CODEWITHSUNDEEP
rpcahierarchical
Rachel Orr
Rachel Orr

Reputation: 11

How can I use my principle component 1 (from PCA) as an axis in a hierchical regression analysis?

I am looking to use my PC1 from a PCA in a hierarchical regression analysis to account for additional variation in R. Is this possible?

I ran my pca with the code below in R


pca<- prcomp(my.data[,c(57:62)], center = TRUE,scale. = TRUE)
summary(pca)
str(pca)
fviz_eig(pca)
fviz_pca_ind(pca,
             col.ind = "cos2", # Color by the quality of representation
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE     # Avoid text overlapping
)

ggbiplot(pca)
print(pca)

#some results!
Rotation (n x k) = (4 x 4):
           PC1        PC2           PC3
EC   0.5389823 -0.4785188  0.0003197419
temp 0.4787782  0.3590390  0.7913858440
pH   0.5495125 -0.3839466 -0.2673991595
DO.  0.4222624  0.7033461 -0.5497326925
            PC4
EC    0.6931938
temp -0.1247834
pH   -0.6921840
DO.   0.1574569

Now I hope to use the PC1 as a variable in my models

Somthing like this m0<- lm(Rel.abund.rotifers~turb+chl.a+PC1,data=my.data)

Any help is very appreciated!

Upvotes: 1

Views: 90

Answers (1)

zephryl
zephryl

Reputation: 17069

Extract the component scores using pca$x, add them to your dataframe using cbind(), then run your model. Example using mtcars:

pca <- prcomp(mtcars[, 3:6])
mtcars2 <- cbind(mtcars, pca$x)
m0 <- lm(mpg ~ cyl + PC1, data = mtcars2)
summary(m0)

Call:
lm(formula = mpg ~ cyl + PC1, data = mtcars2)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.1424 -2.0289 -0.7483  1.3613  6.9373 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 27.99508    4.80433   5.827 2.56e-06 ***
cyl         -1.27749    0.77169  -1.655   0.1086    
PC1         -0.02275    0.01010  -2.251   0.0321 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.008 on 29 degrees of freedom
Multiple R-squared:  0.7669,    Adjusted R-squared:  0.7508 
F-statistic: 47.71 on 2 and 29 DF,  p-value: 6.742e-10

Upvotes: 1

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