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Activity Number: 43 - SPEED: Statistics in Sports; Physical Activity/Sleep Studies, and Nonparametrics Part 1
Type: Contributed
Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
Sponsor: Survey Research Methods Section
Abstract #307254 Presentation
Title: Information Theoretic Measures of Diversity
Author(s): Nikhil S Padhye* and Marcia C de Oliveira Otto
Companies: University of Texas Health Science Center at Houston and University of Texas Health Science Center at Houston
Keywords: Diversity; Entropy; Information theory; Nonlinear Dynamics; Simpson index; Dietary Science

Studies of nutritional and dietary diversity rely on measures such as the Berry-Simpson index and Jaccard index of similarity, which are borrowed from methods in economics and ecology. We study the ability of these indices to discriminate between dietary patterns and their distributional properties on simulated data. Information theoretic measures based on Renyi entropy are proposed as alternatives that have improved discriminating power and quasi-normal distributions on a large sample. The extension of the indices beyond an aggregation of pairwise comparisons is discussed along with their relationships to the entropy measures. Lastly, we address the question of stratifying diversity metrics, which is generally a non-additive process. This is demonstrated by splitting metrics into categories of healthy and unhealthy foods. Consideration of fuzzy membership of foods in the healthy category results in the proposal of fuzzy entropy as a supplementary measure that should be taken into account after stratification of the diversity measures.

Authors who are presenting talks have a * after their name.

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