1
$\begingroup$

In PCA, if we have ax1+bx2+c*x3 = y, say we get 2 principal components(d1,d2) out of x1,x2,x3. Can we know which of the x1,x2,x3 and in how much magnitude were used to create the d1 and d2? If not, how is PCA useful for determining which variables affect your outcome when all you get is a mishmash of original variables?

$\endgroup$
1
  • $\begingroup$ This link here might give a good example online.stat.psu.edu/stat505/lesson/11/11.4. In general PCA is used for creating informative (in the sense of variance of your data explained) low-dimensional representation of your original data were you are not so much interested in keeping your original data interpretation. $\endgroup$
    – Fiodor1234
    May 10, 2021 at 10:51

1 Answer 1

0
$\begingroup$

A common method for understanding how the PCs are related to the original variables is to calculate the correlation between the variables and the PC. It is important to use correlations rather than the coefficients that define the linear combinations to avoid scaling effects.

It can sometimes happen, however, that certain variables will have low correlations individually, but higher correlations in combinations with other variables. You can use the variable pairs heat map to understand not only how individual variables correlate with a PC, but also how sums and differences of standardized variables are correlated with a PC. In the graph shown below, the diagonal shows absolute correlations between the individual variables and the PC; the upper triangle shows absolute correlations between the differences $Z_i − Z_j$ and the PC; and the lower triangle shows absolute correlations between the sums $Z_i + Z_j$ and the PC.

enter image description here

Further details are given in Teaching Principal Components Using Correlations, Multivariate Behavioral Research Volume 52, 2017 - Issue 5.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.