How to fit a linear regression model with two principal components in R?
linear-regression, pca, r
Solution
Answer: you don't want pc$rotation, it's the rotation matrix and not the matrix of rotated values (scores).
Make up some data:
x1 = runif(100)
x2 = runif(100)
y = rnorm(2+3*x1+4*x2)
d = cbind(x1,x2)
pc = prcomp(d)
dim(pc$rotation)
## [1] 2 2
Oops. The "x" component is what we want. From ?prcomp:
x: if ‘retx’ is true the value of the rotated data (the centred (and scaled if requested) data multiplied by the ‘rotation' matrix) is returned.
dim(pc$x)
## [1] 100 2
lm(y~pc$x[,1]+pc$x[,2])
##
## Call:
## lm(formula = y ~ pc$x[, 1] + pc$x[, 2])
## Coefficients:
## (Intercept) pc$x[, 1] pc$x[, 2]
## 0.04942 0.14272 -0.13557
Problem
Let's say I have a data matrix d ``` pc = prcomp(d) # pc1 and pc2 are the principal components pc1 = pc$rotation[,1] pc2 = pc$rotation[,2] ``` Then this should fit the linear regression model right? ``` r = lm(y ~ pc1+pc2) ``` But then I get this error : ``` Errormodel.frame.default(formula = y ~ pc1+pc2, drop.unused.levels = TRUE) : unequal dimensions('pc1') ``` I guess there a packages out there who do this automatically, but this should work too?