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Methods for estimating uncertainty in factor analytic solutions

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Paatero, P., Eberly, S., Brown, S. G., Norris, G. A.·2014·Atmospheric Measurement Techniques

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Abstract

Abstract. The EPA PMF (Environmental Protection Agency positive matrix factorization) version 5.0 and the underlying multilinear engine-executable ME-2 contain three methods for estimating uncertainty in factor analytic models: classical bootstrap (BS), displacement of factor elements (DISP), and bootstrap enhanced by displacement of factor elements (BS-DISP). The goal of these methods is to capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. It is shown that the three methods complement each other: depending on characteristics of the data set, one method may provide better results than the other two. Results are presented using synthetic data sets, including interpretation of diagnostics, and recommendations are given for parameters to report when documenting uncertainty estimates from EPA PMF or ME-2 applications.

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Research works printed but not linked: 24

  1. Abdollahi, H., Maeder, M., and Tauler, R.: Calculation and meaning of feasible band boundaries in multivariate curve resolution of a two-component system, Anal. Chem., 81, 2115–2122, 2009. · doi:10.1021/ac8022197
  2. Amato, F. and Hopke, P. K.: Source apportionment of the ambient PM2.5 across St. Louis using constrained positive matrix factorization, Atmos. Environ., 46, 329–337, 2012. · DOI
  3. Amato, F., Pandolfi, M., Escrig, A., Querol, X., Alastuey, A., Pey, J., Perez, N., and Hopke, P. K.: Quantifying road dust resuspension in urban environment by multilinear engine: a comparison with PMF2, Atmos. Environ., 43, 2770–2780, 2009. · DOI · Paper page
  4. Anderson, T. W.: An Introduction to Multivariate Statistical Analysis, 2nd Edn., Wiley, New York, 1984.
  5. Brown, S. G., Lee, T., Norris, G. A., Roberts, P. T., J. L. Collett, Jr., Paatero, P., and Worsnop, D. R.: Receptor modeling of near-roadway aerosol mass spectrometer data in Las Vegas, Nevada, with EPA PMF, Atmos. Chem. Phys., 12, 309–325, https://doi.org/10.5194/acp-12-309-2012, 2012. · DOI
  6. Brown, S. G., Paatero, P., Eberly, S., and Norris, G.: Methods for estimating uncertainty in PMF solutions: examples using ambient air and water quality data, in preparation, 2014. · DOI · Paper page
  7. Eberly, S. I. and Reff, A.: Evaluation of rotational control in multi-linear engine based receptor modeling approaches. Poster presented at the American Association for Aerosol Research Conference, Reno, NV, 24–28 September, 2007.
  8. Efron, B. and Tibshirani, R. J.: An introduction to the bootstrap, Chapman & Hall, New York, 1993. · DOI · Paper page
  9. Engel-Cox, J. A. and Weber S. A.: Compilation and assessment of recent positive matrix factorization and UNMIX receptor model studies on fine particulate matter source apportionment for the eastern United States, J. Air Waste Manage. Assoc., 57, 1307–1316, 2007. · doi:10.3155/1047-3289.57.11.1307
  10. Gemperline, P. J.: Computation of the range of feasible solutions in self-modeling curve resolution algorithms, Anal. Chem., 71, 5398–5404, 1999. · doi:10.1021/ac990648y
  11. Hedberg, E., Gidhagen, L., and Johansson, C.: Source contributions to PM10 and arsenic concentrations in Central Chile using positive matrix factorization, Atmos. Environ., }{39, 549–561, 2005. · doi:10.1016/j.atmosenv.2004.11.001
  12. Henry, R. C.: Current factor analysis models are ill-posed, Atmos. Environ., 21, 1815–1820, 1987. · DOI
  13. Henry, R. C.: History and fundamentals of multivariate air quality receptor models, Chemometrics and Intelligent Laboratory Systems, 37, 525–530, 1997. · doi:10.1016/s0169-7439(96)00048-2
  14. Jaumot, J. and Tauler, R.: MCR-BANDS: a user friendly MATLAB program for the evaluation of rotation ambiguities in Multivariate Curve Resolution. Chemometrics and Intelligent Laboratory Systems, 103, 96–107, 2010. · doi:10.1016/j.chemolab.2010.05.020
  15. Ke, L., Liu, W., Want, Y., Russell, A. G., Edgerton, E. S., and Zheng, M.: Comparison of PM2.5 source apportionment using positive matrix factorization and molecular marker-based chemical mass balance, Sci. Total Environ., 394, 290–302, 2008. · doi:10.1016/j.scitotenv.2008.01.030
  16. Kim, E. and Hopke, P. K.: Source identifications of airborne fine particles using positive matrix factorization and U.S. Environmental Protection Agency positive matrix factorization, J. Air Waste Manage. Assoc., }{57, 811–819, 2007. · DOI
  17. Paatero, P.: Least squares formulation of robust non-negative factor analysis, Chemometrics and Intelligent Laboratory Systems, 37, 23–35, 1997. · DOI · Paper page
  18. Paatero, P. and Hopke, P. K.: Rotational Tools for Factor Analytic Models, J. Chemometrics, 23, 91–100, 2009. · DOI
  19. Paatero, P. and Tapper, U.: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values, Environmetrics, 5, 111–126, 1994. · DOI · Paper page
  20. Paatero, P., Hopke, P. K., Song, X. H., and Ramadan, Z.: Understanding and controlling rotations in factor analytic models, Chemometrics an Intelligent Laboratory Systems, 60, 253–264, 2002. · DOI · Paper page
  21. Poirot, R. L., Wishinski, P. R., Hopke, P. K., and Polissar, A. V.: Comparative application of multiple receptor methods to identify aerosol sources in northern Vermont, Environ. Sci. Technol., 35, 4622–4636, 2001. · doi:10.1021/es010588p
  22. Reff, A., Eberly, S. I., and Bhave, P. V.: Receptor modeling of ambient particulate matter data using positive matrix factorization: review of existing methods, J. Air Waste Manage. Assoc., 57, 146–154, 2007. · DOI · Paper page
  23. Tauler, R.: Calculation of maximum and minimum band boundaries of feasible solutions for species profiles obtained by multivariate curve resolution, J. Chemometrics, 15, 627–646, 2001. · doi:10.1002/cem.654
  24. Ulbrich, I. M., Canagaratna, M. R., Zhang, Q., Worsnop, D. R., and Jimenez, J. L.: Interpretation of organic components from Positive Matrix Factorization of aerosol mass spectrometric data, Atmos. Chem. Phys., 9, 2891–2918, https://doi.org/10.5194/acp-9-2891-2009, 2009. · DOI · Paper page

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Metadata

Authors
Paatero, P., Eberly, S., Brown, S. G., & Norris, G. A.
Venue
Atmospheric Measurement Techniques
Published
2014-03-27
Volume
7
Issue
3
Pages
781-797
ISSN
  • 1867-1381 (ISSN-L)
  • 1867-8548
OpenAlex
W2026802068
Cited by
571
References
0
FWCI
19.64
Type
journal article
Language
en
Open access
gold

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CoChat. (2026). Citation check: Methods for estimating uncertainty in factor analytic solutions. https://app.cochat.ai/papers/10.5194/amt-7-781-2014
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Paatero, P., Eberly, S., Brown, S. G., & Norris, G. A. (2014). Methods for estimating uncertainty in factor analytic solutions. Atmospheric Measurement Techniques. https://doi.org/10.5194/amt-7-781-2014

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