Statistical Inference in Orthogonal Regression for Three-Part Compositional Data Using a Linear Model with Type-II Constraints

Abstract

Orthogonal regression is a proper tool to analyze relations between two variables when three-part compositional data, i.e., three-part observations carrying relative information (like proportions or percentages), are under examination. When linear statistical models with type-II constraints (constraints involving other parameters besides the ones of the unknown model) are employed for estimating the parameters of the regression line, approximate variances and covariances of the estimated line coefficients can be determined. Moreover, the additional assumption of normality enables to construct confidence domains and perform hypotheses testing. The theoretical results are applied to a real-world example.

Keywords:

• Compositional data
• Linear regression model with type-II constraints
• Orthogonal regression

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62F03, 62F10, 62F25, 62F30, 62H99

Acknowledgments

The authors are grateful to the referees for helpful comments and suggestions. This work was supported by the Council of the Czech Government MSM 6198959214.