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An in-depth investigation of the influence of sample size on PCA-MLR, PMF, and FA-NNC source apportionment results

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Abstract

The mechanism by which parameters influence the source apportionment results of receptor models is not well understood. Three mature receptor models, namely, principal component analysis-multiple linear regression (PCA-MLR), positive matrix factorization (PMF) and factor analysis with nonnegative constraints (FA-NNC), were comparatively employed for source apportionment of 16 polycyclic aromatic hydrocarbons in 30 street dust samples. The results indicated that the FA-NNC and PMF models produced results with a higher degree of similarity than the results obtained with the PCA-MLR model. Moreover, when the sample size was gradually decreased, similar source profiles were extracted that were consistent with results obtained from all samples. However, the overall contribution rates were not as stable as the source profiles. The PCA-MLR results remained the most stable in both aspects. FA-NNC and PMF performed better in regards to the stability of contribution rates and source profiles, respectively. Improvements in the goodness of fit of overall and individual pollutants were always accompanied by a decrease in the relevance among the variables, indicating that while the model simulation effect was improved, the credibility of the results decreased. Thus, finding an appropriate number of sample size is more appropriate than simply involving too many samples in source apportionment models.

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Acknowledgements

This work is supported by the National Key Research and Development Program [2016YFA0602304], the Fund for the State Key Program of National Natural Science of China [Grant number 41530635], the Innovative Research Group of the National Natural Science Foundation of China [Number 51721093], and the Interdisciplinary Research Funds of Beijing Normal University.

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  1. State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing, 100875, China

    Jiashen Feng & Yingxia Li

  2. College of Resources, Environment and Planning, Dezhou University, Dezhou, 253023, China

    Ningning Song

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  1. Jiashen Feng
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JF did the methodology, software, formal analysis, visualization and writing—original Draft part of this research. NS did the conceptualization, investigation, validation, data curation part of this research. YL did the supervision, project administration, funding acquisition, writing—review & editing part of this research.

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Correspondence to Yingxia Li.

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Feng, J., Song, N. & Li, Y. An in-depth investigation of the influence of sample size on PCA-MLR, PMF, and FA-NNC source apportionment results. Environ Geochem Health 45, 5841–5855 (2023). https://doi.org/10.1007/s10653-023-01598-5

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