# In nutritional substitution analysis, why is nutrient intake modeled as a percentage when there are only two intakes?

I saw the modeling method of nutritional substitution analysis in the following article. Substitution analysis in nutritional epidemiology: proceed with caution

In short, you can do the following modeling. Here, α1 means the effect size of each serving of A replacing B.

f(Y)~α1×A＋α2×B＋α3×(A＋B＋C)

My question is, if there is no C in the model, that is, there are only two intakes (when they replace each other), does this method work? f(Y)~α1×A＋α3×(A＋B)

Another paper used percentages. It explored the substitution of tea and coffee. Coffee or Tea? A prospective cohort study on the associations of coffee and tea intake with overall and cause-specific mortality in men versus women

The modeling is f(Y)~α1× tea /(tea＋coffee)＋α3× (tea＋coffee). That is, α1 is the percentage of tea intake in the total intake of tea and coffee.

The paper claims that the reason for using percentages instead of continuous values ​​is because tea and coffee intake are nonlinear, not the traditional negative linear correlation.

Standard substitution analyzes assume a linear relationship between the exposure variables and disease risk/mortality [18], so that the effect of substituting equal amounts, e.g., replacing one cup of tea with one cup of coffee, can be estimated. Since the associations with coffee and tea were significantly nonlinear (see “Results”), the approach used here was by calculating the percentage tea of ​​the total cups of coffee and tea consumed per day. This variable was categorized and used in multivariate analyses, while additionally controlling for total coffee and tea intake.

Here I don’t quite understand, if the model with only two intakes is also valid, what is the difference between direct modeling and percentages. Thank you.