Multivariate functional clustering and its application to typhoon data

Abstract

We propose a multivariate nonlinear mixed effects model for clustering multiple longitudinal data. Advantages of the nonlinear mixed effects model are that it is easy to handle unbalanced data which highly occur in the longitudinal study, and it can take into account associations among longitudinal variables at a given time point. The joint modeling for multivariate longitudinal data, however, requires a high computational cost because numerous parameters are included in the model. To overcome this issue, we perform a pairwise fitting procedure based on a pseudo-likelihood function. Unknown parameters included in each bivariate model are estimated by the maximum likelihood method along with the EM algorithm, and then the number of basis functions included in the model is selected by model selection criteria. After estimating the model, a non-hierarchical clustering algorithm by self-organizing maps is applied to the predicted coefficient vectors of individual specific random effect functions. We present the results of the application of the proposed method to the analysis of data of typhoons that occurred between 2000 and 2017 in Asia.