# What to do when predictors are proportions that sum up to one?

I have a situation as the one described in the links below:

Interpreting proportions that sum to one as independent variables in linear regression

Predictor variables sum up to 1 but not necessarily correlated - is it a problem?

i.e., multiple collinearity due to having proportions that sum up to one as predictors (in my case, it's the proportion/percentage of people for mutually exclusive and collectively exhaustive age groups).

I feel the same discomfort expressed here:

https://statmodeling.stat.columbia.edu/2018/07/10/wants-model-proportion-given-predictors-sum-1/

Removing the constant is not an option since I am running an ordered logit regressions, where I read there's no constant:

https://www.statalist.org/forums/forum/general-stata-discussion/general/704001-exclude-constant-in-stata-generalized-ordered-logistic-regression

Is there an alternative to arbitrarily chose a group as reference category and omit the related variable from the regression? The point is: I'd like to use generalized ordered logistic regression, so to evaluate the "proportionality of odds" assumption for each variable. Clearly, in this way the selected model would change basing on the reference category I choose. How could I avoid such arbitrariness?

• You could look into using log-ratio transformation, see stats.stackexchange.com/questions/259208/… Dec 6, 2022 at 19:03
• Thank you. What I find interesting is the last row, expressing the difference between the last percentage and the sum of the previous ones. Unfortunately, such interpretation only holds for the last group: I'd need a similar interpretation for all groups. I understand, however, that there's no escape to the fact one has to reduce dimensionality by at least 1. At this point, maybe it's better to perform a PCA after that, at least if there's no hierarchy and I understand it well that PCA makes results independent from the chosen order. Dec 18, 2022 at 15:47