Statistical modelling of measurement error in wet chemistry soil data

There is a growing demand for high-quality soil data. However, soil measurements are subject to many error sources. We aimed to quantify uncertainties in synthetic and real-world wet chemistry soil data through a linear mixed-effects model, including batch and laboratory effects. The use of synthetic data allowed us to investigate how accurately the model parameters were estimated for various experimental measurement designs, whereas the real-world case served to explore if estimates of the random effect variances were still accurate for unbalanced datasets with few replicates. The variance estimates for synthetic pHH2O data were unbiased, but limited laboratory information led to imprecise estimates. The same was observed for unbalanced synthetic datasets, where 20, 50 and 80% of the data were removed randomly. Removal led to a sharp increase of the interquartile range (IQR) of the variance estimates for batch effect and the residual. The model was also fitted to real-world pHH2O and total organic carbon (TOC) data, provided by the Wageningen Evaluating Programmes for Analytical Laboratories (WEPAL). For pHH2O, the model yielded unbiased estimates with relatively small IQRs. However, the limited number of batches with replicate measurements (5.8%) caused the batch effect to be larger than expected. A strong negative correlation between batch effect and residual variance suggested that the model could not distinguish well between these two random effects. For TOC, batch effect was removed from the model as no replicates were available within batches. Again, unbiased model estimates were obtained. However, the IQRs were relatively large, which could be attributed to the smaller dataset with only a single replicate measurement. Our findings demonstrated the importance of experimental measurement design and replicate measurements in the quantification of uncertainties in wet chemistry soil data. Highlights Accurate uncertainty quantification depends on the experimental measurement design. Linear mixed-effects models can be used as a tool to quantify uncertainty in wet chemistry soil data. Lack of replicate measurements leads to poor estimates of error variance components. Measurement error in wet chemistry soil data should not be ignored.