Effects of collinearity, unknown source and removed factors on the NCPCRCMB receptor model solution

Traditional chemical mass balance (CMB) model is sensitive to collinearity problem among source profiles, which may result in unreliable information. A Nonnegative Constrained Principal Component Regression Chemical Mass Balance (NCPCRCMB) model was developed in our previous work to solve the collinearity problem for source apportionment. In this work, the effects of both source collinearity and presence of unknown source on NCPCRCMB model were investigated, through synthetic datasets with different degrees of collinearity among source profiles and different proportions of unknown source (the ratio of unknown source contribution to the total contribution of the known sources). The results suggest that, compared with USEPA CMB8.2, the NCPCRCMB model could obtain more stable outcomes, even if when dealing with the datasets with strong collinearity problem. NCPCRCMB model can tolerate high levels of both source collinearity degrees and unknown source proportions. When collinearity was very high and contributions of two collinear sources were very different, the results of NCPCRCMB might not be satisfactory. In addition, a method to determine the number of removed factors (a pivotal step for NCPCRCMB model), was proposed and validated by synthetic datasets as well as an ambient dataset from Kaifeng, China. The results of both synthetic datasets and ambient dataset indicate that investigating source profiles weighted by Initial Effective Variance could be more reasonable when determining the number of removed factors for NCPCRCMB model.