andrewcparnell
commented
4 years ago Hi jwschloemer,
The maths is exactly the same as the two isotope version. I don't know how mathematical you are, but our 2013 Environmetrics paper shows the maths for any number of isotopes. At a very basic level with say 2 sources and 3 isotopes, it's just:
iso_1 = p_1 s_11 + p_2 s_21 + e iso_2 = p_1 s_12 + p_2 s_22 + e iso_3 = p_1 s_13 + p_2 s_23 + e
Where iso are the data isotope values, p are the dietary proportions, and s_kj is the source value for isotope j on source k.
It's a bit more complicated than that because the above expression leads to an over-determined model so you make everything stochastic and it falls out fine.
Hope that helps a bit.
Andrew
I am running a three-tracer model where each sample has values from tracers one and two, but only occasional values for tracer 3. For example:
Sample Tracer 1 Tracer 2 Tracer 3 1 -21 -8 NA 2 -20 -8 -2 3 -19 -8 -1
The model is based on the standard SIMMR script. Despite inconsistent availability, the model is improved with the addition of tracer three. I gather that this is because the algorithm is run for each tracer independently, with proportions then being calculated for each tracer. I'm a bit lost in the maths on how the three tracers are then combined to provide an overall estimate of source contribution to the mixture.
Is there a clear explanation of this process?