Linear Association in Compositional Data Analysis

Multiple linear regression modeling for compositional data

Compositional data, containing relative information, occur regularly inmany disciplines and practical situations. Multivariate statistics methods including regression analysis have been adopted to model compositional data, but the existing research is still scattered and fragmented. This paper contributes to modeling the linear regression relationship for compositional data as both dependent an...

Correlation Analysis for Compositional Data

Compositional data need a special treatment prior to correlation analysis. In this paper we argue why standard transformations for compositional data are not suitable for computing correlations, and why the use of raw or log-transformed data is neither meaningful. As a solution, a procedure based on balances is outlined, leading to sensible correlation measures. The construction of the balances...

Compositional Invariant Generation via Linear Recurrence Analysis

This paper presents a new method for automatically generating numerical invariants for imperative programs. Given a program, our procedure computes a binary input/output relation on program states which over-approximates the behaviour of the program. It is compositional in the sense that it operates by decomposing the program into parts, computing an abstract meaning of each part, and then comp...

A Concise Guide to Compositional Data Analysis

Robust factor analysis for compositional data

Factor analysis as a dimension reduction technique is widely used with compositional data. Using the method for raw data or for improperly transformed data will, however, lead to biased results and consequently to misleading interpretations. Although some procedures, suitable for factor analysis with compositional data, were already developed, they require pre-knowledge of variable groups, or a...