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st: Interpreting PCA output
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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