Selecting an Appropriate Multivariate Source Apportionment Model Result

Two easily available multivariate source apportionment models, Unmix and positive matrix factorization (PMF), often produce nearly the same source apportionment. However, this paper gives two examples in which this is not the case: a simulated air pollution data set of 8 species and 200 samples and a water quality data set of 32 PCB congeners and 106 sediment core samples from Sheboygan River Inner Harbor, WI. In the first case, a basic form of PMF fails primarily because the source compositions do not have any species with zero or near zero concentrations. Unmix produces source compositions and contributions that are much closer to the true values. A version of PMF with an adjustable parameter also gives good results. In the second case, each model found 5 sources for the Sheboygan PCB sediment data. PMF determined sources compositions were consistent with the original 50/50% Aroclor 1248/1254 mixture, a previously determined prominent dechlorination profile (processes H' + M), and three other partially dechlorinated profiles. The Unmix determined source compositions were not as successful as the Unmix results depended heavily on just three data points. Source apportionment results favor Unmix when edges in the data are well-defined and PMF when several zeros are present in the loading and score matrices. Since both models are seen to have potential weaknesses, both should be applied in all cases. If the two methods do not produce similar results the methods given in the paper can be used to select the model result most likely to be closest to the truth.