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
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and provide commented, minimal, self-contained, reproducible code.
