數(shù)據(jù)分析少不了和數(shù)據(jù)中的異常值打交道,Winsorize處理在SAS中經(jīng)常使用。
Winsorize即極值處理,原理是將數(shù)據(jù)中的異常值修建,使之與正常分布的最大值與最小值相同。例如,你的數(shù)據(jù)整體位于[70,90]這個(gè)區(qū)間,而分析的數(shù)據(jù)中有些值特別大或者特別小,比如出現(xiàn)了60、65、95與125這種數(shù)值,這時(shí)Winsorize處理就能夠?qū)⑦@些特別大或者特別小的值進(jìn)行調(diào)整,讓這些異常值變成你自己定義的一個(gè)合理范圍中。對(duì)于上限,如果定義比90高出10%記為異常值,那么95這個(gè)值就會(huì)被SAS處理,放在Winsorize處理后的數(shù)據(jù)集里,而125將被看做異常值,不會(huì)放入Winsorize處理后的數(shù)據(jù)集里;同理,對(duì)于下限也是如此。
數(shù)據(jù)中含有缺失值和重復(fù)值時(shí),進(jìn)行Winsorize處理稍微會(huì)復(fù)雜一些。可以先對(duì)數(shù)據(jù)排序,但是缺失值首先會(huì)對(duì)計(jì)算造成不小的影響,所以Winsorize處理很方便解決這些常見難題。
SAS?Winsorize?處理過程:
%let?DSName?=sashelp.heart;
proc?iml;
/*?SAS/IML?moduleto?Winsorize?each?column?of?a?matrix.
Input?proportion?of?observations?toWinsorize:?prop?<?0.5.
Ex:?y=?Winsorize(x,?0.1)?computes?the?two-side?10%?Winsorized?data?*/
start?Winsorize(x,prop);
p?=?ncol(x);?/*?number?of?columns?*/
w?=?x;?/*?copy?of?x?*/
do?i?=?1?to?p;
z?=?x[,i];?/*?copy?i_th?column?*/
n?=?countn(z);?/*?count?nonmissing?values?*/
k?=?ceil(prop*n);?/*?number?of?obs?to?trim?from?each?tail?*/
r?=?rank(z);?/*?rank?values?in?i_th?column?*/
/*?find?target?values?and?obs?with?smaller/largervalues?*/
lowIdx?=?loc(r<=k?&?r^=.);
lowVal?=?z[loc(r=k+1)];
highIdx?=?loc(r>=n-k+1);
highVal?=?z[loc(r=n-k)];
/*?Winsorize?(replace)?k?smallest?and?klargest?values?*/
w[lowIdx,i]?=?lowVal;
w[highIdx,i]?=?highVal;
end;
return(w);
finish;
/*?test?thealgorithm?on?numerical?vars?in?a?data?set?*/
use?&DSName;
read?all?var?_NUM_into?X[colname=varNames];
close;
winX?=?Winsorize(X,0.1);
代碼中,矩陣winX包含經(jīng)過Winsorize處理過的數(shù)據(jù),如果你想輸出SASWinsorize處理后的數(shù)據(jù),數(shù)據(jù)集屬于小數(shù)據(jù)集,可以使用代碼:%letDSName?=?sashelp.class;?進(jìn)行實(shí)現(xiàn)。
大批量數(shù)據(jù)處理之前,想驗(yàn)證SAS?Winsorize過程是否正確,可以借助SAS/IML計(jì)算出來的縮尾均值(?Winsorized?means),與SAS?PROC?UNIVARIATE?計(jì)算出來的縮尾均值進(jìn)行比較。
/*?Compute?Winsorized?mean,?which?is?mean?of?the?Winsorized?data?*/
winMean?=?mean(winX);
print?winMean[c=varNames?f=8.4];
/*?Validation:?compute?Winsorized?means?byusing?UNIVARIATE?*/
ods?exclude?all;
proc?univariate?data=&dsname?winsorized=0.1;
ods?output?WinsorizedMeans=winMeans;
run;
ods?exclude?none;
proc?print?data=winMeans;
var?VarName?Mean;
run;
——SAS中文論壇