Disentangling the effect of a ratio from the effects of the numerator & denominator in linear models

My question: What is the most appropriate way to analyse cases in which two variables and their ratio are all believed to influence some outcome? I would ideally like guidance in a regression framework, but am open to other approaches as well.

Background: In the fields of oceanography & limnology, the Redfield ratio is the ratio of nitrogen to phosphorus (or N:P) in water. This ratio is believed to have important implications for the biology of aquatic systems and so it is frequently used as an independent variable in a regression framework. The absolute values of the numerator and denominator (N & P) are believed to strongly influence these systems as well, distinct from their ratio.

However, in most analyses, the ratio is the only one of the three included as an independent variable; the numerator and denominator (N & P) are excluded because of worries about multicollinearity.

I believe this approach is flawed, and would like to know 1) if it's possible to construct a linear model that allows us to rigorously estimate the distinct effects of numerator, denominator & the ratio, and 2) if so, how to go about it.

• What is "some outcome" ? Is it a continuous variable or binomially scaled ? What is your linear model ?
– user10619
Aug 24, 2017 at 14:14
• @subhashc.davar A continuous variable. As for the model structure, that is part of my question above; how do we construct one in a meaningful & appropriate manner? The details don't matter a great deal here, I'm after some insight into the statistics/experimental design.
– mkt
Aug 29, 2017 at 11:04
• To me, postulating a correct model depends on logic and one should not apply a particular statistical model without valid reasons. Further ,I do not think that variables with absolute values and ratio led variables can be linearly combined without approprlate transformations/ rescaling etc.
– user10619
Aug 30, 2017 at 9:20