1

I have 5 numerical variables (same units) (A, B, C, D, E and F) for N=13 countries.

We could say I combine the variables into a composite variable called A. The formula is : A = (B + C + D + E + F) divided by 5.

I want to know which variable between (B, C, D, E or F) is the "most important", I mean which one contributes the most in explaining A. I am asking that question because as we can remark the variable "A" is strongly related to the 5 other variables. To answer my question, I have planned to calculate the squared Pearson or Spearman semi-partial correlations. Do you agree ? If not, what would you do ?

In my opinion, I can combine the variables into a composite variable. There is a downside to this approach in that each of the five variables has measurement error. Thus, the composite includes the combined measurement error for all five variables. Does this perturb the use of the squared semi-partial correlation ?

By the way another problem is that the same variable appears on both sides of the equation, so we are correlating a variable with a composite variable that contains the same variable. This will inflate the semi-partial correlation ?

varin sacha
  • 753
  • 2
  • 8
  • 18
  • Why is it necessary to sum the variables? You likely could do better--perhaps much better--by taking a suitable linear combination of them. This approach would amount to *regressing* $A$ against the others. The theory of multiple (least squares) regression explains why it is not generally meaningful to assign "importance" to individual variables unless they are mutually orthogonal. BTW, you haven't exhibited any equation with the same variable on both sides, so what is that last paragraph trying to ask? – whuber Nov 10 '17 at 22:17
  • Hi Whuber, thanks for your response. Because I have 5 scores which adding/summing together and dividing by 5 composed a final score. So, adding the variables and dividing by 5 is necessary to obtain the final score for each of the 13 countries. You are right with my last paragraph. So what to do? Trying to fit a linear regression? – varin sacha Nov 10 '17 at 23:23

0 Answers0