1.判断是否适合做主成份分析，变量标准化
Kaiser-Meyer-Olkin抽样充分性测度也是用于测量变量之间相关关系的强弱的重要指标，是通过比较两个变量的相关系数与偏相关系数得到的。
KMO介于0于1之间。KMO越高，表明变量的共性越强。如果偏相关系数相对于相关系数比较高，则KMO比较低，主成分分析不能起到很好的数据约化效果。
根据Kaiser（1974），一般的判断标准如下：
0.00-0.49,不能接受（unacceptable）;
0.50-0.59,非常差（miserable）；
0.60-0.69，勉强接受（mediocre）；
0.70-0.79,可以接受（middling）；
0.80-0.89，比较好（meritorious）；
0.90-1.00,非常好（marvelous）。
SMC即一个变量与其他所有变量的复相关系数的平方，也就是复回归方程的可决系数。
SMC比较高表明变量的线性关系越强，共性越强，主成分分析就越合适。
. estat smc. estat kmo. estat anti//暂时不知道这个有什么用
得到结果，说明变量之间有较强的相关性，适合做主成份分析。
Squared multiple correlations of variables with all other variables
-----------------------
Variable | smc
-------------+---------
x1 | 0.8923
x2 | 0.9862
y1 | 0.9657
y2 | 0.9897
y3 | 0.9910
y4 | 0.9898
y5 | 0.9769
y6 | 0.9859
y7 | 0.9735
-----------------------
变量标准化
. egen z1=std(x1)
2.对变量进行主成份分析
. pca x1 x2 y1 y2 y3 y4 y5 y6 y7 . pca x1 x2 y1 y2 y3 y4 y5 y6 y7, comp(1)
得到下面两个表格,第一个表格中的各项分别为特征根、difference这个不知道是啥、方差贡献率、累积方差贡献率。
*第二个表格即为因子载荷矩阵，它和SPSS中的成份矩阵和成份得分系数矩阵的关系为：
成份矩阵/sqrt(对应的特征值)=因子载荷矩阵=sqrt(对应的特征值)*成份得分系数矩阵
*系数越大，说明主成份对该变量的代表性越大。
Principal components/correlation Number of obs = 19
Number of comp. = 9
Trace = 9
Rotation: (unrotated = principal) Rho = 1.0000
--------------------------------------------------------------------------
Component | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Comp1 | 7.57604 6.59246 0.8418 0.8418
Comp2 | .983579 .731224 0.1093 0.9511
Comp3 | .252355 .162221 0.0280 0.9791
Comp4 | .0901337 .0323568 0.0100 0.9891
Comp5 | .0577769 .0387149 0.0064 0.9955
Comp6 | .019062 .00931458 0.0021 0.9977
Comp7 | .00974741 .00259494 0.0011 0.9987
Comp8 | .00715247 .00299772 0.0008 0.9995
Comp9 | .00415475 . 0.0005 1.0000
--------------------------------------------------------------------------
Principal components (eigenvectors)
----------------------------------------------------------------------------------------------------------------------
Variable | Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9 | Unexplained
-------------+------------------------------------------------------------------------------------------+-------------
x1 | 0.1292 0.9388 0.1499 0.0240 0.0387 0.1398 0.2098 0.0776 0.0884 | 0
x2 | 0.3485 0.2337 -0.2455 0.1139 0.1515 -0.4559 -0.6523 -0.2378 -0.1946 | 0
y1 | 0.3482 -0.0578 0.4193 0.1836 -0.7127 0.1420 -0.2687 0.2227 -0.1264 | 0
y2 | 0.3476 -0.1604 0.4115 0.3539 0.1732 -0.1441 0.2073 -0.4811 0.4834 | 0
y3 | 0.3528 -0.1002 0.3289 -0.3145 0.3512 0.2787 0.1233 -0.2021 -0.6335 | 0
y4 | 0.3566 -0.1297 0.1355 -0.1226 0.3995 -0.2039 -0.0372 0.7516 0.2350 | 0
y5 | 0.3505 -0.0056 -0.2152 -0.7536 -0.3081 -0.0449 0.0658 -0.2047 0.3460 | 0
y6 | 0.3523 -0.0477 -0.4099 0.2705 -0.2076 -0.3276 0.6130 0.0922 -0.3127 | 0
y7 | 0.3482 -0.0761 -0.4809 0.2693 0.1291 0.7093 -0.1366 0.0146 0.1750 | 0
----------------------------------------------------------------------------------------------------------------------
. estat loading,cnorm(eigen)
利用上述命令可以得到SPSS中的成分矩阵
Principal component loadings (unrotated)
component normalization: sum of squares(column) = eigenvalue
--------------------------------------------------------------------------------------------------------
| Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9
-------------+------------------------------------------------------------------------------------------
x1 | .3556 .9311 .07533 .007206 .009293 .0193 .02071 .006566 .005701
x2 | .9591 .2318 -.1233 .03421 .03642 -.06295 -.0644 -.02011 -.01254
y1 | .9584 -.05736 .2106 .05512 -.1713 .0196 -.02653 .01884 -.008146
y2 | .9568 -.159 .2067 .1062 .04163 -.0199 .02047 -.04069 .03116
y3 | .9712 -.09934 .1652 -.09441 .08441 .03848 .01218 -.01709 -.04083
y4 | .9814 -.1286 .06808 -.03679 .09602 -.02815 -.00367 .06357 .01515
y5 | .9647 -.005542 -.1081 -.2262 -.07406 -.006196 .006492 -.01731 .0223
y6 | .9696 -.04732 -.2059 .08121 -.04991 -.04523 .06052 .007799 -.02015
y7 | .9584 -.07548 -.2416 .08084 .03102 .09793 -.01348 .001237 .01128
--------------------------------------------------------------------------------------------------------
.
3.画碎石图
. screeplot
4.画载荷图
. loadingplot
5.因子分析
. factor x1 x2 y1 y2 y3 y4 y5 y6 y7, pcf
(obs=19)
Factor analysis/correlation Number of obs = 19
Method: principal-component factors Retained factors = 1
Rotation: (unrotated) Number of params = 9
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 7.57604 6.59246 0.8418 0.8418
Factor2 | 0.98358 0.73122 0.1093 0.9511
Factor3 | 0.25235 0.16222 0.0280 0.9791
Factor4 | 0.09013 0.03236 0.0100 0.9891
Factor5 | 0.05778 0.03871 0.0064 0.9955
Factor6 | 0.01906 0.00931 0.0021 0.9977
Factor7 | 0.00975 0.00259 0.0011 0.9987
Factor8 | 0.00715 0.00300 0.0008 0.9995
Factor9 | 0.00415 . 0.0005 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(36) = 358.55 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
x1 | 0.3556 | 0.8736
x2 | 0.9591 | 0.0801
y1 | 0.9584 | 0.0816
y2 | 0.9568 | 0.0845
y3 | 0.9712 | 0.0568
y4 | 0.9814 | 0.0368
y5 | 0.9647 | 0.0693
y6 | 0.9696 | 0.0599
y7 | 0.9584 | 0.0815
---------------------------------------
利用predict命令可以直接得到SPSS中的成分得分系数矩阵，也就是基于factor命令将变量标准化
. predict f1
(regression scoring assumed)
Scoring coefficients (method = regression)
------------------------
Variable | Factor1
-------------+----------
x1 | 0.04693
x2 | 0.12660
y1 | 0.12650
y2 | 0.12630
y3 | 0.12819
y4 | 0.12954
y5 | 0.12734
y6 | 0.12798
y7 | 0.12651
------------------------
时间： 2024-08-07 18:23:54