how to tell if its better to standardize your data matrix first when you do principal
masterinex wrote:
this is how my data matrix looks like . This is just for the first 10
observations , but the pattern is similar for the other observations.
1 12.3 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 32.0
27.4 17.1
2 6.1 173.25 72.25 38.5 93.6 83.0 98.7 58.7 37.3 23.4 30.5
28.9 18.2
3 25.3 154.00 66.25 34.0 95.8 87.9 99.2 59.6 38.9 24.0 28.8
25.2 16.6
4 10.4 184.75 72.25 37.4 101.8 86.4 101.2 60.1 37.3 22.8 32.4
29.4 18.2
5 28.7 184.25 71.25 34.4 97.3 100.0 101.9 63.2 42.2 24.0 32.2
27.7 17.7
6 20.9 210.25 74.75 39.0 104.5 94.4 107.8 66.0 42.0 25.6 35.7
30.6 18.8
7 19.2 181.00 69.75 36.4 105.1 90.7 100.3 58.4 38.3 22.9 31.9
27.8 17.7
8 12.4 176.00 72.50 37.8 99.6 88.5 97.1 60.0 39.4 23.2 30.5
29.0 18.8
9 4.1 191.00 74.00 38.1 100.9 82.5 99.9 62.9 38.3 23.8 35.9
31.1 18.2
10 11.7 198.25 73.50 42.1 99.6 88.6 104.1 63.1 41.7 25.0 35.6
30.0 19.2
and after standardizing it .
1 -0.831228836 -0.898881671 -0.98330178 -0.77420686 -0.952294055
-0.712961621 -0.814552365 -0.0625400993 -0.53901713 -0.825399059 -0.08244945
2 -1.588060506 -0.185928394 0.75868364 0.23560461 -0.889886435
-0.931523054 -0.155497233 -0.1252522485 -0.53901713 0.295114747 -0.59529632
3 0.755676279 -0.908262635 -1.56396359 -1.74011349 -0.615292906
-0.444727135 -0.077038289 0.0628841989 0.15515266 0.743320270 -1.17652277
4 -1.063161122 0.245595958 0.75868364 -0.24734870 0.133598535
-0.593746294 0.236797489 0.1674044475 -0.53901713 -0.153090775 0.05430971
5 1.170713001 0.226834030 0.37157577 -1.56449410 -0.428070046
0.757360745 0.346640011 0.8154299886 1.58687786 0.743320270 -0.01406987
6 0.218569932 1.202454304 1.72645331 0.45512884 0.470599683
0.201022552 1.272455554 1.4007433805 1.50010664 1.938534997 1.18257281
7 0.011051571 0.104881496 -0.20908604 -0.68639717 0.545488828
-0.166558039 0.095571389 -0.1879643976 -0.10516101 -0.078389855 -0.11663925
8 -0.819021874 -0.082737788 0.85546060 -0.07172932 -0.140994994
-0.385119472 -0.406565855 0.1465003978 0.37208072 0.145712907 -0.59529632
9 -1.832199755 0.480120063 1.43612241 0.05998522 0.021264819
-0.981196107 0.032804234 0.7527178395 -0.10516101 0.593918429 1.25095239
10 -0.904470611 0.752168024 1.24256848 1.81617909 -0.140994994
-0.375184861 0.691859366 0.7945259389 1.36994980 1.490329474 1.14838302
this is the result of applying PCA to the data matrix
Standard deviations:
[1] 30.6645414 7.5513852 3.6927427 2.8703435 2.5363007 1.9136933
1.5624131 1.3689630 1.2976189
[10] 1.1633458 1.1118231 0.7847148 0.4802303
Rotation:
PC1 PC2 PC3 PC4 PC5
PC6 PC7 PC8
var1 0.18110712 -0.74864138 -0.46070566 -0.365658769 0.192810075
-0.132529979 0.023764851 0.03674873
var2 0.86458284 0.34243386 -0.05766909 -0.235504989 -0.046075934
0.001493006 -0.024535011 0.13439659
var3 0.03765598 0.20097537 -0.15709612 -0.343218776 -0.295201121
-0.073295697 -0.086930370 -0.54389141
var4 0.05965733 0.01737951 0.09854179 -0.030801791 0.125735684
0.341795876 -0.001735808 0.37152696
var5 0.23845698 -0.20616399 0.68948870 0.025904812 0.391188182
-0.428933369 -0.101780281 -0.16965893
var6 0.29928369 -0.47394636 0.24791449 0.341235161 -0.511378719
0.447071255 -0.077534385 -0.13198544
var7 0.19503685 0.01385823 -0.24126047 0.531403827 -0.127426510
-0.410568454 0.608163973 -0.01265457
var8 0.13261863 0.06839078 -0.37740589 0.535332339 0.366103479
0.032376851 -0.574484605 -0.05645694
var9 0.06246705 0.04407384 -0.09545362 0.037993146 -0.036651080
0.012347288 -0.192976142 -0.13027876
var10 0.03027791 0.05533988 -0.03749859 -0.009257423 0.011026593
-0.010770032 -0.104041067 0.12125263
var11 0.07435322 0.04334969 -0.02666944 0.032036374 0.464035624
0.454970952 0.347507539 -0.60527541
var12 0.04328710 0.04731771 0.00360668 -0.054200633 0.275901346
0.297800123 0.324323749 0.30487145
var13 0.02095652 0.02146485 0.03598618 -0.022510780 0.005192075
0.103988977 0.031541374 0.07877455
PC9 PC10 PC11 PC12 PC13
var1 -0.005328345 0.030549780 -0.049283616 -0.02211988 0.015660892
var2 0.170766596 -0.144031738 0.028862963 0.06984674 0.006293703
var3 -0.282549313 0.548650592 0.131284937 -0.14740722 -0.002384605
var4 0.024070488 0.614154008 -0.551480394 -0.03446124 -0.178123011
var5 -0.157551008 0.147685248 0.008044148 -0.04068258 0.007778992
var6 -0.058675551 0.006344813 0.130814072 -0.04088919 -0.028655330
var7 -0.099243751 0.171852216 -0.149231752 -0.06690208 -0.014693444
var8 0.006629025 0.199158097 0.187226774 -0.02511968 0.070896819
var9 -0.658214712 -0.320120384 -0.500003990 0.37630539 -0.023642902
var10 -0.259704149 -0.273030750 -0.074006053 -0.83676032 -0.348034215
var11 0.157450716 -0.148991117 -0.153561998 -0.08742543 -0.056513679
var12 -0.560837576 0.098418477 0.542670501 0.10593629 -0.007670188
var13 -0.110526479 -0.012776152 -0.165279275 -0.32037870 0.914832392
this is the result of applying PCA to the standardized data matrix
Standard deviations:
[1] 2.9252556 1.1792994 0.8623322 0.7219158 0.6812740 0.5863879 0.4981330
0.4630637 0.4414004 0.4212403
[11] 0.2776168 0.2208503 0.1366760
Rotation:
PC1 PC2 PC3 PC4 PC5
PC6 PC7 PC8
var1 0.2214240 -0.528940022 -0.22438633 -0.0324934310 0.10237112
-0.47563754 0.33100129 -0.19102715
var2 0.3345528 0.023162612 -0.10713782 -0.0001760222 0.11352232
0.04469088 -0.10098447 0.18643834
var3 0.1517554 0.605551504 -0.38237721 0.0314469316 0.59507576
-0.18321494 0.08116801 0.08111090
var4 0.2862444 -0.018344029 0.34874004 -0.1945368511 0.29590927
0.30061030 -0.39160283 -0.20869249
var5 0.3027658 -0.244481933 0.03265146 -0.1559266926 0.12932226
0.02393963 -0.16226550 0.45698236
var5 0.3005716 -0.329554056 -0.13879142 -0.1626911071 0.11072123
-0.05063054 -0.06388229 0.08496036
var6 0.3160710 -0.061820244 -0.23144824 0.1247108501 -0.06038088
0.16065274 -0.18772748 0.07057902
var7 0.2973041 0.006421036 -0.17862551 0.3873606332 -0.28005086
0.34119818 -0.13590921 -0.16267799
var8 0.2955016 0.144234590 -0.26323414 -0.0068912717 -0.18117677
-0.01771120 0.03379585 -0.62830066
var9 0.2552571 0.326437989 -0.09749610 -0.2291093560 -0.61898234
-0.22847105 0.01411768 0.38312210
var10 0.2822210 0.016911093 0.28838652 0.4287108516 0.07554337
0.28403417 0.66673623 0.19445840
var11 0.2491444 0.135956228 0.53597029 0.3883062869 -0.01492335
-0.60228918 -0.26232244 -0.08966993
var12 0.2637809 0.185151550 0.33956904 -0.5971722620 -0.04476545
0.08083909 0.34854493 -0.20909842
PC9 PC10 PC11 PC12 PC13
var1 -0.40247469 0.05379733 0.063919267 0.26040567 0.015743241
var2 0.07150091 0.02906931 -0.009540692 0.02481489 0.899751898
var3 -0.11290113 0.06735920 0.100968481 -0.03902708 -0.182276335
var4 -0.52110479 -0.28262405 -0.150175234 0.06709027 -0.070349152
var5 0.36282385 -0.25907897 0.461043958 0.30566521 -0.256838644
var6 0.13245560 0.04742256 -0.174886071 -0.81057186 -0.147622115
var7 0.17950233 0.40472605 -0.602790052 0.38468466 -0.223865462
var8 -0.24062368 0.33426221 0.545545641 -0.12880676 -0.077404092
var9 0.37912190 -0.49731546 -0.023067506 0.04355862 -0.002718371
var10 -0.34729467 -0.21088629 -0.112243026 -0.03892369 -0.069031092
var11 -0.01252875 -0.22996539 -0.162156246 -0.04827985 -0.052013577
var12 0.14733228 0.12821614 0.009932520 -0.05164105 -0.025625894
var13 0.15194616 0.45367703 0.139390086 0.04590545 -0.004970894
In this case is it better to standardize the matrix or leave it as it is ?
Also , how do I compare which method gives the better result?
I also found that the proportion of the first principle after standardizing
it was reduce alot , would that mean that it is a bad idea to standardize
the matrix?
any suggestions are welcome.
I told you that you need to do the interpretation and it depends on the variables (are measured in the same units?). Nobody can give you an answer without knowledge about the variables. And note, as Hadley mentioned before, that there are certainly statistical consultants available in your area, which is unknown for us given you post anonymously from some hotmail.com account - which is also not very helpful to get further answers.... Uwe Ligges