标题: VARIMAX rotation of PLS loadings [打印本页] 作者: shiyiming 时间: 2010-10-22 13:39 标题: VARIMAX rotation of PLS loadings From oloolo's blog on SasProgramming
<p><a href="http://feedads.g.doubleclick.net/~a/a3PKM8XkTJW_yOaAsnWmtLk6x8E/0/da"><img src="http://feedads.g.doubleclick.net/~a/a3PKM8XkTJW_yOaAsnWmtLk6x8E/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/a3PKM8XkTJW_yOaAsnWmtLk6x8E/1/da"><img src="http://feedads.g.doubleclick.net/~a/a3PKM8XkTJW_yOaAsnWmtLk6x8E/1/di" border="0" ismap="true"></img></a></p>Partial Least Square is one of several supervised dimension reduction techniques and attracts attention in recent years. In the one hand, PLS is able to generate a series of scores that maximize linear correlation between dependent variables and independent variables, on the other hand, the loading of PLS can be regarded as similar counterpart from factor analysis, hence we can rotate the loadings from PLS therefore eliminate some of the non-significant variable in terms of prediction.<br />
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<pre style="background-color: #ebebeb; border: 1px dashed rgb(153, 153, 153); color: #000001; font-family: Andale Mono,Lucida Console,Monaco,fixed,monospace; font-size: 12px; line-height: 14px; overflow: auto; padding: 5px; width: 100%;"><code>
%macro PLSRotate(Loading, TransMat, PatternOut, PatternShort,
method=VARIMAX, threshold=0.25);
/* VARIMAX rotation of PLS loadings. Only variables having
large loadings after rotation will enter the final model.
Loading dataset contains XLoadings output from PROC PLS
and should have variable called NumberOfFactors
TransMat is the generated Transformation matrix;
PatternOut is the output Pattern after rotation;
PatternShort is the output Pattern with selected variables
*/
%local covars;
proc sql noprint;
select name into :covars separated by ' '
from sashelp.vcolumn
where libname="WORK" & memname=upcase("&Loading")
& upcase(name) NE "NUMBEROFFACTORS"
& type="num"
;
quit;
%put &covars;
data &Loading.(type=factor);
set &Loading;
_TYPE_='PATTERN';
_NAME_=compress('factor'||_n_);
run;
ods select none;
ods output OrthRotFactPat=&PatternOut;
ods output OrthTrans=&TransMat;
proc factor data=&Loading method=pattern rotate=&method simple;
var &covars;
run;
ods select all;
data &PatternShort;
set &PatternOut;
array _f{*} factor:;
_cntfac=0;
do _j=1 to dim(_f);
_f[_j]=_f[_j]*(abs(_f[_j])>&threshold); _cntfac+(_f[_j]>0);
end;
if _cntfac>0 then output;
drop _cntfac _j;
run;
%mend;
</code></pre><br />
Here I try to replicate the case study in [1] which elaborated how to do and properties of VARIMAX rotation to PLS loadings. The PROC PLS output, after various tweaks on convergence criteria and singularity conditions, is still a little different from the result reported in [1] for factors other than the leading one, therefore, I will directly use the U=PS matrix in pp.215.<br />
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<pre style="background-color: #ebebeb; border: 1px dashed rgb(153, 153, 153); color: #000001; font-family: Andale Mono,Lucida Console,Monaco,fixed,monospace; font-size: 12px; line-height: 14px; overflow: auto; padding: 5px; width: 100%;"><code>