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Sidoti, Salvatore A.

2016-Nov-13 05:46 UTC

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

Let's say I perform 4 measurements on an animal: three are linear
measurements in millimeters and the fourth is its weight in milligrams. So, we
have a data set with mixed units.

Based on these four correlated measurements, I would like to obtain one
"score" or value that describes an individual animal's size. I
considered simply taking the geometric mean of these 4 measurements, and that
would give me a "score" - larger values would be for larger animals,
etc.

However, this assumes that all 4 of these measurements contribute equally to an
animal's size. Of course, more than likely this is not the case. I then
performed a PCA to discover how much influence each variable had on the overall
data set. I was hoping to use this analysis to refine my original approach.

I honestly do not know how to apply the information from the PCA to this
particular problem...

I do know, however, that principle components 1 and 2 capture enough of the
variation to reduce the number of dimensions down to 2 (see analysis below with
the original data set).

Note: animal weights were ln() transformed to increase correlation with the 3
other variables.

df <- data.frame(
  weight = log(1000*c(0.0980, 0.0622, 0.0600, 0.1098, 0.0538, 0.0701, 0.1138,
0.0540, 0.0629, 0.0930,
             0.0443, 0.1115, 0.1157, 0.0734, 0.0616, 0.0640, 0.0480, 0.1339,
0.0547, 0.0844,
             0.0431, 0.0472, 0.0752, 0.0604, 0.0713, 0.0658, 0.0538, 0.0585,
0.0645, 0.0529,
             0.0448, 0.0574, 0.0577, 0.0514, 0.0758, 0.0424, 0.0997, 0.0758,
0.0649, 0.0465,
             0.0748, 0.0540, 0.0819, 0.0732, 0.0725, 0.0730, 0.0777, 0.0630,
0.0466)),
  interoc = c(0.853, 0.865, 0.811, 0.840, 0.783, 0.868, 0.818, 0.847, 0.838,
0.799,
              0.737, 0.788, 0.731, 0.777, 0.863, 0.877, 0.814, 0.926, 0.767,
0.746,
              0.700, 0.768, 0.807, 0.753, 0.809, 0.788, 0.750, 0.815, 0.757,
0.737,
              0.759, 0.863, 0.747, 0.838, 0.790, 0.676, 0.857, 0.728, 0.743,
0.870,
              0.787, 0.773, 0.829, 0.785, 0.746, 0.834, 0.829, 0.750, 0.842),
  cwidth = c(3.152, 3.046, 3.139, 3.181, 3.023, 3.452, 2.803, 3.050, 3.160,
3.186,
             2.801, 2.862, 3.183, 2.770, 3.207, 3.188, 2.969, 3.033, 2.972,
3.291,
             2.772, 2.875, 2.978, 3.094, 2.956, 2.966, 2.896, 3.149, 2.813,
2.935,
             2.839, 3.152, 2.984, 3.037, 2.888, 2.723, 3.342, 2.562, 2.827,
2.909,
             3.093, 2.990, 3.097, 2.751, 2.877, 2.901, 2.895, 2.721, 2.942),
  clength = c(3.889, 3.733, 3.762, 4.059, 3.911, 3.822, 3.768, 3.814, 3.721,
3.794,
              3.483, 3.863, 3.856, 3.457, 3.996, 3.876, 3.642, 3.978, 3.534,
3.967,
              3.429, 3.518, 3.766, 3.755, 3.706, 3.785, 3.607, 3.922, 3.453,
3.589,
              3.508, 3.861, 3.706, 3.593, 3.570, 3.341, 3.916, 3.336, 3.504,
3.688,
              3.735, 3.724, 3.860, 3.405, 3.493, 3.586, 3.545, 3.443, 3.640))

pca_morpho <- princomp(df, cor = TRUE)

summary(pca_morpho)

Importance of components:
                         		Comp.1    	Comp.2    	Comp.3    	Comp.4
Standard deviation     	1.604107 	0.8827323 	0.7061206 	0.3860275
Proportion of Variance 	0.643290 	0.1948041 	0.1246516 	0.0372543
Cumulative Proportion  	0.643290 	0.8380941 	0.9627457 	1.0000000

Loadings:
        		Comp.1 	Comp.2	Comp.3 	Comp.4
weight  	-0.371  	0.907        			-0.201
interoc 	-0.486 	-0.227 	-0.840       
cwidth  	-0.537 	-0.349  	0.466 		-0.611
clength 	-0.582         			0.278  	0.761

               		Comp.1	Comp.2	Comp.3	Comp.4
SS loadings      	1.00   		1.00   		1.00   		1.00
Proportion Var   	0.25   		0.25   		0.25 		0.25
Cumulative Var   	0.25   		0.50   		0.75   		1.00

Any guidance will be greatly appreciated!

Salvatore A. Sidoti
PhD Student
The Ohio State University
Behavioral Ecology

Bert Gunter

2016-Nov-13 15:25 UTC

head link

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

While you may get a reply here, this list is about R programming, not
about statistics. So

1. Do your homework and read a tutorial on PCA on the web or
elsewhere. Isn't this what a PhD student is supposed to do?

2. Post on a statistics list like stats.stackexchange.com.

3. Consult your professor or other local statistical resource.

Cheers,
Bert
Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Sat, Nov 12, 2016 at 9:46 PM, Sidoti, Salvatore A.
<sidoti.23 at buckeyemail.osu.edu> wrote:> Let's say I perform 4 measurements on an animal: three are linear
measurements in millimeters and the fourth is its weight in milligrams. So, we
have a data set with mixed units.
>
> Based on these four correlated measurements, I would like to obtain one
"score" or value that describes an individual animal's size. I
considered simply taking the geometric mean of these 4 measurements, and that
would give me a "score" - larger values would be for larger animals,
etc.
>
> However, this assumes that all 4 of these measurements contribute equally
to an animal's size. Of course, more than likely this is not the case. I
then performed a PCA to discover how much influence each variable had on the
overall data set. I was hoping to use this analysis to refine my original
approach.
>
> I honestly do not know how to apply the information from the PCA to this
particular problem...
>
> I do know, however, that principle components 1 and 2 capture enough of the
variation to reduce the number of dimensions down to 2 (see analysis below with
the original data set).
>
> Note: animal weights were ln() transformed to increase correlation with the
3 other variables.
>
> df <- data.frame(
>   weight = log(1000*c(0.0980, 0.0622, 0.0600, 0.1098, 0.0538, 0.0701,
0.1138, 0.0540, 0.0629, 0.0930,
>              0.0443, 0.1115, 0.1157, 0.0734, 0.0616, 0.0640, 0.0480,
0.1339, 0.0547, 0.0844,
>              0.0431, 0.0472, 0.0752, 0.0604, 0.0713, 0.0658, 0.0538,
0.0585, 0.0645, 0.0529,
>              0.0448, 0.0574, 0.0577, 0.0514, 0.0758, 0.0424, 0.0997,
0.0758, 0.0649, 0.0465,
>              0.0748, 0.0540, 0.0819, 0.0732, 0.0725, 0.0730, 0.0777,
0.0630, 0.0466)),
>   interoc = c(0.853, 0.865, 0.811, 0.840, 0.783, 0.868, 0.818, 0.847,
0.838, 0.799,
>               0.737, 0.788, 0.731, 0.777, 0.863, 0.877, 0.814, 0.926,
0.767, 0.746,
>               0.700, 0.768, 0.807, 0.753, 0.809, 0.788, 0.750, 0.815,
0.757, 0.737,
>               0.759, 0.863, 0.747, 0.838, 0.790, 0.676, 0.857, 0.728,
0.743, 0.870,
>               0.787, 0.773, 0.829, 0.785, 0.746, 0.834, 0.829, 0.750,
0.842),
>   cwidth = c(3.152, 3.046, 3.139, 3.181, 3.023, 3.452, 2.803, 3.050, 3.160,
3.186,
>              2.801, 2.862, 3.183, 2.770, 3.207, 3.188, 2.969, 3.033, 2.972,
3.291,
>              2.772, 2.875, 2.978, 3.094, 2.956, 2.966, 2.896, 3.149, 2.813,
2.935,
>              2.839, 3.152, 2.984, 3.037, 2.888, 2.723, 3.342, 2.562, 2.827,
2.909,
>              3.093, 2.990, 3.097, 2.751, 2.877, 2.901, 2.895, 2.721,
2.942),
>   clength = c(3.889, 3.733, 3.762, 4.059, 3.911, 3.822, 3.768, 3.814,
3.721, 3.794,
>               3.483, 3.863, 3.856, 3.457, 3.996, 3.876, 3.642, 3.978,
3.534, 3.967,
>               3.429, 3.518, 3.766, 3.755, 3.706, 3.785, 3.607, 3.922,
3.453, 3.589,
>               3.508, 3.861, 3.706, 3.593, 3.570, 3.341, 3.916, 3.336,
3.504, 3.688,
>               3.735, 3.724, 3.860, 3.405, 3.493, 3.586, 3.545, 3.443,
3.640))
>
> pca_morpho <- princomp(df, cor = TRUE)
>
> summary(pca_morpho)
>
> Importance of components:
>                                         Comp.1          Comp.2         
Comp.3          Comp.4
> Standard deviation      1.604107        0.8827323       0.7061206      
0.3860275
> Proportion of Variance  0.643290        0.1948041       0.1246516      
0.0372543
> Cumulative Proportion   0.643290        0.8380941       0.9627457      
1.0000000
>
> Loadings:
>                         Comp.1  Comp.2  Comp.3  Comp.4
> weight          -0.371          0.907                           -0.201
> interoc         -0.486  -0.227  -0.840
> cwidth          -0.537  -0.349          0.466           -0.611
> clength         -0.582                          0.278   0.761
>
>                         Comp.1  Comp.2  Comp.3  Comp.4
> SS loadings             1.00            1.00            1.00           
1.00
> Proportion Var          0.25            0.25            0.25           
0.25
> Cumulative Var          0.25            0.50            0.75           
1.00
>
> Any guidance will be greatly appreciated!
>
> Salvatore A. Sidoti
> PhD Student
> The Ohio State University
> Behavioral Ecology
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Jim Lemon

2016-Nov-13 20:53 UTC

head link

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

Hi Salvatore,
If by "size" you mean volume, why not directly measure the volume of
your animals? They appear to be fairly small. Sometimes working out
what the critical value actually means can inform the way to measure
it.

Jim


On Sun, Nov 13, 2016 at 4:46 PM, Sidoti, Salvatore A.
<sidoti.23 at buckeyemail.osu.edu> wrote:> Let's say I perform 4 measurements on an animal: three are linear
measurements in millimeters and the fourth is its weight in milligrams. So, we
have a data set with mixed units.
>
> Based on these four correlated measurements, I would like to obtain one
"score" or value that describes an individual animal's size. I
considered simply taking the geometric mean of these 4 measurements, and that
would give me a "score" - larger values would be for larger animals,
etc.
>
> However, this assumes that all 4 of these measurements contribute equally
to an animal's size. Of course, more than likely this is not the case. I
then performed a PCA to discover how much influence each variable had on the
overall data set. I was hoping to use this analysis to refine my original
approach.
>
> I honestly do not know how to apply the information from the PCA to this
particular problem...
>
> I do know, however, that principle components 1 and 2 capture enough of the
variation to reduce the number of dimensions down to 2 (see analysis below with
the original data set).
>
> Note: animal weights were ln() transformed to increase correlation with the
3 other variables.
>
> df <- data.frame(
>   weight = log(1000*c(0.0980, 0.0622, 0.0600, 0.1098, 0.0538, 0.0701,
0.1138, 0.0540, 0.0629, 0.0930,
>              0.0443, 0.1115, 0.1157, 0.0734, 0.0616, 0.0640, 0.0480,
0.1339, 0.0547, 0.0844,
>              0.0431, 0.0472, 0.0752, 0.0604, 0.0713, 0.0658, 0.0538,
0.0585, 0.0645, 0.0529,
>              0.0448, 0.0574, 0.0577, 0.0514, 0.0758, 0.0424, 0.0997,
0.0758, 0.0649, 0.0465,
>              0.0748, 0.0540, 0.0819, 0.0732, 0.0725, 0.0730, 0.0777,
0.0630, 0.0466)),
>   interoc = c(0.853, 0.865, 0.811, 0.840, 0.783, 0.868, 0.818, 0.847,
0.838, 0.799,
>               0.737, 0.788, 0.731, 0.777, 0.863, 0.877, 0.814, 0.926,
0.767, 0.746,
>               0.700, 0.768, 0.807, 0.753, 0.809, 0.788, 0.750, 0.815,
0.757, 0.737,
>               0.759, 0.863, 0.747, 0.838, 0.790, 0.676, 0.857, 0.728,
0.743, 0.870,
>               0.787, 0.773, 0.829, 0.785, 0.746, 0.834, 0.829, 0.750,
0.842),
>   cwidth = c(3.152, 3.046, 3.139, 3.181, 3.023, 3.452, 2.803, 3.050, 3.160,
3.186,
>              2.801, 2.862, 3.183, 2.770, 3.207, 3.188, 2.969, 3.033, 2.972,
3.291,
>              2.772, 2.875, 2.978, 3.094, 2.956, 2.966, 2.896, 3.149, 2.813,
2.935,
>              2.839, 3.152, 2.984, 3.037, 2.888, 2.723, 3.342, 2.562, 2.827,
2.909,
>              3.093, 2.990, 3.097, 2.751, 2.877, 2.901, 2.895, 2.721,
2.942),
>   clength = c(3.889, 3.733, 3.762, 4.059, 3.911, 3.822, 3.768, 3.814,
3.721, 3.794,
>               3.483, 3.863, 3.856, 3.457, 3.996, 3.876, 3.642, 3.978,
3.534, 3.967,
>               3.429, 3.518, 3.766, 3.755, 3.706, 3.785, 3.607, 3.922,
3.453, 3.589,
>               3.508, 3.861, 3.706, 3.593, 3.570, 3.341, 3.916, 3.336,
3.504, 3.688,
>               3.735, 3.724, 3.860, 3.405, 3.493, 3.586, 3.545, 3.443,
3.640))
>
> pca_morpho <- princomp(df, cor = TRUE)
>
> summary(pca_morpho)
>
> Importance of components:
>                                         Comp.1          Comp.2         
Comp.3          Comp.4
> Standard deviation      1.604107        0.8827323       0.7061206      
0.3860275
> Proportion of Variance  0.643290        0.1948041       0.1246516      
0.0372543
> Cumulative Proportion   0.643290        0.8380941       0.9627457      
1.0000000
>
> Loadings:
>                         Comp.1  Comp.2  Comp.3  Comp.4
> weight          -0.371          0.907                           -0.201
> interoc         -0.486  -0.227  -0.840
> cwidth          -0.537  -0.349          0.466           -0.611
> clength         -0.582                          0.278   0.761
>
>                         Comp.1  Comp.2  Comp.3  Comp.4
> SS loadings             1.00            1.00            1.00           
1.00
> Proportion Var          0.25            0.25            0.25           
0.25
> Cumulative Var          0.25            0.50            0.75           
1.00
>
> Any guidance will be greatly appreciated!
>
> Salvatore A. Sidoti
> PhD Student
> The Ohio State University
> Behavioral Ecology
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Sidoti, Salvatore A.

2016-Nov-14 01:37 UTC

head link

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

Hi Jim,

Nice to see you again! First of all, apologies to all for bending the rules a
bit with respect to the mailing list. I know this is a list for R programming
specifically, and I have received some great advice in this regard in the past.
I just thought this was an interesting applied problem that would generate some
discussion about PCA in R.

Yes, that is an excellent question! Indeed, why not just volume? Since this is
still a work in progress and we have not published as of yet, I would rather not
be more specific about the type of animal at this time ;>}. Nonetheless, I
can say that the animals I study change "size" depending on their
feeding and hydration state. The abdomen in particular undergoes drastic size
changes. That being said, there are key anatomical features that remain fixed in
the adult.

Now, there *might* be a way to work volume into the PCA. Although volume is not
a reliable metric since the abdomen size is so changeable while the animal is
alive, but what about preserved specimens? I have many that have been marinating
in ethanol for months. Wouldn't the tissues have equilibrated by now?
Probably... I could measure volume by displacement or suspension, I suppose.

In the meantime, here's a few thoughts:

1) 	Use the contribution % (known as C% hereafter) of each variable on principle
components 1 and 2.

2) 	The total contribution of a variable that explains the variations retained
by PC1 an PC2 is calculated by:
	
	sum(C%1 * eigenvalue1, C%2 * eigenvalue2)

3) Scale() to mean-center the columns of the data set.

4) Use these total contributions as the weights of an arithmetic mean.

For example, we have an animal with the following data (mean-centered):
weight:	1.334
interoc:	-0.225
clength:	0.046
cwidth:	-0.847

The contributions of these variables on PC1 and PC2 are (% changed to
proportions):
weight:	0.556
interoc:	0.357
clength:	0.493
cwidth:	0.291

To calculate size:
1.334(0.556) - 0.225(0.357) + 0.046(0.493) - 0.847(0.291) = 0.43758
Then divide by the sum of the weights:
0.43758 / 1.697 = 0.257855 = "animal size"

This value can then be used to rank the animal according to its size for further
analysis...

Does this sound like a reasonable application of my PCA data?

Salvatore A. Sidoti
PhD Student
Behavioral Ecology

-----Original Message-----
From: Jim Lemon [mailto:drjimlemon at gmail.com] 
Sent: Sunday, November 13, 2016 3:53 PM
To: Sidoti, Salvatore A. <sidoti.23 at buckeyemail.osu.edu>; r-help
mailing list <r-help at r-project.org>
Subject: Re: [R] Principle Component Analysis: Ranking Animal Size Based On
Combined Metrics

Hi Salvatore,
If by "size" you mean volume, why not directly measure the volume of
your animals? They appear to be fairly small. Sometimes working out what the
critical value actually means can inform the way to measure it.

Jim


On Sun, Nov 13, 2016 at 4:46 PM, Sidoti, Salvatore A.
<sidoti.23 at buckeyemail.osu.edu> wrote:> Let's say I perform 4 measurements on an animal: three are linear
measurements in millimeters and the fourth is its weight in milligrams. So, we
have a data set with mixed units.
>
> Based on these four correlated measurements, I would like to obtain one
"score" or value that describes an individual animal's size. I
considered simply taking the geometric mean of these 4 measurements, and that
would give me a "score" - larger values would be for larger animals,
etc.
>
> However, this assumes that all 4 of these measurements contribute equally
to an animal's size. Of course, more than likely this is not the case. I
then performed a PCA to discover how much influence each variable had on the
overall data set. I was hoping to use this analysis to refine my original
approach.
>
> I honestly do not know how to apply the information from the PCA to this
particular problem...
>
> I do know, however, that principle components 1 and 2 capture enough of the
variation to reduce the number of dimensions down to 2 (see analysis below with
the original data set).
>
> Note: animal weights were ln() transformed to increase correlation with the
3 other variables.
>
> df <- data.frame(
>   weight = log(1000*c(0.0980, 0.0622, 0.0600, 0.1098, 0.0538, 0.0701,
0.1138, 0.0540, 0.0629, 0.0930,
>              0.0443, 0.1115, 0.1157, 0.0734, 0.0616, 0.0640, 0.0480,
0.1339, 0.0547, 0.0844,
>              0.0431, 0.0472, 0.0752, 0.0604, 0.0713, 0.0658, 0.0538,
0.0585, 0.0645, 0.0529,
>              0.0448, 0.0574, 0.0577, 0.0514, 0.0758, 0.0424, 0.0997,
0.0758, 0.0649, 0.0465,
>              0.0748, 0.0540, 0.0819, 0.0732, 0.0725, 0.0730, 0.0777,
0.0630, 0.0466)),
>   interoc = c(0.853, 0.865, 0.811, 0.840, 0.783, 0.868, 0.818, 0.847,
0.838, 0.799,
>               0.737, 0.788, 0.731, 0.777, 0.863, 0.877, 0.814, 0.926,
0.767, 0.746,
>               0.700, 0.768, 0.807, 0.753, 0.809, 0.788, 0.750, 0.815,
0.757, 0.737,
>               0.759, 0.863, 0.747, 0.838, 0.790, 0.676, 0.857, 0.728,
0.743, 0.870,
>               0.787, 0.773, 0.829, 0.785, 0.746, 0.834, 0.829, 0.750,
0.842),
>   cwidth = c(3.152, 3.046, 3.139, 3.181, 3.023, 3.452, 2.803, 3.050, 3.160,
3.186,
>              2.801, 2.862, 3.183, 2.770, 3.207, 3.188, 2.969, 3.033, 2.972,
3.291,
>              2.772, 2.875, 2.978, 3.094, 2.956, 2.966, 2.896, 3.149, 2.813,
2.935,
>              2.839, 3.152, 2.984, 3.037, 2.888, 2.723, 3.342, 2.562, 2.827,
2.909,
>              3.093, 2.990, 3.097, 2.751, 2.877, 2.901, 2.895, 2.721,
2.942),
>   clength = c(3.889, 3.733, 3.762, 4.059, 3.911, 3.822, 3.768, 3.814,
3.721, 3.794,
>               3.483, 3.863, 3.856, 3.457, 3.996, 3.876, 3.642, 3.978,
3.534, 3.967,
>               3.429, 3.518, 3.766, 3.755, 3.706, 3.785, 3.607, 3.922,
3.453, 3.589,
>               3.508, 3.861, 3.706, 3.593, 3.570, 3.341, 3.916, 3.336,
3.504, 3.688,
>               3.735, 3.724, 3.860, 3.405, 3.493, 3.586, 3.545, 3.443, 
> 3.640))
>
> pca_morpho <- princomp(df, cor = TRUE)
>
> summary(pca_morpho)
>
> Importance of components:
>                                         Comp.1          Comp.2         
Comp.3          Comp.4
> Standard deviation      1.604107        0.8827323       0.7061206      
0.3860275
> Proportion of Variance  0.643290        0.1948041       0.1246516      
0.0372543
> Cumulative Proportion   0.643290        0.8380941       0.9627457      
1.0000000
>
> Loadings:
>                         Comp.1  Comp.2  Comp.3  Comp.4
> weight          -0.371          0.907                           -0.201
> interoc         -0.486  -0.227  -0.840
> cwidth          -0.537  -0.349          0.466           -0.611
> clength         -0.582                          0.278   0.761
>
>                         Comp.1  Comp.2  Comp.3  Comp.4
> SS loadings             1.00            1.00            1.00           
1.00
> Proportion Var          0.25            0.25            0.25           
0.25
> Cumulative Var          0.25            0.50            0.75           
1.00
>
> Any guidance will be greatly appreciated!
>
> Salvatore A. Sidoti
> PhD Student
> The Ohio State University
> Behavioral Ecology
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Michael Friendly

2016-Nov-14 02:10 UTC

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[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

Salvatore,

I won't comment on whether to use log weight "to increase the 
correlation"  -- that depends on whether that makes sense, and whether 
the relationships with other variables is more nearly linear.

Try this with your pca of the correlation matrix:

biplot(pca_morpho)

You'll see that the  first component is defined largely by the
large correlations among length, interoc,and cwidth
while component2 is largely determined by weight.

You should probably do some reading on PCA or get some
statistical consulting at OSU to decide what to do with this.

  hope this helps

-Michael


On 11/13/16 12:46 AM, Sidoti, Salvatore A. wrote:> Let's say I perform 4 measurements on an animal: three are linear
measurements in millimeters and the fourth is its weight in milligrams. So, we
have a data set with mixed units.
>
> Based on these four correlated measurements, I would like to obtain one
"score" or value that describes an individual animal's size. I
considered simply taking the geometric mean of these 4 measurements, and that
would give me a "score" - larger values would be for larger animals,
etc.
>
> However, this assumes that all 4 of these measurements contribute equally
to an animal's size. Of course, more than likely this is not the case. I
then performed a PCA to discover how much influence each variable had on the
overall data set. I was hoping to use this analysis to refine my original
approach.
>
> I honestly do not know how to apply the information from the PCA to this
particular problem...
>
> I do know, however, that principle components 1 and 2 capture enough of the
variation to reduce the number of dimensions down to 2 (see analysis below with
the original data set).
>
> Note: animal weights were ln() transformed to increase correlation with the
3 other variables.
>
> df <- data.frame(
>   weight = log(1000*c(0.0980, 0.0622, 0.0600, 0.1098, 0.0538, 0.0701,
0.1138, 0.0540, 0.0629, 0.0930,
>              0.0443, 0.1115, 0.1157, 0.0734, 0.0616, 0.0640, 0.0480,
0.1339, 0.0547, 0.0844,
>              0.0431, 0.0472, 0.0752, 0.0604, 0.0713, 0.0658, 0.0538,
0.0585, 0.0645, 0.0529,
>              0.0448, 0.0574, 0.0577, 0.0514, 0.0758, 0.0424, 0.0997,
0.0758, 0.0649, 0.0465,
>              0.0748, 0.0540, 0.0819, 0.0732, 0.0725, 0.0730, 0.0777,
0.0630, 0.0466)),
>   interoc = c(0.853, 0.865, 0.811, 0.840, 0.783, 0.868, 0.818, 0.847,
0.838, 0.799,
>               0.737, 0.788, 0.731, 0.777, 0.863, 0.877, 0.814, 0.926,
0.767, 0.746,
>               0.700, 0.768, 0.807, 0.753, 0.809, 0.788, 0.750, 0.815,
0.757, 0.737,
>               0.759, 0.863, 0.747, 0.838, 0.790, 0.676, 0.857, 0.728,
0.743, 0.870,
>               0.787, 0.773, 0.829, 0.785, 0.746, 0.834, 0.829, 0.750,
0.842),
>   cwidth = c(3.152, 3.046, 3.139, 3.181, 3.023, 3.452, 2.803, 3.050, 3.160,
3.186,
>              2.801, 2.862, 3.183, 2.770, 3.207, 3.188, 2.969, 3.033, 2.972,
3.291,
>              2.772, 2.875, 2.978, 3.094, 2.956, 2.966, 2.896, 3.149, 2.813,
2.935,
>              2.839, 3.152, 2.984, 3.037, 2.888, 2.723, 3.342, 2.562, 2.827,
2.909,
>              3.093, 2.990, 3.097, 2.751, 2.877, 2.901, 2.895, 2.721,
2.942),
>   clength = c(3.889, 3.733, 3.762, 4.059, 3.911, 3.822, 3.768, 3.814,
3.721, 3.794,
>               3.483, 3.863, 3.856, 3.457, 3.996, 3.876, 3.642, 3.978,
3.534, 3.967,
>               3.429, 3.518, 3.766, 3.755, 3.706, 3.785, 3.607, 3.922,
3.453, 3.589,
>               3.508, 3.861, 3.706, 3.593, 3.570, 3.341, 3.916, 3.336,
3.504, 3.688,
>               3.735, 3.724, 3.860, 3.405, 3.493, 3.586, 3.545, 3.443,
3.640))
>
> pca_morpho <- princomp(df, cor = TRUE)
>
> summary(pca_morpho)
>
> Importance of components:
>                          		Comp.1    	Comp.2    	Comp.3    	Comp.4
> Standard deviation     	1.604107 	0.8827323 	0.7061206 	0.3860275
> Proportion of Variance 	0.643290 	0.1948041 	0.1246516 	0.0372543
> Cumulative Proportion  	0.643290 	0.8380941 	0.9627457 	1.0000000
>
> Loadings:
>         		Comp.1 	Comp.2	Comp.3 	Comp.4
> weight  	-0.371  	0.907        			-0.201
> interoc 	-0.486 	-0.227 	-0.840
> cwidth  	-0.537 	-0.349  	0.466 		-0.611
> clength 	-0.582         			0.278  	0.761
>
>                		Comp.1	Comp.2	Comp.3	Comp.4
> SS loadings      	1.00   		1.00   		1.00   		1.00
> Proportion Var   	0.25   		0.25   		0.25 		0.25
> Cumulative Var   	0.25   		0.50   		0.75   		1.00
>
> Any guidance will be greatly appreciated!
>
> Salvatore A. Sidoti
> PhD Student
> The Ohio State University
> Behavioral Ecology
>

R help - Nov 2016 - Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics

[R] Principle Component Analysis: Ranking Animal Size Based On Combined Metrics