Modelling and testing on multivariate longitudinal data for nested design with application to player-by-player basketball analytics

Suppose that on several subjects/individuals, each one belonging to a mutually exclusive group of interest, we may observe multiple times a multivariate repeated measure in which each univariate component can be either binary or numeric or ordered categorical. By modelling this kind of nested design as a longitudinal linear fixed effect model and by using the union-intersection approach with the emphasis placed on the ranking of location effects, the goal of the present paper is proposing a multivariate testing approach for doing inference on both between and within groups analysis. Our approach may be effective for handling with some real problems in research fields such as behavioural and social sciences as well as in sport analytics. Via a Monte-Carlo simulation study we investigated the properties of the proposed testing and ranking methodology and we proved its validity under different random distributions. Finally, by using play-by-play basketball data, we present an application to player-based data sport analytics.