Abstract

Regression models for compositional data are common in several areas

of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in these models using residuals that are approximately

standard normally distributed. However, for regression models for compositional

data, there has not been any multivariate residual that meets this requirement. In

this work, we introduce a class of asymptotically standard normally distributed

residuals for compositional data based on bootstrap.

Monte Carlo simulation

studies indicate that the distributions of the residuals of this class are well approximated by the standard normal distribution in small samples. Two other

simulation studies suggest that residuals of this class can detect a wrong linear

predictor, while one of them performs well in identifying an incorrect response

distribution. The usefulness of this residual is illustrated through an application

on sleep stages. The class of residuals proposed here can also be used in other

classes of multivariate regression models.

Key words and phrases: Bootstrap, compositional data, diagnostic analysis, quan- tile residual

Information

Preprint No.SS-2025-0172
Manuscript IDSS-2025-0172
Complete AuthorsGustavo H. A. Pereira, Jianwen Cai
Corresponding AuthorsGustavo H. A. Pereira
Emailsgpereira@ufscar.br

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Acknowledgments

This work was partially supported by S˜ao Paulo Research Foundation (FAPESP),

grant number 2020/16334-9. We also thank an associate editor and two

anonymous reviewers for their helpful comments.

Supplementary Materials

The Supplementary Material includes the proof of Theorem 1 (Section S1),

three tables from the simulation studies presented in Section 3.1 (Section

S2), and analyses of misspecification detection (Section S3).

Supplementary materials are available for download.