回归分析中的病态阵及其改进_莫惠栋.pdfVIP

32 1 Vol32, No1 2006 1 1~ 6 ACTA AGRONOMICA SINICA pp 1- 6 Jan, 2006 莫惠栋 ( , 225009) : , XX d t( XX) 0, ( XX ) - 1, , d t( XX 0 XX ! X R , d t( R) [ - 001, 001] [ - 00001, 00001] 0 , XX ! ! XX X , XX , ( 1) , ( 2) , ( 3) , (4) M - : ; ; + : Q332; S11 4 Illconditioned Matrix and Its Improvement in Regression MO HuiDong (Laboratory of Quantitativ G n tics,Yangzhou Univ rsity,Yangzhou 225009,Jiangsu, China) Abstract: In r gr ssion analysis, th information matrix XX is an important factor b caus of b = ( XX ) - 1 XY . If th d t rminant valu of XX , d t( XX ) , is clos to z ro , th inv rs of th XX , ( XX ) - 1 , will xtr m ly inflat , th rror m an squar for r gr ssion co ffici nt will larg ly incr as , and in cons qu nc th r gr ssion fitting will b poor robustn ss and low pr cision. Thus th matrix XX of d t( XX ) ∀0 is call d illcondition d matrix! . In this pap r th d t rminant valu of corr lativ matrix R of X variabl s, d t( R ) , is us d as a synth tic ind x for illconditioning, i. . if th d t( R ) li s in th int rvals[ 001, 001] and [ 00001, 00001] but nonz ro, th corr sponding matrix XX can b r gard d as illcondition d and s riously illcondition d, r sp ctiv ly. Th illcondition d XX r sults from th lin ar d p nd ncy among columns in X matrix. Thr diagnostic crit ria, including lin ar corr lation co ffici nt, multipl d t rmination co ffici nt and condition ind x, can m asur th d gr of th column d p nd ncy. In ord r to improv or liminat th illconditioning of XX , four m thods, i. . ( 1) to r duc th original r gr ssion mod l, ( 2) to coll ct th n w data, ( 3) to add th r strictiv condition for r gr ssion co ffici nts and ( 4) to adopt th noncustomary r gr ssion