Assessing positive matrix factorization model fit: a new method to estimate uncertainty and bias in factor contributions at the daily time scale

A Positive Matrix Factorization receptor model for aerosol pollution source apportionment was fit to a synthetic dataset simulating one year of daily measurements of ambient PM2.5 concentrations, comprised of 39 chemical species from nine pollutant sources. A novel method was developed to estimate model fit uncertainty and bias at the daily time scale, as related to factor contributions. A balanced bootstrap is used to create replicate datasets, with the same model then fit to the data. Neural networks are trained to classify factors based upon chemical profiles, as opposed to correlating contribution time series, and this classification is used to align factor orderings across results associated with the replicate datasets. Factor contribution uncertainty is assessed from the distribution of results associated with each factor. Comparing modeled factors with input factors used to create the synthetic data assesses bias. The results indicate that variability in factor contribution estimates does not necessarily encompass model error: contribution estimates can have small associated variability yet also be very biased. These results are likely dependent on characteristics of the data.