Hi @kendalynnm - this PR (i) cleans up the code so it's more robust as a base to go forward, but more importantly (ii) changes the von Fischer and Hedin (2002) Equation 11 to correct for what I think are two mistakes:
Equation 11 computes n{t} / m{t} (a fraction) and then adds it to AP{p} (a percentage; see Appendix A). This makes no sense. They must have left out a multiply-by-100 on that first term.
But why are we even adding AP{p} anyway? I see that comes from the rearrangement of Equation 7, and I get that in theory it's correcting for the isotopic mix of P...but in the first part of the equation (bullet above) we just computed AP{t} (per Appendix A definition). I'm happy to be corrected, but don't see how this is right.
The model fit now looks better:
Note that the model passes exactly through the first timepoint. That's because that point is taken as t=0, so the various P and k values cancel out, producing the same observed value (AP{0}) every time.
This was really bugging me :)
Hi @kendalynnm - this PR (i) cleans up the code so it's more robust as a base to go forward, but more importantly (ii) changes the von Fischer and Hedin (2002) Equation 11 to correct for what I think are two mistakes:
The model fit now looks better:
Note that the model passes exactly through the first timepoint. That's because that point is taken as t=0, so the various P and k values cancel out, producing the same observed value (AP{0}) every time.