Matthias Templ

Imputation of missing values for compositional data using classical and robust methods

New imputation algorithms for estimating missing values in compositional data are introduced. A first proposal uses the k-nearest neighbor procedure based on the Aitchison distance, a distance measure especially designed for compositional data. It is important to adjust the estimated missing values to the overall size of the compositional parts of the neighbors. As a second proposal an iterative model-based imputation technique is introduced which initially starts from the result of the proposed k-nearest neighbor procedure. The method is based on iterative regressions, thereby accounting for the whole multivariate data information. The regressions have to be performed in a transformed space, and depending on the data quality classical or robust regression techniques can be employed. The proposed methods are tested on a real and on simulated data sets. The results show that the proposed methods outperform standard imputation methods. In the presence of outliers, the model-based method with robust regressions is preferable.

Exploring incomplete data using visualization techniques

Visualization of incomplete data allows to simultaneously explore the data and the structure of missing values. This is helpful for learning about the distribution of the incomplete information in the data, and to identify possible structures of the missing values and their relation to the available information. The main goal of this contribution is to stress the importance of exploring missing values using visualization methods and to present a collection of such visualization techniques for incomplete data, all of which are implemented in the

Bayesian-multiplicative treatment of count zeros in compositional data sets:

{{\sf R}}

Simplicial principal component analysis for density functions in Bayes spaces

package VIM. Providing such functionality for this widely used statistical environment, visualization of missing values, imputation and data analysis can all be done from within

Robust estimation of economic indicators from survey samples based on Pareto tail modelling

{{\sf R}}

Independence in Contingency Tables Using Simplicial Geometry

without the need of additional software.