Questionnaire data analysis using information geometry (original) (raw)

2020, Scientific Reports

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, pavi...

Modeling High-Dimensional Survey Data Using Latent Structure Analyses

2011

The Linear Latent Structures (LLS) analysis assumes that the mutual correlations observed in survey variables reflect a hidden property of subjects that can b e described by low-dimensional random vector. The statistical properties of LLS analysis, the alg orithm for parameter estimates and its implementation, simulation studies, and application of LLS model to the National Long Term Care Survey (NLTCS) data are discussed. The results of analyses are compared numerically and analytically to predictions of the Latent Class and Grade of Membership analyses. Simulation studies demonstrate high quality of reconstruction of the major model components and demonstrate its potential to analyze survey datasets with 1000 or more questions. Applying the LLS model to the 1994 and 1999 NLTCS datasets (5,000+ individuals) with responses to over 200 questions on behavior factors, functional status, and comorbidities resulted in identified population structure with basis represented pure-type indiv...

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