The accuracy of two- and three-way positive matrix factorization models: Applying simulated multisite data sets

<div><p>The application of three-way data sets (combined multisite data sets) for source apportionment has become common, but its influence on the performance of receptor modeling techniques has not yet been explored systematically. To study the influence of site-to-site correlations of source contributions and the spatial variability of source profiles on two- and three-way positive matrix factorization (PMF), simulated three-way data sets were constructed and modeled by different applications of PMF (PMF2 for each site individually, PMF2 for data sets combining all sites together, and PMF3 for all sites). In addition, the performance of PMF was evaluated under conditions of collinearity and different source categories at two sites. The results indicated that if the sites were contributed by sources with identical profiles, the site-to-site correlations of source contributions would not influence the PMF2, and the three-way blocks could be used by PMF2. However, the PMF2 using three-way data sets was sensitive to the spatial variability of source profiles. For the three-way model, PMF3 could perform well only when all of the sources exhibited strong site-to-site associations among all sites, and at the same time, the spatial variability of source profiles were sufficiently small. It might due to the algorithm that, for each source, PMF3 produces the same source profile and the same temporal variation in daily contributions among all sites. </p><p></p><p><i>Implications:</i> The application of multisite data sets for source apportionment has become common. However, limited work investigated the accuracy of two- and three-way PMFs when using multisite data sets. If the application of PMFs using multisite data sets were not appropriate, the results would be unreasonable. The unreasonable results would supply confused information for PM control strategies. In this work, simulated multisite data sets were modeled by different applications of PMFs. The effort to assess and compare the performance of two- and three-way PMFs using multisite data sets is very limited. The findings could provide information for multisite source apportionment.</p><p></p><p></p></div