# Binary logistic regression with compositional proportional predictors

I am running a binary logistic regression with compositional predictors that sum to 100% (demographic categories). I've looked at several postings about this, but can't find a good solution to my problem. Would dropping a single predictor be useful in cases where 0% of the data comes from that category? I.e., if my predictors are race, and I drop "Hispanic/Latino", the hispanic/latino rate in my data ranges from 0% to 6% in each of my cases, so in many/most cases the data is still correlated.

Would a transformation be appropriate here?

I do have the ability to calculate a (rough) number for each category, since I do have the total number of individuals in each case, but I am more interested in effect of the proportion of the racial categories on my independent variable.

I've found these, but they don't present a solution.

What regression model to use when independent variables are percentages to predict % outcome?

Proportions (compositions) in logistic regression

• I see explicit solutions in the first thread you reference, so could you please elaborate on what you might be looking for in addition to them?
– whuber
Jan 10 '17 at 17:02
• I'm sorry if it wasn't clear: for a majority of the cases, 5/7 of my categories are 0%. So I'm not certain if dropping a category with low explanatory power, or several categories even, would help: they would still sum to 100%, and be correlated due to the racial population of the city I'm researching. In the first case referenced, it could be expected that none of those categories (bone/muscle/fat) would be 0, which is not the case in my data. Jan 10 '17 at 17:09
• I'm afraid I don't follow: could you explain the distinctions between a "case," a "category," and a "predictor"?
– whuber
Jan 10 '17 at 17:12
• Each of my cases represents a group that is broken down by demographic data that I'm using as predictors for my binary outcome. In this case, mutually exclusive race categories that sum to 100%. Jan 10 '17 at 17:57

$z = log(\frac{x_i}{x_1}), i=2,..,D$ (number of categories) and then perform logistic regression on z.