文章基本信息

标题：Questionnaire data analysis using information geometry
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作者：Omri Har-Shemesh ; Rick Quax ; J. Stephen Lansing 等
期刊名称：Scientific Reports
电子版ISSN：2045-2322
出版年度：2020
卷号：10
期号：1
页码：1-9
DOI：10.1038/s41598-020-63760-8
出版社：Springer Nature
摘要：The analysis of questionnaires often involves representing the high-dimensional responses in a low-dimensional space (e.g., PCA, MCA, or t-SNE). However questionnaire data often contains categorical variables and common statistical model assumptions rarely hold. Here we present a non-parametric approach based on Fisher Information which obtains a low-dimensional embedding of a statistical manifold (SM). The SM has deep connections with parametric statistical models and the theory of phase transitions in statistical physics. Firstly we simulate questionnaire responses based on a non-linear SM and validate our method compared to other methods. Secondly we apply our method to two empirical datasets containing largely categorical variables: an anthropological survey of rice farmers in Bali and a cohort study on health inequality in Amsterdam. Compare to previous analysis and known anthropological knowledge we conclude that our method best discriminates between different behaviours, paving the way to dimension reduction as effective as for continuous data.