Association measures for interval variables

M. Rosário Oliveira (), Margarida Azeitona (), António Pacheco () and Rui Valadas ()
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M. Rosário Oliveira: Universidade de Lisboa
Margarida Azeitona: Universidade de Lisboa
António Pacheco: Universidade de Lisboa
Rui Valadas: Universidade de Lisboa

Advances in Data Analysis and Classification, 2022, vol. 16, issue 3, No 2, 520 pages

Abstract: Abstract Symbolic Data Analysis (SDA) is a relatively new field of statistics that extends conventional data analysis by taking into account intrinsic data variability and structure. Unlike conventional data analysis, in SDA the features characterizing the data can be multi-valued, such as intervals or histograms. SDA has been mainly approached from a sampling perspective. In this work, we propose a model that links the micro-data and macro-data of interval-valued symbolic variables, which takes a populational perspective. Using this model, we derive the micro-data assumptions underlying the various definitions of symbolic covariance matrices proposed in the literature, and show that these assumptions can be too restrictive, raising applicability concerns. We analyze the various definitions using worked examples and four datasets. Our results show that the existence/absence of correlations in the macro-data may not be correctly captured by the definitions of symbolic covariance matrices and that, in real data, there can be a strong divergence between these definitions. Thus, in order to select the most appropriate definition, one must have some knowledge about the micro-data structure.

Keywords: Symbolic data analysis; Interval-valued variables; Symbolic covariance matrix; 62H20; 62H30; 60E05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-021-00445-8

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