I've been added to a group project and I can't follow the reasoning, and this is my first time working with PCA. For an example let's say the study is on how feral cats impact smaller mammals (rats, mice, rabbits, and moles) across different setting factors (elevation, temperature, city (yes or no, 1 or 0), farm land (yes or no, 1 or 0), and small town (yes or no, 1 or 0)). The data table would look something like this...
Site / Cat / Rat / Mouse / Rabbit / Mole / Elev(m) / Temp(F) / City / Farmland / Smalltown
1 / 3 / 4 / 3 / 5 / 3 / 0 / 50 / 0 / 1 / 0
2 / 2 / 5 / 3 / 1 / 2 / 80 / 56 / 0 / 0 / 1
3 / 5 / 1 / 2 / 1 / 3 / 13 / 78 / 1 / 0 / 0
4 / 0 / 8 / 4 / 3 / 1 / 23 / 40 / 0 / 0 / 1
5 / 1 / 2 / 0 / 8 / 3 / 7 / 69 / 0 / 1 / 0
What they did was a PCA test only on Rat, Mouse, Rabbit, and Mole. (These are made up results)
pca_smallmam <- prcomp(data[c(3:6)], center = TRUE, scale. = TRUE)
. PC1 PC2 PC3 PC4
Rat 0.4 / 0.2 / ... / ...
Mouse 0.3 / 0.6 / ... / ...
Rabbit 0.2 / 0.7 / ... / ...
Mole 0.1 / 0.75/ ... / ...
Then for each site they multiplied the PC1 result for each small mammal to the original number counted from the table to create a "small mammal number" column
Site 1 Small Mammal Number = (4x0.4) + (3x0.3) + (5x0.2) + (3x0.1) = 3.8
Site 2 Small Mammal Number = (5x0.4) + (3x0.3) + (1x0.2) + (2x0.1) = 3.3 etc...
Site / Cat / SmallMammal / Elev(m) / Temp(F) / City / Farmland / Smalltown
1 / 3 / 3.8 / 0 / 50 / 0 / 1 / 0
2 / 2 / 3.3 / 80 / 56 / 0 / 0 / 1
3 / 5 / ... / 13 / 78 / 1 / 0 / 0
4 / 0 / ... / 23 / 40 / 0 / 0 / 1
5 / 1 / ... / 7 / 69 / 0 / 1 / 0
Going forward they used this SmallMammal number for a quantile regression model and an AIC test with the whole data to determine if cats and any of the different setting factors impact the small mammal community.
Again, I am new to PCA so maybe this is completely logical, but I don't think this is what PCA tests are used for? When I asked my partners to explain why they did this all I received was a "because". Is someone able to give more details on if this is the proper use of a PCA test?
Thank you!
I've tried researching PCAs and seeing if I'm misunderstanding their use.