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Title: Modeling multivariate circular-linear data in a biomechanical study Authors:  Priyanka Nagar - University of Pretoria (South Africa) [presenting]
Andriette Bekker - University of Pretoria (South Africa)
Mohammad Arashi - Ferdowsi University of Mashhad (Iran)
Cor-Jacques Kat - University of Pretoria (South Africa)
Annette-Christi Barnard - Walk-A-Mile Centre for Advanced Orthopaedics (South Africa)
Abstract: High-dimensional data containing circular and linear variables is common in biomechanical and orthopedic data. In most cases, the circular and linear variables are considered in isolation. The joint distribution modelling based on high-dimensional data containing circular and linear data is vital given the large amounts of directional data and the vast applications thereof. We propose a modelling framework applicable to the 6D joint distribution of circular-linear data based on vine copulas. The pair-copula decomposition concept of vine copulas represents the dependence structure as a combination of circular-linear, circular-circular and linear-linear pairs modelled by their respective copulas. This allows us to assess the dependencies in the joint distribution. The motivation comes from the modelling of biomechanical data, i.e. the fracture displacements, that are used as a measure in external fixator comparisons. A case study based on the rotational and translational variables from an external fixator experiment illustrates the distribution's application.