Linear mixed-effects model for longitudinal complex data with diversified characteristics

The increasing richness of data encourages a comprehensive understanding of economic and financial activities, where variables of interest may include not only scalar (point-like) indicators, but also functional (curve-like) and compositional (pie-like) ones. In many research topics, the variables are also chronologically collected across individuals, which falls into the paradigm of longitudinal analysis. The complicated nature of data, however, increases the difficulty of modeling these variables under the classic longitudinal framework. In this study, we investigate the linear mixed-effects model (LMM) for such complex data. Different types of variables are first consistently represented using the corresponding basis expansions so that the classic LMM can then be conducted on them, which generalizes the theoretical framework of LMM to complex data analysis. A number of simulation studies indicate the feasibility and effectiveness of the proposed model. We further illustrate its practical utility in a real data study on Chinese stock market and show that the proposed method can enhance the performance and interpretability of the regression for complex data with diversified characteristics.