保存和使用来自 PCA 的特征向量答案

【问题标题】：Save and use eigenvectors from PCA保存和使用来自 PCA 的特征向量
【发布时间】：2019-02-06 09:12:50
【问题描述】：

我在 Stata 中执行了主成分分析 (PCA)。

我的数据集包含 9 个国家/地区的 8 个财务指标。

例如：

* Example generated by -dataex-. To install: ssc install dataex
clear
input str7 Country double(Investment Profit Income Tax Repayment Leverage Interest Liquidity) int Year
"France"    -.1916055239385184  .046331346724579184  .16438012750896466    .073106839282063 30.373216652548326  4.116650784492168  3.222219873614461  .01453109309122077 2010
"UK"       -.09287803170279468   .10772082765154019  .19475363707485557  .05803923583546618 31.746409646181174  9.669982727208433 1.2958094802269167 .014273374324088752 2010
"US"       -.06262935107629553   .08674901201182428   .1241593221865416  .13387194413811226 25.336612638526013  11.14330064161111  1.954785887176916 .008355601163285917 2010
"Italy"   -.038025847122363045    .1523162032749684  .23885658237030563   .2057478638900476  31.02007902336988 2.9660938817562292   6.12544787693943 .011694993164234125 2010
"Germany"  -.05454795914578491   .06287079763890834  .09347194572148769  .08730237262847926 35.614342337621174  12.03770488195981 1.1958205191308358 .012467084153714813 2010
"Spain "   -.09133982259799572    .1520056836126315  .20905656056324853  .21054797530580743 30.133833346916546 2.0623245902645073  5.122615899157435 .013545432336873187 2010
"Sweden"   -.05403262462960799   .20463787181576967  .22924827352771968  .05655833155565016  20.30540887860061 10.392313613725324  .8634381995636089 .008030624504967313 2010
"Norway "  -.07560184571862992   .08383822093909514  .15469418498932822  .06569716455818478 29.568228705840234 14.383460621594622 1.5561013535825234 .012843159364225464 2010
"Algeria"   -.0494187835163535  .056252436429004446  .09174672864585759  .08143181185307143  34.74103858167055 15.045254276254616 1.2074942921860699 .011578038401820303 2010
"France"   -.03831442432584342   .14722819896988698  .22035417794604084  .12183886462162773  28.44763045286005 12.727100288710087  1.405629911115614 .011186908059399987 2011
"UK"       -.05002189329928202   .16833493262244398   .2288402623558823  .04977050186975224 27.640103129372747  11.17376089844228 1.1764542835994092 .008386726178729322 2011
"US"        -.0871005985124144   .10270482619857023   .1523559355903486  .06775742210623094 26.840586700880362 10.783899184031576  1.454011947763254 .013501919089967212 2011
"Italy"     -.1069324103590126   -.5877872620957578 -.47469302172710803   .2004436360021364 23.133243742952658 5.3936761686065875  4.532771849692548 .012586313916956204 2011
"Germany"  -.05851794344524515   .09960345907923154    .136805115392161   .1373407846168154   32.6182637042919 14.109738344526052 1.5077699357228835 .013200993625042274 2011
"Spain "   -.10650743527105216 -.015785638597076792   .1808727613216441  .05038848927405154  28.22206251292902 10.839614113486853 1.5021425852392374 .012076771099482617 2011
"Sweden"   -.09678946710644694   .11801761803893955  .18569993056826523   .1481844716617448 27.439283362903794  5.771154420635893  5.493437819181101 .013820243145673811 2011
"Norway "  -.04263379351591438   .09931719473864983  .14469611775596314   .0796835513869996  26.68561168581991  14.06385602832082 1.5200488174887825  .01029136242440406 2011
"Algeria"  -.04871983526465598    .2139061303228528   .2728647845448156 .056537570099712456  22.50263575072073 16.919641035094685  .7539881754626142 .009734650338902404 2011
end

在轮换之后，我将我的第一个组成部分称为“负债”，将第二个组成部分称为“盈利能力”。

我有 2011 年、2012 年、2013 年、2014 年等的相同数据。我想使用 Stata 为 2010 年计算的权重矩阵，并将其分别应用于 2011、2012、2013 年。我的目标是随着时间的推移比较各国之间的债务和盈利能力。

为此，我使用estimate save 和estimates use 命令（Stata 手册第 20 章关于估计和估计后 PCA 命令帮助）。

但是，我无法理解 Stata 正在保存什么。它是保存为 2010 年计算的分数还是特征值和特征向量？

这是我使用的代码：

tempfile pca
save `pca'
use `pca' if Year==2010
global xlist Investment Profit Income Tax Repayment Leverage Interest Liquidity
pca $xlist, components(2)
estimates save pcaest, replace
predict score
summarize score
use `pca' if Year==2011, clear
estimates use pcaest
predict score
summarize score

您觉得这个方法和代码正确吗？
我还想保存权重矩阵并创建一个新向量Z=b|1,1]*investment+...。

【问题讨论】：

请使用 Stata 中的dataex 命令向我们提供示例数据。屏幕截图没有帮助，没有数据，我们无法复制任何内容，从而为您提供帮助。请阅读How to Ask 以及如何创建minimal reproducible example 并相应地编辑您的问题。
@PearlySpencer 完成 :) 感谢您的反馈
我想保存特征向量矩阵。PCA 的目的是找到分量 Z(z1..zP)，它们是原始变量 X1 的线性组合。我的原始变量是 2010 年的。PCA 计算矩阵 W 或特征向量矩阵。因此，我有 Z=W' X1。现在，假设 X2 是我 2011 年的数据。如果我使用第一步计算的矩阵 W 并将其乘以 X2。我应该获得 2011 年的组件，这将与 2010 年相当。也许我完全错了。但这对我来说似乎是合乎逻辑的。不过不知道-estimates save-这个命令好不好。
我没有使用 PCA 的经验，但要在运行 pca 命令后得到特征向量 = 组件的矩阵，请键入 matrix A = e(L)。同样，对于特征值矩阵（已排序），您键入 matrix B = e(Ev)。
据我所知，您的代码中没有任何旋转。

标签： command stata pca

【解决方案1】：

使用 2010 年的玩具示例：

clear

input str7 Country double(Investment Profit Income Tax Repayment Leverage Interest Liquidity) int Year
"France"    -.1916055239385184  .046331346724579184  .16438012750896466    .073106839282063 30.373216652548326  4.116650784492168  3.222219873614461  .01453109309122077 2010
"UK"       -.09287803170279468   .10772082765154019  .19475363707485557  .05803923583546618 31.746409646181174  9.669982727208433 1.2958094802269167 .014273374324088752 2010
"US"       -.06262935107629553   .08674901201182428   .1241593221865416  .13387194413811226 25.336612638526013  11.14330064161111  1.954785887176916 .008355601163285917 2010
"Italy"   -.038025847122363045    .1523162032749684  .23885658237030563   .2057478638900476  31.02007902336988 2.9660938817562292   6.12544787693943 .011694993164234125 2010
"Germany"  -.05454795914578491   .06287079763890834  .09347194572148769  .08730237262847926 35.614342337621174  12.03770488195981 1.1958205191308358 .012467084153714813 2010
"Spain "   -.09133982259799572    .1520056836126315  .20905656056324853  .21054797530580743 30.133833346916546 2.0623245902645073  5.122615899157435 .013545432336873187 2010
"Sweden"   -.05403262462960799   .20463787181576967  .22924827352771968  .05655833155565016  20.30540887860061 10.392313613725324  .8634381995636089 .008030624504967313 2010
"Norway "  -.07560184571862992   .08383822093909514  .15469418498932822  .06569716455818478 29.568228705840234 14.383460621594622 1.5561013535825234 .012843159364225464 2010
"Algeria"   -.0494187835163535  .056252436429004446  .09174672864585759  .08143181185307143  34.74103858167055 15.045254276254616 1.2074942921860699 .011578038401820303 2010
end

我得到以下结果：

local xlist Investment Profit Income Tax Repayment Leverage Interest Liquidity
pca `xlist', components(2)

Principal components/correlation                 Number of obs    =          9
                                                 Number of comp.  =          2
                                                 Trace            =          8
    Rotation: (unrotated = principal)            Rho              =     0.7468

    --------------------------------------------------------------------------
       Component |   Eigenvalue   Difference         Proportion   Cumulative
    -------------+------------------------------------------------------------
           Comp1 |      3.43566      .896796             0.4295       0.4295
           Comp2 |      2.53887      1.23215             0.3174       0.7468
           Comp3 |      1.30672      .750756             0.1633       0.9102
           Comp4 |      .555959      .472866             0.0695       0.9797
           Comp5 |     .0830926     .0181769             0.0104       0.9900
           Comp6 |     .0649157     .0526462             0.0081       0.9982
           Comp7 |     .0122695    .00975098             0.0015       0.9997
           Comp8 |    .00251849            .             0.0003       1.0000
    --------------------------------------------------------------------------

Principal components (eigenvectors) 

    ------------------------------------------------
        Variable |    Comp1     Comp2 | Unexplained 
    -------------+--------------------+-------------
      Investment |   0.0004   -0.3837 |       .6262 
          Profit |   0.3896   -0.3794 |       .1131 
          Income |   0.4621   -0.1162 |        .232 
             Tax |   0.4146    0.1236 |       .3706 
       Repayment |  -0.1829    0.4747 |       .3131 
        Leverage |  -0.4685   -0.2596 |      .07464 
        Interest |   0.4580    0.2625 |       .1045 
       Liquidity |  -0.0082    0.5643 |       .1913 
    ------------------------------------------------

要查看pca 命令返回的项目类型：

 ereturn list

scalars:
                  e(N) =  9
                  e(f) =  2
                e(rho) =  .7468162625387222
              e(trace) =  8
              e(lndet) =  -13.76082122673546
               e(cond) =  36.93476257313668

macros:
            e(cmdline) : "pca Investment Profit Income Tax Repayment Leverage Interest Liquidity, components(2)"
                e(cmd) : "pca"
              e(title) : "Principal components"
       e(marginsnotok) : "_ALL"
          e(estat_cmd) : "pca_estat"
         e(rotate_cmd) : "pca_rotate"
            e(predict) : "pca_p"
              e(Ctype) : "correlation"
         e(properties) : "nob noV eigen"

matrices:
                e(sds) :  1 x 8
              e(means) :  1 x 8
                  e(C) :  8 x 8
                e(Psi) :  1 x 8
                 e(Ev) :  1 x 8
                  e(L) :  8 x 2

functions:
             e(sample)

将包含特征向量的返回矩阵保存为下一年的变量的一种方法是创建矩阵的副本并加载 2011 年的数据：

matrix A = e(L)

clear

input str7 Country double(Investment Profit Income Tax Repayment Leverage Interest Liquidity) int Year
"France"   -.03831442432584342   .14722819896988698  .22035417794604084  .12183886462162773  28.44763045286005 12.727100288710087  1.405629911115614 .011186908059399987 2011
"UK"       -.05002189329928202   .16833493262244398   .2288402623558823  .04977050186975224 27.640103129372747  11.17376089844228 1.1764542835994092 .008386726178729322 2011
"US"        -.0871005985124144   .10270482619857023   .1523559355903486  .06775742210623094 26.840586700880362 10.783899184031576  1.454011947763254 .013501919089967212 2011
"Italy"     -.1069324103590126   -.5877872620957578 -.47469302172710803   .2004436360021364 23.133243742952658 5.3936761686065875  4.532771849692548 .012586313916956204 2011
"Germany"  -.05851794344524515   .09960345907923154    .136805115392161   .1373407846168154   32.6182637042919 14.109738344526052 1.5077699357228835 .013200993625042274 2011
"Spain "   -.10650743527105216 -.015785638597076792   .1808727613216441  .05038848927405154  28.22206251292902 10.839614113486853 1.5021425852392374 .012076771099482617 2011
"Sweden"   -.09678946710644694   .11801761803893955  .18569993056826523   .1481844716617448 27.439283362903794  5.771154420635893  5.493437819181101 .013820243145673811 2011
"Norway "  -.04263379351591438   .09931719473864983  .14469611775596314   .0796835513869996  26.68561168581991  14.06385602832082 1.5200488174887825  .01029136242440406 2011
"Algeria"  -.04871983526465598    .2139061303228528   .2728647845448156 .056537570099712456  22.50263575072073 16.919641035094685  .7539881754626142 .009734650338902404 2011
end

然后你可以简单地使用svmat 命令：

svmat A

list A* if _n < 9

     +-----------------------+
     |        A1          A2 |
     |-----------------------|
  1. |  .0003921    -.383703 |
  2. |  .3895898   -.3793983 |
  3. |  .4621098   -.1162487 |
  4. |  .4146066    .1235683 |
  5. | -.1828703    .4746658 |
     |-----------------------|
  6. | -.4685374   -.2596268 |
  7. |   .457974    .2624738 |
  8. | -.0081538    .5643047 |
     +-----------------------+

编辑：

根据cmets修改：

use X1, clear

local xlist Investment Profit Income Tax Repayment Leverage Interest Liquidity

forvalues i = 1 / 5 {
    pca `xlist' if year == 201`i', components(2)
    matrix A201`i' = e(L)
    svmat A201`i'

    generate B201`i'1 = (A201`i'1 * Investment) + (A201`i'1 * Profit) + ///
                        (A201`i'1 * Income) + (A201`i'1 * Tax) + ///
                        (A201`i'1 * Repayment) + (A201`i'1 * Leverage) + ///
                        (A201`i'1 * Interest) + (A201`i'1 * Liquidity)

    generate B201`i'2 = (A201`i'2 * Investment) + (A201`i'2 * Profit) + ///
                        (A201`i'2 * Income) + (A201`i'2 * Tax) + ///
                        (A201`i'2 * Repayment) + (A201`i'2 * Leverage) + ///
                        (A201`i'2 * Interest) + (A201`i'2 * Liquidity)
}

【讨论】：

好的！我知道了。使用 2011 数据库时如何取回矩阵？
这取决于你如何拥有不同年份的数据，但想法是一样的：如果你每次使用pca 命令后都保存矩阵，你可以简单地使用@ 创建变量987654330@ 命令并重复。请参阅我修改后的答案。您也可以使用循环自动执行此操作。
这很有用，谢谢。但正如我在问题中所说。我不熟悉Stata中的矩阵。 svmat A 之后的下一步是什么？
什么意思？这取决于你想做什么。 svmat 命令从指定的矩阵创建变量。你想对变量做什么？
我想带来新的数据集 X1，这是我的原始数据集。但我只想保留 2011 年的数据。然后，我想创建一个新向量 Z1（8 行 1 行）等于 X1（8 行 8 行）乘以 A1（8 行一行）。另一个向量 Z2（8 行 1 行）等于 X1（8 行 8 行）乘以 A2（8 行 1 行）。 Z1 和 Z2 将是我 2011 年的分数。然后，我想带来 2012 年的数据，并做同样的事情。 Z