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st: Interpreting PCA output


From   "Mona Mowafi" <mmowafi@hsph.harvard.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Interpreting PCA output
Date   Wed, 23 Jul 2008 14:55:18 -0400

Dear Statalisters,

I'm new to the list and hope you will be able to help me with an analysis problem before me.  I have conducted a principal components analysis to identify principal components for 67 underlying indicators or household asset.  The first principal component is clearly important, but in fact, according to commonly used "rule of 1", so are the rest of the first 20 principal components.  Using a scree test, I may choose to only use the first 5 principal components.  But in any case, I am not sure how one is supposed to interpret the 2nd, 3rd, 4th, etc eigenvectors from the output.  I am interested ultimately in using this information to make a household asset index.  Below is output for the pca and the first 6 eigenvectors; any guidance is truly appreciated...

. pca  brick_floor- rent
(obs=1986)

            (principal components; 67 components retained)
Component    Eigenvalue     Difference    Proportion    Cumulative
------------------------------------------------------------------
     1       10.58980         6.31570      0.1581         0.1581
     2        4.27410         1.12919      0.0638         0.2218
     3        3.14490         0.92808      0.0469         0.2688
     4        2.21683         0.35149      0.0331         0.3019
     5        1.86534         0.05292      0.0278         0.3297
     6        1.81241         0.08547      0.0271         0.3568
     7        1.72694         0.07186      0.0258         0.3825
     8        1.65509         0.11397      0.0247         0.4072
     9        1.54112         0.07386      0.0230         0.4302
    10        1.46726         0.11175      0.0219         0.4521
    11        1.35551         0.05339      0.0202         0.4724
    12        1.30213         0.04294      0.0194         0.4918
    13        1.25919         0.02020      0.0188         0.5106
    14        1.23899         0.06286      0.0185         0.5291
    15        1.17613         0.01255      0.0176         0.5467
    16        1.16359         0.04429      0.0174         0.5640
    17        1.11929         0.04648      0.0167         0.5807
    18        1.07282         0.02036      0.0160         0.5967
    19        1.05245         0.02185      0.0157         0.6124
    20        1.03061         0.03595      0.0154         0.6278
    21        0.99466         0.01827      0.0148         0.6427
    22        0.97639         0.01409      0.0146         0.6572
    23        0.96230         0.01505      0.0144         0.6716
    24        0.94725         0.02694      0.0141         0.6857
    25        0.92031         0.01587      0.0137         0.6995
    26        0.90445         0.03741      0.0135         0.7130
    27        0.86704         0.00379      0.0129         0.7259
    28        0.86325         0.04267      0.0129         0.7388
    29        0.82058         0.00605      0.0122         0.7511
    30        0.81452         0.04780      0.0122         0.7632
    31        0.76673         0.00904      0.0114         0.7747
    32        0.75769         0.00963      0.0113         0.7860
    33        0.74806         0.01431      0.0112         0.7971
    34        0.73375         0.02619      0.0110         0.8081
    35        0.70756         0.02048      0.0106         0.8186
    36        0.68708         0.02651      0.0103         0.8289
    37        0.66057         0.01184      0.0099         0.8388
    38        0.64873         0.01271      0.0097         0.8484
    39        0.63603         0.01272      0.0095         0.8579
    40        0.62331         0.03455      0.0093         0.8672
    41        0.58875         0.00943      0.0088         0.8760
    42        0.57932         0.02995      0.0086         0.8847
    43        0.54937         0.00653      0.0082         0.8929
    44        0.54285         0.00880      0.0081         0.9010
    45        0.53405         0.03693      0.0080         0.9089
    46        0.49712         0.00493      0.0074         0.9164
    47        0.49219         0.01327      0.0073         0.9237
    48        0.47893         0.01813      0.0071         0.9309
    49        0.46079         0.01901      0.0069         0.9377
    50        0.44178         0.02659      0.0066         0.9443
    51        0.41519         0.01621      0.0062         0.9505
    52        0.39898         0.01088      0.0060         0.9565
    53        0.38810         0.02810      0.0058         0.9623
    54        0.36000         0.01442      0.0054         0.9676
    55        0.34558         0.02612      0.0052         0.9728
    56        0.31946         0.01212      0.0048         0.9776
    57        0.30734         0.04505      0.0046         0.9822
    58        0.26229         0.04934      0.0039         0.9861
    59        0.21295         0.01219      0.0032         0.9893
    60        0.20076         0.06411      0.0030         0.9922
    61        0.13665         0.02796      0.0020         0.9943
    62        0.10869         0.01855      0.0016         0.9959
    63        0.09014         0.02437      0.0013         0.9973
    64        0.06577         0.01890      0.0010         0.9982
    65        0.04687         0.01038      0.0007         0.9989
    66        0.03649         0.00162      0.0005         0.9995
    67        0.03486               .      0.0005         1.0000

               Eigenvectors
    Variable |      1          2          3          4          5          6
-------------+-----------------------------------------------------------------
 brick_floor |  -0.07630   -0.23204   -0.09185    0.07030    0.20153    0.05964
ceramic_fl~r |   0.14833    0.12855    0.07916   -0.07045   -0.20488   -0.04336
concrete_c~g |   0.16770   -0.17513   -0.01447    0.13227   -0.21285    0.09973
wood_ceiling |  -0.16622    0.17407    0.01156   -0.13642    0.22240   -0.10292
concrete_w~s |   0.08676   -0.00912   -0.15682    0.47772    0.05521   -0.07872
 brick_walls |  -0.06586   -0.01776    0.16192   -0.47567   -0.06592    0.08020
       house |  -0.03016    0.03528    0.09484   -0.14226   -0.08032   -0.19785
   apartment |   0.14941   -0.18834    0.04541    0.16144    0.02763    0.02685
        room |  -0.14219    0.19297   -0.14336   -0.08431    0.03529    0.15165
 cramp_sleep |  -0.07824   -0.04067    0.02921   -0.02359   -0.01669    0.02895
private_ki~n |   0.16129   -0.21582    0.12403    0.10601   -0.08314   -0.15987
  no_kitchen |  -0.15274    0.20865   -0.11764   -0.09373    0.07340    0.16145
 cook_natgas |   0.17092    0.16664   -0.04849    0.16799    0.23906    0.04539
 cook_gascyl |  -0.15438   -0.18669    0.06377   -0.16274   -0.23824   -0.06351
 toilet_west |   0.21192   -0.09819    0.09984   -0.02423   -0.07856    0.11888
 toilet_trad |  -0.20167    0.10353   -0.07758   -0.02214    0.07727   -0.13008
toilet_pri~e |   0.14301   -0.16941    0.10053    0.07372   -0.07696   -0.13427
water_publ~e |   0.10006   -0.15175   -0.03439    0.08121    0.01060    0.10168
water_nomo~r |  -0.07429   -0.00716   -0.09385    0.00762    0.20063    0.02231
electric_p~c |   0.09205   -0.13248   -0.04842    0.04491   -0.01663    0.08734
         fly |  -0.07749   -0.01768    0.16951    0.11612   -0.10216    0.19412
    mosquito |  -0.07706   -0.01516    0.18443    0.13160   -0.07420    0.20501
   cockroach |  -0.12348   -0.02771    0.20063    0.13519   -0.02150    0.22557
        ants |  -0.06784   -0.01822    0.22929    0.13374    0.01465    0.23421
        tick |  -0.11207    0.08370    0.23312    0.15331    0.03920   -0.05440
      bedbug |  -0.11202    0.08299    0.22064    0.10569    0.05574   -0.06415
      lizard |  -0.10738    0.05332    0.30122    0.11873    0.04626    0.09388
        mice |  -0.11066    0.01468    0.31369    0.09663   -0.00530    0.15554
      weasel |  -0.12547    0.05483    0.28680    0.05943    0.02006    0.12289
    scorpion |  -0.09703    0.10672    0.24974    0.04847    0.10230   -0.18118
       snake |  -0.10226    0.11135    0.25299    0.04411    0.08136   -0.15972
      income |  -0.00600    0.04484   -0.07573    0.02371   -0.05943    0.02135
  retirement |   0.05524    0.02200   -0.03111    0.04056    0.18372    0.02013
      fridge |   0.13406   -0.16793    0.11221   -0.02306    0.17885   -0.08189
     freezer |   0.14115    0.19663    0.03044    0.00412    0.02421   -0.01042
    wash_reg |  -0.14875   -0.15968   -0.01968    0.08134    0.09217   -0.14201
   wash_auto |   0.21841    0.07507    0.09897   -0.09310   -0.03196    0.11550
       stove |  -0.05703    0.07579   -0.09172    0.15704   -0.34162    0.06937
  stove_oven |   0.11087   -0.16103    0.12869   -0.10988    0.35041   -0.11370
  stove_kero |  -0.06861    0.00575   -0.01323    0.01034    0.06548    0.04779
        dish |   0.11218    0.19341   -0.01718    0.09901   -0.01813   -0.04560
water_heater |   0.20675   -0.05374    0.10558   -0.04776   -0.04384    0.06866
         fan |   0.06845   -0.12253    0.05974   -0.09310    0.21042   -0.00783
      heater |   0.10825    0.17775    0.00114    0.06989    0.01400   -0.01545
aircondition |   0.17022    0.22600    0.00914    0.02516    0.06374   -0.00809
      sewing |   0.04578    0.03130    0.01746    0.00145    0.04972    0.05434
      vacuum |   0.19231    0.14536    0.08078   -0.07525   -0.01094    0.08002
       phone |   0.17818   -0.04826    0.08824   -0.03170    0.10298    0.02493
      mobile |   0.14047    0.00565    0.08387   -0.11477   -0.03711    0.05208
    computer |   0.17871    0.12763    0.05294   -0.05691    0.01535    0.05730
    internet |   0.14861    0.18058    0.01615   -0.00900    0.05456    0.00501
       radio |  -0.01553    0.05462   -0.00863    0.17377    0.10710   -0.02144
    recorder |   0.03353    0.06611   -0.04181    0.13212    0.05746   -0.04276
   radio_rec |   0.10950    0.00035    0.08559   -0.09254    0.00422    0.02643
TV_blackwh~e |  -0.07094    0.09398   -0.04952    0.13706   -0.06334    0.02539
    TV_color |   0.12911   -0.13853    0.10979   -0.13729    0.16114   -0.02967
   video_DVD |   0.14890    0.17284    0.02874    0.05901    0.09594    0.01743
 sat_connect |  -0.01977   -0.13573   -0.02642    0.00126    0.07430   -0.01647
         sat |   0.16508    0.10641    0.09391   -0.08888   -0.02591    0.02977
        bike |  -0.02023   -0.00760   -0.01145    0.06135   -0.07469   -0.08132
   motorbike |   0.00032   -0.02630    0.04840   -0.00099   -0.05241   -0.01627
         car |   0.16851    0.21048    0.04136   -0.01024    0.00690   -0.02575
    car_taxi |   0.00148   -0.02295    0.02800   -0.00292   -0.07526   -0.04119
     subsidy |   0.00205   -0.08412   -0.00266    0.04802    0.23888   -0.01436
    home_own |  -0.06373   -0.00646    0.16419    0.03041   -0.04215   -0.35548
    apmt_own |   0.10963    0.08824    0.00795    0.04161   -0.14873   -0.20021
        rent |  -0.01266   -0.07626   -0.09948   -0.06589    0.18381    0.45523
        rent |  -0.08992    0.00294   -0.07201    0.00207    0.02707    0.07998
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