Imputation of values above an upper detection limit in compositional data

Abstract

Geochemical data frequently contain censored values. An imputation method for right-censored compositional data is proposed, based on the Tobit model, in order to get a complete and reliable data set. An algorithm is developed and implemented using regressions in an iterative scheme, where the imputed values are updated step-by-step. Optionally, classical least-squares or robust regressions can be carried out, with or without variable selection. The performance of the algorithm is evaluated using two real geochemical data sets, considering various different scenarios. Compared to commonly used substitution methods, the proposed method leads to an improved data quality. The procedure is available in the R package robCompositions.