Question

Ethnicity principal component Analysis -

We know that black has 2 PCs and white has 4 PCs. How can we analyze the relationship with the outcome Y?

(e.g. Y = a*PC1 + b*PC2 for black. and Y = c*PC1+ d*PC2 + e*PC3 + f*PC4 for white. Is it correct?)

Only professional in Biology/Genetic to answer. Thanks! #Biostatistics

Answer 1

For principal component Analysis, we sum components in order of matrix. That is depending upon the variables use while listing the principal components of blacks and whites.

For 2 PCs, if we have one variable x1,t (1 for original and t for lagged), we use

PC_1,t = P’₁X_t = p₁₁x_1,t

PC_2,t = P’₂X_t = p₂₁x_2,t

Y component for both PC = PC_1,t + PC_2,t = p₁₁x_1,t + p₂₁x_2,t

Here we can take p₂₁ as PC2 and p₁₁ as PC1. The variables x_2,t as ‘b’ and x_1,t as ‘a’, then we get the equation

Y = aPC1 + bPC2

That is also same for 4 PCs of white and collective them add for equation Y as cPC1+ dPC2 + ePC3 + fPC4.