SAS因子分析简介

SAS/STAT/FACTOR过程使用SAS/STAT的FACTOR过程可以进行因子分析、分量分析和因子旋转。对因子模型可以使用正交旋转和斜交旋转，可以用回归法计算得分系数，同时把因子得分的估计存贮在输出数据集中；用FACTOR过程计算的所有主要统计量也能存贮在输出数据集中。FACTOR过程用法很简单，主要使用如下语句：PROC FACTOR DATA= 数据集 选项;VAR 原始变量;RUN;输出结果包括特征值情况、因子载荷、公因子解释比例，等等。为了计算因子得分，一般在PROC FACTOR语句中加一个SCORE选项和“OUTSTAT=输出数据集”选项，然后用如下的得分过程计算公因子得分：PROC SCORE DATA=原始数据集 SCORE=FACTOR过程的输出数据集 OUT=得分输出数据集;VAR 用来计算得分的原始变量集合;RUN;PROC FACTOR ;The following options are available in the PROC FACTOR statement. ALLALPHA=pCONVERGE=pCORRCOVARIANCECOVER DATA=SAS-data-setEIGENVECTORSGAMMA=pHEYWOODHKPOWER=pMAXITER=nMETHOD=nameMINEIGEN=pMSANFACTORS=nNOBS=nNOCORRNOINTNOPRINTNORM=COV|KAISER|NONE|RAW|WEIGHTNPLOT=nOUT=SAS-data-setOUTSTAT=SAS-data-setPLOTPOWER=nPREPLOTPREROTATE=namePRINTPRIORS=namePROPORTION=pRANDOM=nRCONVERGE=pREORDERRESIDUALSRITER=nROTATE=nameSCORESCREESESIMPLESINGULAR=pTARGET=SAS-data-setULTRAHEYWOODVARDEF=DF|N|WDF|WEIGHT|WGTWEIGHT三、例子DATA example8_2;INPUT diqv$ x1-x6; Cards;北京 1026530.8162353223654955天津 816449.1349292406213182河北 3376 77.76392116684710266山西 281933.9733051206265922内蒙 301354.5128631208194915辽宁 6103124.0237061756616719吉林 370328.6531741609433891黑龙江 442748.5133751766387637上海 15204128.9371914245455286江苏 5785101.09463424566712039浙江 614941.8862212966378721安徽 252155.7437951302356593福建 538618.3545062048304537江西 237626.2833761537315423山东 4473102.54426417154810463河南 247571.3632991231507661湖北 334137.7540281511569744湖南 270143.146991425479137广东 638051.8274382699428848广西 277232.5247911446275571海南 48205.354770151951653四川 251680.97400211586418885贵州 155322.0739311086223934云南 249048.4840851010266395陕西 234426.313309962 466215甘肃 192514.843152880 174131青海 29104.163319102971176宁夏 26857.943382998 71028新疆 395326.6541631136213932 ;proc factor data= example8_2;var x1-x6; run;程序运行的结果： Initial Factor Method: Principal Components Prior Communality Estimates: ONE Eigenvalues of the Correlation Matrix: Total = 6 Average = 1 Eigenvalue Difference Proportion Cumulative 1 3.32465039 1.53397281 0.5541 0.5541 2 1.79067758 1.29809455 0.2984 0.8526 3 0.49258303 0.22859204 0.0821 0.9347 4 0.26399099 0.17552552 0.0440 0.9787 5 0.08846547 0.04883292 0.0147 0.9934 6 0.03963255 0.0066 1.0000 2 factors will be retained by the MINEIGEN criterion. Factor Pattern Factor1 Factor2 x1 0.83173 -0.48814 x2 0.73239 0.43062 x3 0.77993 -0.43431 x4 0.89373 -0.40302 x5 0.69159 0.60703 x6 0.45951 0.80462（默认采用主成分法确定因子载荷矩阵）前两个主成份解释了85.26%的方差，按照缺省的选择因子个数的准则MINEIGEN，取大于1的特征值，所以取两个因子。因子模式阵（factor pattern，即因子载荷阵）是最重要的结果。 Variance Explained by Each Factor Factor1 Factor2 3.3246504 1.7906776 Final Communality Estimates: Total = 5.115328 x1 x2 x3 x4 x5 x6 0.93005305 0.72182667 0.79692502 0.96118012 0.84678120 0.85856190上述是公因子的方差贡献，和各原始变量的共同度。反映了公因子对各原始变量的解释能力。第一主成份（因子）在所有五个变量上都有正的载荷，可见这个因子综合反映了发展状况。第二主成份在人均GDP，人均收入，和农村家庭人均纯收入上有负的载荷。但是我们得到的因子解释不够清楚，于是考虑用因子旋转。proc factor data= example8_2 rotate=varimax;var x1-x6; run;Rotation Method: Varimax Orthogonal Transformation Matrix 1 2 1 0.81035 0.58595 2 -0.58595 0.81035 Rotated Factor Pattern Factor1 Factor2 x1 0.96002 0.09178 x2 0.34117 0.77810 x3 0.88650 0.10505 x4 0.96038 0.19709 x5 0.20474 0.89714 x6 -0.09910 0.92127 Variance Explained by Each Factor Factor1 Factor2 2.7979881 2.3173399 Final Communality Estimates: Total = 5.115328 x1 x2 x3 x4 x5 x6 0.93005305 0.72182667 0.79692502 0.96118012 0.84678120 0.85856190这时的两个公因子的实际意义要好解释一些。为了产生因子得分函数，需要在FACTOR过程中使用SCORE选项。为了产生各样品的因子得分值，还要用OUTSTAT=选项输出得分系数数据集并调用SCORE过程。比如，为了计算方差最大正交旋转的主成分得分，可以用如下程序：PROC FACTOR DATA= example8_2 ROTATE=VARIMAX SCORE OUTSTAT=OUTF; TITLE2 主成分分析及VARIMAX正交旋转;RUN;PROC SCORE DATA= example8_2 SCORE=OUTF OUT=OUTS; TITLE2 VARIMAX正交旋转后的主成分得分;RUN;Rotation Method: Varimax Scoring Coefficients Estimated by Regression Squared Multiple Correlations of the Variables with Each Factor Factor1 Factor2 1.0000000 1.0000000 Standardized Scoring Coefficients Factor1 Factor2 x1 0.36246 -0.07432 x2 0.03760 0.32395 x3 0.33222 -0.05909 x4 0.34971 -0.02487 x5 -0.03007 0.39659 x6 -0.15129 0.44511