Heteroskedastic linear regression model with compositional response and covariates

ABSTRACT

Compositional data are known as a sort of complex multidimensional data with the feature that reflect the relative information rather than absolute information. There are a variety of models for regression analysis with compositional variables. Similar to the traditional regression analysis, the heteroskedasticity still exists in these models. However, the existing heteroskedastic regression analysis methods cannot apply in these models with compositional error term. In this paper, we mainly study the heteroskedastic linear regression model with compositional response and covariates. The parameter estimator is obtained through weighted least squares method. For the hypothesis test of parameter, the test statistic is based on the original least squares estimator and corresponding heteroskedasticity-consistent covariance matrix estimator. When the proposed method is applied to both simulation and real example, we use the original least squares method as a comparison during the whole process. The results implicate the model's practicality and effectiveness in regression analysis with heteroskedasticity.

KEYWORDS:

• Compositional data
• regression model
• heteroskedasticity
• isometric log-ratio coordinates
• error term

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors wish to thank these supports by Natural Science Foundation of Shanxi Province of China (Grant No. 2015011044), Shanxi International Science and Technology Cooperation Project (Grant No. 2015081020), and Graduate Education Innovation Project of Shanxi Province (Grant No. 2017BY001).