(This article was first published on NIR-Quimiometría, and kindly contributed to R-bloggers)
> library(chemometrics)
> fatmsc_nipals<-nipals(fat_msc,a=10,it=160)
> CPs<-seq(1,10,by=1)
> matplot(CPs,t(fatmsc_nipals$T),lty=1,pch=21,
+ xlab="PC_number",ylab="Explained_Var")
In the 2D plot, we can see that with 3 or 4 principal components, almost all the variance is explained. We see also how samples are well projected over the first PC, but how one sample seems to be an outlier when projected over the second PC.
Also another or the same sample seems to be an outlier when projected over the 4th PC.
A look to the PC planes will show us the distribution of the samples.
> pairs(fatmsc_nipals$T[,1:4],col="red")
> pairs(fatmsc_nipals$T[,1:4],col="red")
Let´s calculate the Mahalanobis distances to study better our sample population and to find outliers:
> fatmsc_nipals4pc<-fatmsc_nipals$T[,1:4]
> Moutlier(fatmsc_nipals4pc,quantile =0.975, plot=TRUE)
$md
[1] 3.1025142 1.6787234 1.1155225 1.7130001 2.6460755 1.3341133
[7] 1.6411590 1.8790763 0.8541428 1.1332246 2.3236420 2.8866269
[13] 1.3146715 1.2759619 1.4875943 1.0603605 1.4880568 0.9665029
[19] 1.8239722 1.6562767 1.9359163 1.6708538 2.2936930 1.4845431
[25] 2.6051294 1.1436901 0.3571686 2.0533289 1.4248877 0.7107637
[31] 1.2504387 2.0814050 1.8502729 3.1433570 2.2836840 0.3547710
[37] 2.9424866 2.6208234 0.6914464 2.9649615 1.7914432 2.2730964
[43] 3.0530848 1.1569603 1.5458923 1.3590878 1.9744677 1.8299434
[49] 1.6564926 2.7850876 2.9147344 2.9858931 2.0337672 2.6220121
[55] 2.4169714 0.9873321 2.7614810 3.4578931 4.3510717 2.1840045
[61] 3.4219424 2.6471133 2.5050841 1.6500068 2.2036638 11.6174968
[67] 3.1637271 3.0938694 2.3489142 2.5605777 1.7651892 0.7602064
[73] 0.8169349 1.1276683 1.0530317 0.9008947 1.5501520 0.8291586
[79] 1.8831524 0.5590048 2.3312774 2.0025709 0.7148548 1.9298735
[85] 1.7581300 1.9388953 1.4556749 2.0408671 1.7715642 2.5011261
[91] 4.4534119 2.8088303 4.2640203 0.9677583 6.1127505 1.2239764
[97] 5.9621142 0.9987361 1.5365592 0.8917701 0.6152401 0.8996054
[103] 1.8370282 1.3580873 0.7873400 0.9220825 1.8619488 1.9298884
[109] 1.4912294 0.9832971 0.9842641 1.2018128 0.7935046 0.8925428
[115] 1.2003102 1.4462257 1.2691323 1.8269249 1.2838734 0.9981628
[121] 1.9145605 1.7954542 1.5230153 1.3347716 1.1156095 1.5871748
[127] 1.4889242 1.1780966 1.4165463 1.0057897 1.6742841 1.7999796
[133] 1.2231126 1.3167038 1.7676869 1.7475316 1.5718934 0.7844088
[139] 0.7250911 0.8394164 0.9434329 1.3583476 0.9143295 1.5666855
[145] 0.8250539 0.5027369 1.6273106 1.8940848 0.8493707 1.4611669
[151] 0.3644340 0.7813530 1.6332761 1.0557438 1.2848675 1.0695355
[157] 1.7891441 0.6474083 0.8387371 0.9655893 1.6508979 1.4765710
[163] 2.6846350 1.9820580 2.0689903 1.5834826 1.2542036 0.8494160
[169] 1.3529783 0.8451586 1.6718654 2.5892144 1.3678979 1.4070544
[175] 1.3870741 1.2010282 1.3446915 1.4648297 1.4599712 1.5161282
[181] 1.2140609 2.1280737 1.1751724 1.5939065 0.8337121 1.0548981
[187] 1.2061079 1.1519596 1.4011917 1.1339365 1.3009569 1.1758361
[193] 0.9313623 0.9973675 1.3783733 1.3145118 1.4065661 2.2898204
[199] 1.3149368 1.6195627 1.3458978 1.1028901 1.5325457 1.4918670
[205] 1.6747645 1.0730898 1.3003462 2.2767521 1.2188084 1.4188156
[211] 1.2551781 1.1094945 1.7552917 1.6537534 1.0851287 1.1067528
[217] 1.4062079 1.6325028 2.0682626
$cutoff
[1] 3.338156
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