What methods are there for reforming data so that the number of variables matches the number of degrees of freedom, in a way that does not favor or disfavor particular variables?
For example, if we are studying alloys made of different percentages of the same five elemental metals, and our data observations are the five percentage numbers, obviously the five variables total 100% so there are four degrees of freedom. If we just drop one of the five numbers (and remark that it’s calculable from the other four), the data still completely describe the physical reality, but in treating the data (analyzing, graphing, whatever) we have changed the emphasis on the one metal whose number we dropped relative to the other metals. If that metal percentage has a big impact on strength, say, then parameter estimates from a linear model of strength as a function of the other percentages do implicitly encode that impact, but looking at them, it’s hard to grasp. We’ve shifted our relative appreciation for that factor.
Are there data treatments that don’t have this effect?