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I have a number of correlated independent variables (4) that I need to include in an OLS regression. Thus, I have problems with multicollinearity. The problem is that I cannot drop any of the variables because my research question is to determine which of these four predictors that matters the most.

I want to know which of four parents's educational level matters the most for a specific outcome among married couples. I include information on both the wife and the husband's parents' level of education.

  • one variable measures the wife's mother educational attainment (variable 1)
  • one variable measures the wife's fathers educational attainment (variable 2)
  • One variable measures the husband's mother educational attainment (variable3)
  • one variable measures the husband's fathers educational attainment (variable 4)

The correlation matrix looks like this (The variables are numbered as above)

enter image description here

To make things even worse, I also included the wife and the husband's own educational level. However, these are only included as control variables so I guess it is less of a problem.

So far I solve the problem of multicollinearity by including 4x4 dummy variables. These are the results:

enter image description here

The first digit of the labels indicates the value on variable 1, the second digit the value of variable 2, and so on. So, 1111 = all four parents are having university degree.

So to my two questions:

1) is this a correct/satisfying solution to the problem with multicollinearity? Or should I use another statistical method to answer the question of which variable matters the most?

2) I make two conclusion based on these results. First, for each additional parent with higher education, the higher we estimate Y. Second, the wife's and husband's mothers education has a greater impact than their fathers' education level. The mothers education matters more than the fathers education. Are these conclusions correct?

A long and complicated question. Sorry about that. Hope you have the energy to answer.

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    $\begingroup$ You have flattened out the 2 by 2 by 2 by 2 design into a single variable with 15 levels. Why not use the four binary predictors and their interactions and see if that is easier to interpret. Sometimes it is, sometimes it is not and your way works better. $\endgroup$
    – mdewey
    Commented Dec 6, 2016 at 12:33

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I don't see how you have "solve[d] the problem with multicollinearity" with your chart, and it's not clear that you can determine "which of these four predictors matters the most."

Your chart shows that each parent/in-law's university degree adds about 3 units to your outcome variable. I don't see from your chart alone that any particular parent/in-law matters more. A linear model with interactions would be needed to document any significant differences among the different combinations of educational levels that you show in your chart, in any event. So you will be stuck with collinearity and its associated difficulties with determining which predictor "matters the most."

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