# Re: st: Interpreting PCA output

 From "Joao Ricardo F. Lima" To statalist@hsphsun2.harvard.edu Subject Re: st: Interpreting PCA output Date Wed, 23 Jul 2008 19:29:57 -0300

```Mona,

the first eigenvector is the first principal component. The first PC
has maximal overall variance. The second PC has maximal variance among
all unit lenght linear combinations that are uncorrelated to the first
PC, etc (see MV manual).

Mona said "Using a scree test, I may choose to only use the first 5
principal components."

You must to observe the variance explained by these 5 PC. The Rho in
your case is about 0.3297 or 32.97% (cumulative column), and in my
opinion isnīt an ideal % (see the literature too).

HTH,

JR

2008/7/23 Mona Mowafi <mmowafi@hsph.harvard.edu>:
> 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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>

--
-------------------------------
Joao Ricardo Lima
Professor
UFPB-CCA-DCFS
+553138923914
-------------------------------

*
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