1
$\begingroup$

I have performed correlation analysis between y and seven different variables (x1,x2,x3,x4,x5,x6,x7). In some cases, result shows zero order correlation is positive and partial correlation is negative (for ex. y & x3). How can I explain this result? My results are:

control variables----------zero order corr (partial corr) between y & x1,x2.....x7

x2,x3,x4,x5,x6,x7----------y & x1 = 0.88 (0.41)

x1,x3,x4,x5,x6,x7----------y & x2 = 0.85 (0.08*)

x1,x2,x4,x5,x6,x7----------y & x3 = 0.77 (-0.19)

x1,x2,x3,x5,x6,x7----------y & x4 = 0.44 (0.23)

x1,x2,x3,x4,x6,x7----------y & x5 = 0.38 (-0.02*)

x1,x2,x3,x4,x5,x7----------y & x6 = -0.23 (-0.13)

x1,x2,x3,x4,x5,x6----------y & x7 = -0.57 (-0.19)

  • indicates insignificant partial correlation.

Thank you.

$\endgroup$
2
$\begingroup$

Let me use your $y$ and $x_3$ values. If you look only at the direct effect of $x_3$ on $y$, you will see a strong positive correlation. However, this ignores the other variables that may/may-not be influencing $y$.

If you account for the other variables, you have to account for the influence those variables have on $y$ and on $x_3$. In this case, you see that $x_3$ actually has a negative relationship WHEN the effect of the other variables has been "partialled" out. Conceptually, if you take the residuals from predicting $y$ form everything by $x_3$ and the residuals from predicting $x_3$ with everything (but $y$, of course), these residuals have a negative correlation.

One additional way to think about this is from a causal perspective (so extreme caution must be taken in presenting such an interpretation). $x_3$ may have some influence on the other variables (often called multicollinearity in this context). From the causal perspective, this means if you change $x_3$, you change the other variables, too. Now, when you model the TOTAL effects from $x_3$ on $y$, you have to account for the direct effect (which appears to be negative) and the indirect effect of $x_3$ influencing the other variables which in turn influence $y$. When you combine the negative direct impact with the indirect effects, you end up with an overall "positive" impact.

Hope this helps.

$\endgroup$
  • $\begingroup$ Hi Gregg, It helps a lot. But still I have confusion. As you explained x3 may have some influence on the other variables (often called multicollinearity in this context). So correlation between x1 & x3 is 0.79, x2 & x3 is 0.94, x4 & x3 is 0.36, x5 & x3 is 0.32, x6 & x3 is -0.40 and x7 & x3 is -0.66. Basically these x1,x2....x7 are climatic variables which shows impact on evaporation (y). If I explain direct correlation, climatic variable x3 have large impact on evaporation, on the others hand partial correlation shows x3 have very low impact on evaporation. Please throw some lights. $\endgroup$ – SONY Apr 3 '18 at 6:49
  • $\begingroup$ Think of it this way: x3 impacts BOTH evaporation AND the other variables affecting evaporation. The direct effect from x3 may be small, but if you aggregate the indirect effects from x3 to x_i to y, you obtain the larger impact you see if you were to examine just x3 & y. $\endgroup$ – Gregg H Apr 3 '18 at 13:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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