSS Vrils tht mk iffrn n lrly sn.

31 Lrg vriility in mols for oth tsts. Shools t: Four lustrs of mols livr quit iffrnt fits. Som mols fit som ( hlf) points vry wll, isrgring othrs. Bttr AIC hiv y ompromis fits (inluing ThrS vril).

32 Ozon t Two lustrs of mol fits, not lign with BIC/AIC-mols, rthr onnt to vrs HOCHOZON, FNOH n FNH. BIC- n AIC-slt mols r quit iffrnt. Littl vrition twn mol fits n rsiuls, hoi twn thm somwht ritrry.

33 Ozon t Two lustrs of mol fits, not lign with BIC/AIC-mols, rthr onnt to vrs HOCHOZON, FNOH n FNH. BIC- n AIC-slt mols r quit iffrnt. Littl vrition twn mol fits n rsiuls, hoi twn thm somwht ritrry. Not shown: typility of mols, n osrvtions supporting typil mols.

34 A it of mrkting: This work is support y EPSRC Grnt EP/K/.