Articles | Volume 7, issue 3
Atmos. Meas. Tech., 7, 781–797, 2014
https://doi.org/10.5194/amt-7-781-2014
Atmos. Meas. Tech., 7, 781–797, 2014
https://doi.org/10.5194/amt-7-781-2014

Research article 27 Mar 2014

Research article | 27 Mar 2014

Methods for estimating uncertainty in factor analytic solutions

P. Paatero1, S. Eberly2, S. G. Brown3, and G. A. Norris4 P. Paatero et al.
  • 1University of Helsinki, Dept. of Physics, Helsinki, Finland
  • 2Geometric Tools, LLC, Redmond, Washington, USA
  • 3Sonoma Technology, Inc., Petaluma, California, USA
  • 4US EPA, Office of Research and Development, Research Triangle Park, North Carolina, USA

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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