Advanced multivariate statistical analysis of directly and indirectly observed systems

• Main Author: Shiells, Helen
• Format: Dissertation
• Language: English
• Published: University of Aberdeen 2017
• Subjects: Dementia; Multivariate analysis

This work is developed in two specific areas under the common umbrella of development of mathematical techniques for indirect measurement of complex systems. Both parts are dedicated to fitting hidden parameters to latent aspects of complex systems, which are not accessible to the na¨ive observer. The first application of interest is the inference of networks of causal interactions between processes when not all components of the network have been observed. The second application of interest is multidimensional latent trait analysis, with specific application to neuropsychological data of subjects suffering from dementia. Na¨ive application of Granger causality can lead to incorrect inference of the false links in inferred networks, when not all interacting processes have been observed. Within the framework of this thesis it is shown that in some cases reconstruction of the true network is possible; and consequently discrimination between volume conduction and hidden processes. It is also shown that hidden processes can influence the inferred strength of causal interactions between observed processes. A reliable method is presented for removing nodes from a network such that any inferred network yields minimum spurious interactions. Also, a discussion of bivariate network inference warns against the inadvertent creation of hidden processes when inferring network structure. Clinical observation of patients with dementia demonstrates that individuals show different impairment at different stages; disease presentation and progression is not uniform. Therefore, dementia may not be measurable on a one-dimensional scale, but rather a multidimensional space. To test this hypothesis a novel multidimensional latent trait analysis technique is developed within the framework of this thesis. Common neuropsychological tests are found to be answered by subjects according to three latent traits; labelled cognition, dementia and depression. Final results use the novel analysis to populate a multidimensional space with questions to assess disease progression according to identified latent traits.