[R] principle component values on PCA plots do not match

Jinsong Zhao jszhao at yeah.net
Tue Aug 19 02:41:54 CEST 2014


Hi,

There is a scale factor associated with biplot when plotting the PCA 
result. Please read the help page of biplot.princomp or/and the source 
code of this function.

HIH,
Jinsong

On 2014/8/18 16:31, John Romansic wrote:
> Hi all,
>
> I am using prcomp to do Principle Components Analysis and have run into a
> problem regarding the scale of the axes on my plots.  I am using prcomp to
> analyze a set of 25 morphological measurements taken on each of 161
> individual frogs. I used the biplot function to produce a figure of PC1 vs
> PC2 for each of the individual frogs and arrows that represent the loadings
> of the different morphological measurements on PC1 and PC2. Then I
> constructed a separate, similar plot, using my own coding, that provides a
> number for each individual frogs corresponding to its species as determined
> by genetic analysis, without the arrows. The y-axis on the first plot
> ranges shows PC2 values ranging from about -11 to 11, but the y-axis on the
> second plot shows PC2 values ranging from about -4 to 4, although all the
> data points seem to show up on the figure. I would like to show the same
> PCA results on both plots and I do not understand why the y-axes on these
> two plots do not match. By the way, the x-axes on these two plots seem to
> match, but I think that is just a coincidence. I suspect that my coding for
> the second plot is missing a command regarding scaling of the principle
> components, but it's not obvious to me why those data would have to be
> re-scaled. I thought the scaling is dealt with by prcomp. Within prcomp, I
> used scale=TRUE, which I understand re-scales the original data so that all
> the variables have equal variance.
>
> Does anyone have any suggestions on what might be wrong with my coding?
>
> Below is an example, using a truncated data set, which produces different
> numbers than the example I described above, since this time only 5
> measurements are included for each frog. Nevertheless, the second plot (the
> one with my coding) has the same problem.
>
>> frogs
>      Genetic.species   SVL    HL    HW   BED   FED
> 1                27 47.75 16.46 14.63 13.27  8.29
> 2                25 44.87 16.35 14.67 13.50  8.69
> 3                24 52.57 19.82 16.62 15.12  9.35
> 4                24 56.60 21.18 19.55 17.73 11.09
> 5                20 47.66 18.48 16.33 14.98  9.37
> 6                19 65.96 23.33 20.00 18.88 12.19
> 7                19 58.67 21.12 18.12 17.37 10.47
> 8                19 64.33 23.16 19.99 19.20 11.88
> 9                19 61.03 21.98 19.42 18.22  1.16
> 10               19 62.88 21.90 19.71 17.92 11.65
> 11               19 62.77 21.31 19.30 18.47 11.85
> 12               19 58.64 21.30 19.55 18.17 11.14
> 13               19 63.40 20.74 19.59 18.25 11.03
> 14               19 58.22 19.87 18.82 16.85 10.73
> 15               18 55.43 19.80 18.27 16.01  9.52
> 16               17 60.46 21.40 19.37 16.67 10.44
> 17               16 58.32 19.48 17.55 16.42  9.96
> 18               14 44.64 16.35 14.41 12.77  8.42
> 19               14 48.32 17.88 16.23 14.34  9.01
> 20               13 42.32 15.43 14.40 12.47  7.43
> 21               13 41.87 15.97 14.97 12.46  7.42
> 22               13 45.71 16.87 15.98 13.08  7.77
> 23               12 47.38 17.48 15.77 13.99  9.08
> 24               12 50.28 18.48 17.28 14.87  9.46
> 25               12 48.00 18.52 17.60 15.40  9.63
> 26               12 50.98 18.61 17.87 16.00  9.59
> 27               12 50.76 18.24 17.61 17.72  9.54
> 28               12 50.83 18.90 18.28 15.02  9.53
> 29               11 46.80 19.13 17.10 15.22  9.01
> 30               10 37.55 14.21 12.42 10.79  6.15
> 31               10 40.39 15.32 13.81 11.89  6.80
> 32               10 42.39 14.77 14.72 11.87  6.78
> 33                9 44.08 16.37 15.99 13.09  8.50
> 34                9 47.36 16.16 16.14 13.50  7.72
> 35                8 41.43 15.53 12.73 11.01  6.37
> 36                8 41.45 15.63 13.68 11.32  7.20
> 37                8 38.86 13.82 12.13 10.39  6.28
> 38                8 40.51 14.25 12.68 10.40  6.41
> 39                8 44.64 15.37 13.75 11.37  6.82
> 40                8 45.08 15.64 14.25 11.17  6.68
> 41                8 45.10 16.43 15.03 13.16  7.89
> 42                8 48.94 17.35 16.28 12.31  8.24
> 43                6 44.05 16.60 12.96 12.51  8.19
> 44                6 44.56 16.24 13.86 13.02  8.17
> 45                6 48.01 17.64 15.26 14.59  9.02
> 46                6 48.67 17.84 15.59 14.44  9.36
> 47                6 46.87 18.37 16.18 14.59  9.21
> 48                6 44.32 16.81 14.87 13.55  8.50
> 49                6 44.79 16.14 14.38 13.40  8.91
> 50                6 45.30 16.31 14.62 12.89  8.41
> 51                6 46.36 17.26 15.48 13.30  8.83
> 52                6 46.80 17.55 15.77 13.87  9.01
> 53                6 43.14 15.61 14.23 12.78  8.63
> 54                6 47.99 16.63 15.54 14.00  9.06
> 55                4 63.12 22.52 20.40 17.77 11.60
> 56                4 57.22 20.02 18.44 16.07 10.77
> 57                4 65.55 22.32 20.56 17.53 11.57
> 58                4 60.61 20.74 19.33 16.61 10.20
> 59                4 64.82 22.17 21.27 17.99 10.95
> 60                4 63.03 21.97 21.11 18.25 11.37
> 61                4 64.96 22.93 22.16 19.07 12.30
> 62                4 61.89 21.47 20.78 17.97 10.83
> 63                4 63.34 21.74 21.38 17.60 10.40
> 64                4 65.01 21.74 22.18 19.11 11.47
> 65                4 64.52 21.76 22.49 18.35 10.90
> 66                3 41.34 15.17 12.84 11.87  7.26
> 67                3 48.11 18.45 15.83 14.28  8.65
> 68                3 47.59 17.37 15.01 13.34  8.67
> 69                3 49.25 17.87 15.64 13.74  8.82
> 70                3 44.82 16.47 14.42 13.05  8.35
> 71                3 46.21 16.71 14.70 12.88  8.57
> 72                3 56.24 20.34 18.08 14.72  9.22
> 73                3 53.38 19.64 17.51 14.82  9.12
> 74                3 52.59 19.16 17.23 14.44  9.46
> 75                3 46.27 16.19 14.57 12.39  8.20
> 76                3 49.18 17.68 15.96 14.03  8.98
> 77                3 53.90 20.01 18.20 14.89  9.46
> 78                2 47.62 18.08 15.88 15.02  9.64
> 79                2 48.20 18.04 15.89 14.89  9.23
> 80                2 46.27 16.55 15.19 14.04  8.64
> 81                2 54.04 18.73 17.68 15.79  3.97
> 82                1 53.34 19.76 16.52 15.04  9.36
> 83                1 50.41 17.85 14.96 14.24  8.80
> 84                1 51.71 19.12 16.22 15.16  9.37
> 85                1 49.73 16.91 14.44 13.49  8.64
> 86                1 51.73 18.79 16.07 14.58  8.51
> 87                1 54.50 20.21 17.33 15.45  9.68
> 88                1 54.08 19.96 17.15 15.76  9.78
> 89                1 53.26 18.25 15.70 14.76  9.35
> 90                1 53.20 18.63 16.07 14.79  9.57
> 91                1 47.54 16.61 14.33 13.56  8.33
> 92                1 51.20 18.22 15.73 14.46  9.07
> 93                1 53.56 19.31 16.68 15.33  9.19
> 94                1 48.11 17.11 14.80 13.98  8.15
> 95                1 48.10 17.08 14.78 14.14  8.52
> 96                1 55.97 20.96 18.15 16.06 10.06
> 97                1 56.18 20.43 17.81 16.18 10.27
> 98                1 51.21 18.67 16.34 15.03  9.55
> 99                1 52.25 18.67 16.36 14.26  8.88
> 100               1 51.78 18.58 16.30 14.91  9.21
> 101               1 51.39 18.26 16.02 14.57  9.54
> 102               1 48.45 17.55 15.41 14.16  8.56
> 103               1 54.30 19.08 16.80 15.22  9.69
> 104               1 49.33 16.67 14.73 13.84  8.04
> 105               1 53.41 19.05 16.84 14.86  9.70
> 106               1 48.80 18.56 16.44 14.88  9.31
> 107               1 49.70 18.08 16.03 14.69  9.60
> 108               1 48.28 16.74 14.87 13.72  8.45
> 109               1 51.35 17.86 15.92 14.22  9.07
> 110               1 51.01 17.26 15.39 14.63  9.47
> 111               1 49.89 17.17 15.31 14.21  9.04
> 112               1 54.15 19.69 17.58 15.38 10.17
> 113               1 56.28 20.37 18.20 15.83 10.49
> 114               1 55.30 19.96 17.86 15.66 10.93
> 115               1 44.53 15.56 13.96 12.69  7.81
> 116               1 54.15 18.86 16.93 15.08  9.82
> 117               1 50.59 17.75 15.95 14.66  9.25
> 118               1 52.55 19.63 17.71 15.21  9.98
> 119               1 53.86 19.56 17.66 15.18  9.52
> 120               1 49.91 17.75 16.04 14.21  8.98
> 121               1 52.78 19.21 17.37 15.49  9.92
> 122               1 51.94 18.79 17.00 14.79 10.14
> 123               1 56.60 20.19 18.29 15.86 10.03
> 124               1 51.23 17.66 16.02 14.37  9.30
> 125               1 51.80 19.05 17.30 15.12 10.23
> 126               1 52.78 18.52 16.85 14.80  9.58
> 127               1 51.41 18.13 16.53 14.36  9.02
> 128               1 50.41 18.10 16.52 14.87  9.18
> 129               1 53.48 18.69 17.07 15.19  9.52
> 130               1 53.87 18.60 17.00 15.28  9.92
> 131               1 51.98 18.51 16.93 15.12  9.52
> 132               1 50.56 18.13 16.61 15.12  8.94
> 133               1 50.64 18.16 16.68 14.38  9.04
> 134               1 53.06 18.56 17.06 14.74  9.68
> 135               1 54.64 18.96 17.44 15.61  9.81
> 136               1 48.13 16.91 15.56 14.30  8.96
> 137               1 57.97 21.17 19.48 17.01 10.99
> 138               1 49.93 18.24 16.80 15.20  9.14
> 139               1 47.38 17.02 15.72 14.18  9.14
> 140               1 54.24 19.01 17.60 15.18  9.86
> 141               1 50.17 17.59 16.31 14.53  9.23
> 142               1 49.78 16.77 15.55 13.83  9.12
> 143               1 51.81 18.41 17.09 14.87  9.82
> 144               1 50.84 18.71 17.38 14.79  9.42
> 145               1 49.57 16.41 15.26 13.35  8.80
> 146               1 55.81 19.27 17.92 16.06  9.97
> 147               1 58.03 20.13 18.73 16.28 10.50
> 148               1 48.72 16.62 15.50 14.06  8.60
> 149               1 48.39 17.12 15.97 14.01  9.13
> 150               1 49.01 18.24 17.10 14.76  9.54
> 151               1 50.31 18.23 17.10 15.15  9.76
> 152               1 49.10 17.15 16.11 14.47  8.83
> 153               1 60.04 21.20 19.95 17.53 11.53
> 154               1 46.99 16.87 15.97 13.93  9.10
> 155               1 53.63 19.00 18.08 15.89 10.03
> 156               1 57.88 20.21 19.35 17.34 10.18
> 157               1 54.89 20.06 19.27 16.76 10.78
> 158               1 53.56 19.18 18.52 16.39 10.64
> 159               1 51.50 18.23 17.62 15.21  9.62
> 160               1 63.47 22.12 21.40 17.79 11.65
> 161               1 51.46 17.21 16.90 15.37 10.00
>> frogspca<-prcomp(frogs[2:6],scale=TRUE)
>> summary(frogspca)
> Importance of components:
>                            PC1     PC2     PC3     PC4     PC5
> Standard deviation     2.0950 0.65315 0.27219 0.25087 0.21737
> Proportion of Variance 0.8778 0.08532 0.01482 0.01259 0.00945
> Cumulative Proportion  0.8778 0.96315 0.97796 0.99055 1.00000
>> plot(frogspca)
>> biplot(frogspca)
>> plot( frogspca$x[,1], frogspca$x[,2] , type="n", xlab="PC1", ylab="PC2")
>> text( frogspca$x[,1], frogspca$x[,2], labels=c(Genetic.species))
>>
> Thank you very much for any suggestions you might have,
> John Romansic
>
> 	[[alternative HTML version deleted]]
>
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