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Extracting PCA axes for further analysis

I analyze data on reed fields. The variables that I measured are the depth of water, the height of the reed, the density of the reed, etc. Since some of the variables are dependent on each other, I performed a PCA to reduce these variables to two PCA axes (N = 104).

To run the PCA, I used the vegan package in R. My data looks like this:

 row.names Waterpeil hoogte_max Som Leeftijd_riet PFD oppervlakte onderlaag_num afst_rand 1 1 5 2.5 51 0.15686274 1.616921 8.127192 2 24.154590 2 3 9 2.5 44 0.13636364 1.564643 9.023642 2 8.349288 3 4 0 2.5 84 0.30952381 1.352548 8.498775 2 26.226896 4 5 0 3.5 58 0.43103448 1.384183 9.301617 1 57.320000 5 6 40 2.5 52 0.42307692 1.361262 10.316058 1 45.470000 6 7 5 3.0 19 0.00000000 1.429287 9.927788 1 36.720000 7 9 0 2.5 64 0.28125000 1.355100 8.029911 2 19.560000 8 11 120 3.5 29 0.03448276 1.336117 11.147484 1 252.630000 9 14 0 2.0 27 0.07407407 1.847756 7.445060 2 1.864342 10 16 20 2.5 57 0.24561404 1.582308 8.425177 2 9.490196 11 17 5 3.0 54 0.01851852 1.348305 9.315008 2 15.960000 12 18 0 1.5 5 1.00000000 1.643657 8.063648 2 6.526300 13 21 0 2.0 18 0.05555556 1.394964 8.752185 2 37.576955 14 22 20 2.0 48 0.16666667 1.617045 8.911028 1 11.592383 15 25 0 2.5 71 0.42253521 1.749114 7.271499 2 6.572772 16 26 0 2.0 50 0.30000000 1.464582 7.349908 2 9.849276 17 27 5 2.5 61 0.34426229 1.511217 8.379012 2 14.082827 18 28 5 2.0 123 0.06504065 1.538188 8.271017 2 11.658142 19 29 100 3.0 75 0.44000000 1.896483 7.968603 1 9.071897 20 30 100 3.0 95 0.55789474 1.768147 8.367626 1 2.300783 21 32 0 3.0 74 0.45945946 1.458793 9.453464 2 57.210000 22 33 15 3.0 66 0.24242424 1.572704 7.620507 1 8.700000 23 34 5 3.0 83 0.38554217 1.436063 11.636262 1 50.613265 24 35 5 2.5 58 0.31034483 1.313440 9.370347 2 52.605041 25 36 20 2.5 91 0.28571429 1.544032 8.451961 1 9.713351 26 37 10 2.5 34 0.23529412 1.524725 9.348687 2 6.920026 27 38 20 2.5 48 0.41666667 1.584892 7.780915 1 11.302639 28 39 40 2.5 51 0.15686274 1.535552 6.994035 1 18.999423 29 40 35 2.5 48 0.45833333 1.460579 9.073331 1 12.869075 30 41 5 3.0 58 0.43103448 1.747669 7.628542 2 3.860225 31 42 25 2.5 36 0.52777778

I did this, this is the result for the first two axes:

 y<-rda(nestendca2) summary(y) PC1 PC2 Waterpeil 13.816422 -2.312641 hoogte_max 0.094747 -0.014497 Som 2.955029 10.812549 Leeftijd_riet 0.016476 0.019629 PFD 0.007361 -0.003386 oppervlakte 0.052943 0.039657

Now I want to realize these two axes in logistic regression, linking it to the success of breeding of a bird of prey that reproduces in these fields.

How can i do this?

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2 answers

If you are using the princomp package, you can extract such downloads as follows:

 PCA <- princomp(data,cor=T) PCA PCA$loadings Loadings <- as.data.frame(PCA$loadings[,1:2])

If you are using prcomp, you can do:

 PCA2 <- prcomp(data) Loadings <- as.data.frame(PCA2$rotation[,1:2])

If you use vegan:

 PCA3 <- rda(data) Loadings <- as.data.frame(PCA3$CA$v.eig[,1:2])
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Assuming you are using prcomp in R. Here is one way to do this

 pca <- prcomp(~ Murder + Rape + Assault, data = USArrests, scale = TRUE) (loadings <- pca$rotation) ## PC1 PC2 PC3 ## Murder -0.58260 0.53395 -0.61276 ## Rape -0.53938 -0.81798 -0.19994 ## Assault -0.60798 0.21402 0.76456 axes <- predict(pca, newdata = USArrests) head(axes, 4) ## PC1 PC2 PC3 ## Alabama -1.19803 0.83381 -0.162178 ## Alaska -2.30875 -1.52396 0.038336 ## Arizona -1.50333 -0.49830 0.878223 ## Arkansas -0.17599 0.32473 0.071112

Now you can use these new columns (axes) in your logistic regression, if you want. I will show you just an example using a simple linear model.

 dat <- cbind(USArrests, axes) lm(UrbanPop ~ PC1 + PC2, data = dat) ## Call: ## lm(formula = UrbanPop ~ PC1 + PC2, data = dat) ## Coefficients: ## (Intercept) PC1 PC2 ## 65.54 -2.58 -7.71
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