Hi,

It's certainly a problem that is not easy to solve. You might find some inspiration from an article where different solutions for this problem are described including your imputation try. Take a look at the attached article, and try the method displayed in Box 1. I had some success in former times, but then my problem was smaller....

Wish you good luck!

Marcel

Often in environmental sampling one faces the issue that concentration data is lost due to difficulties with sampling or chemical analysis. The most rigorous way to handle missing data is to exclude the entire sample record. As in your case, that rigorous procedure causes the total number of samples to be too small for statistical data analyses. I recommend to use Positive Matrix Factorization (PMF) for your problem. PMF takes the uncertainties (of each chemical compound in each sample) in addition to concentrations as input and a user-defined number of sources (factors). You can download it from US EPA (https://www.epa.gov/air-research/positive-matrix-factorization-model-environmental-data-analyses). The correct procedure for handling missing data (no matter if random or systematic) in PMF analysis is described in Brown et al. (2015) [Brown, S. G., Eberly, S., Paatero, P., Norris, G. A. 2015. Methods for estimating uncertainty in PMF solutions: Examples with ambient air and water quality data and guidance on reporting PMF results, Sci. Total Environ. 518-519, 626–635]. It is recommended to use the median concentration of the given chemical compound (Hg) together with an uncertainty of four times the median. According to Brown et al. (2015), the scaled residuals in the PMF solution for the data points corresponding to the replaced missing values should be inspected to ensure that they are clearly less than one. If not, the PMF analysis should be repeated so that uncertainties of missing values are increased sufficiently. If that still doesn't work it might be better to exclude the respective sample. Hope this was helpful.

In the absence of continuing to collect additional data to increase the degrees of freedom of your model, I agree with Matthias that you should explore the EPA implemented PMF model. It provides objective tools that allow you to estimate variability in the source contribution estimates (block bootstrap) and to evaluate rotational ambiguity of your solution (DISP). If some of your measurements do not help explain your observed mercury concentrations, you can remove these from the analysis and possibly increase the number of observations available for subsequent runs. Good luck.