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I have two main explanatory variables of interest in the model I use. It is only when I include them both that the coefficients are significant. The correlation between them is 0.98 and the vif-value is high, indicating collinearity. May this bias the results? I read somewhere that multicollinearity only inflates standard errors, which make p-values too large, and that it doesn’t bias coefficients. So it shouldn’t alter the interpretation of the coefficient unless they lose statistical significance.

Is this true? Do you think the model still could be valid despite high correlations?

My objective of the model is not to make predictions but to see how particularly one central factor, which I measure through two similar explanatory variables, affects the dependent variable.

Eric_B
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  • Doesn't alter the interpretation of the coefficients even if they "lose statistical significance". Your last sentence suggests you're not much interested in separating the effects of the two explanatory variables in any case. – Scortchi - Reinstate Monica Jun 23 '14 at 10:16
  • @Scortchi Ok, good to hear. But is there a risk that the high collinearity causes big changes in the parameter estimates, for instance that they reverse each other signs or something like that? – Eric_B Jun 23 '14 at 11:10
  • From my limited understanding, I thought collinearity does adversely impact interpretation of the coefficients. Take an extreme case, that of collinearity being 1. Then, how does model 1v1 - .4v2 compare with model .8v1 - .2v2 in terms of interpretation? – Theja Tulabandhula Jun 23 '14 at 11:19
  • Yes, the high variance of each individual coefficient estimate could cause it to be of the incorrect sign. Examine this by using the standard errors to form confidence intervals, which will be wider than if there were no collinearity - there's no additional problem of interpretation. "Fixes" for collinearity do bias the coefficients, but reduce their variance. Principal component regression might be particularly suited to this case - the first PC representing your "central factor". – Scortchi - Reinstate Monica Jun 23 '14 at 11:37

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