Linear mixed-effects model for multivariate longitudinal compositional data

Compositional data analysis is becoming increasing important in economic research, where the variables of interest may be structural indicators, such as the investment proportion of industries. In many applications, the measurements of these indicators are collected from countries/regions on a yearly/monthly basis, which falls into the paradigm of longitudinal data. Typically, data from the same individual may show potential association due to unobserved shared factors. To incorporate the dependence within the individual, we investigate the linear mixed-effects model for multivariate longitudinal compositional data. We develop and implement a maximum likelihood estimation procedure through the expectation maximization algorithm. We also investigate the statistical inferences of fixed effects coefficients and the selection of random effects via a proposed Bayesian information criterion. The proposed method shows desirable properties and performs well in finite samples, as comprehensive numerical studies indicate. We further illustrate the practical utility of the proposed method in a real data study based on China's industrial structure, and show that it can improve the performance and enhance the interpretability of the regression on multivariate compositional data.