Model-based replacement of rounded zeros in compositional data: Classical and robust approaches

zCompositions — R package for multivariate imputation of left-censored data under a compositional approach

“…Even so, the alr transformation works properly for statistical modelling and simplifies ordinary estimation in the space of coordinates. Importantly, as shown in [11], analogous results are obtained using either alr or ilr for that purpose.…”

“…A common left-censoring problem in data sets susceptible to a compositional analysis is the presence of rounded zeros [10,11]. That is, small values that have been rounded off to zero due to the number of significant digits considered.…”

Exploring Compositional Data with the Robust Compositional Biplot

“…According to the origin of zero values, either as a result of an imprecise measurement of a trace element in the composition (i.e. rounding zeros) or the result of structural processes (structural zeros), special care has to be taken prior to a further processing of the observations [3,14]. The Aitchison geometry forms a Euclidean vector space of dimension D 1, that makes it possible to express the compositions in coordinates with respect to an orthonormal basis on the simplex.…”

Improving processing by adaption to conditional geostatistical simulation of block compositions

“…This was not the case with Weltje's (1997) end-member algorithms, where the final results might present negative components. On the side of the disadvantages, the log-ratio methodology cannot deal directly with components of zero or below the detection limit, and some missing data techniques must be applied, prior to or within the end-member unmixing or (geo) statistical treatment (Tjelmeland and Lund, 2003;Hron et al, 2010;Martín-Fernández et al, 2012). It is often proposed to impute the zeroes by some reasonable values, often a constant fraction of the detection limit.…”