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Re: st: Problem with proportions as explanatory variables in panel data regression

From   Maarten buis <>
Subject   Re: st: Problem with proportions as explanatory variables in panel data regression
Date   Tue, 14 Dec 2010 10:04:45 +0000 (GMT)

--- On Tue, 14/12/10, F. Javier Sese wrote:
> I am modeling the dependent variable (Y) as a function of three main  
> explanatory variables (X1-X3) and a vector of control variables (Z).
> X1-X3 are proportions: they range between zero and one and add up to  
> one for each observation (X1 + X2 + X3 = 1). Given the nature of  
> X1-X3, there is a high negative correlation between them (an increase  
> in one variable leads to a decrease in the other two), which gives  
> rise to a potential collinearity problem that may be causing some  
> unexpected results in the signs and statistical significance of the  
> coefficients. In my dataset, X1 and X2 have a correlation coefficient  
> of -0.81; X1 and X3 of -0.42; X2 and X3 of -0.19.
> Given that the main focus of my research is on understanding the  
> impact of these three variables on Y, I would really appreciate it if  
> someone can provide me with some guidance on how to obtain reliable  
> parameter estimates for the coefficients b1-b3.

Multicolinearity is in it self never a problem: it leads to a reduction
in the power of our tests, but that is just an accurate representation
of the amount of information available in the data.

The real problem with your data is conceptual. We usually interpret
coefficients as a change in y for a unit change in x while keeping all
else constant. How can you change one proportion while keeping the 
others constant? You can't. You can find a discussion of this problem
and possible solutions in chapter 12 of J. Aitchison (2003 [1986])
"The Statistical Analysis of Compositional Data". Caldwell, NJ: The
Blackburn Press.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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