Graphical Models With Latent Variables and Their Application in Cognitive Approaches to Neuropsychological Disorders

Many studies in the medical sciences involve the measurement of several aspects on each individual on repeated occasions. Often, scientific interest is in studying the inter-relationships, which might be causal, between measurements. Graphical modelling provides a strategy for translating substantive hypotheses about causal relationships into a statistical model. Further, scientifically relevant results from the statistical analysis of the data can be communicated through an intuitively natural graphical representation of the fitted model. The aim of this project is to make use of recent developments in the area of graphical models to advance research in medical contexts, including developmental psychology, neuropsychology and brain ageing. This project will focus on two areas: 1) assessment of decline in the cognitive functions of Alzheimer‘s patients and 2) identification of particular executive and social-cognitive problems associated with focal epilepsy in children. Evaluation of data to study development and deterioration of cognitive performance in individuals requires the consideration of latent variables to represent qualities of individual subjects that cannot be measured directly. Often the directly observed data are qualitative, for example success or failure on a psychometric test. A major goal is to develop a flexible modelling strategy for data of this kind.

This proposal applies recent advances in graphical models to the issue of developmental change within psychological disorders. I will address two key issues where graphical models can be applied in this field. First, their use will be explored to assess models of decline in the cognitive functions of Alzheimer‘s patients. Secondly, they will be employed to identify particular executive and social-cognitive problems associated with focal epilepsy in children, which have been discussed by clinicians but not fully reported in the research literature
Graphical models are useful because they represent stochastic dependence structures amongst multivariate measurements in a way that relates naturally to substantive scientific hypotheses about the underlying inter-relationships. Research in psychology typically involves the analysis of longitudinal multivariate binary, ordinal or continuous data or a combination of these. In addition, latent variables are often present as a natural choice to represent unobservable, but typically inter-related, characteristics of participants.
In this proposal I will restrict my attention to those graphs in which the latent variables have a substantive interpretation. I will adopt the assumption that the distribution of the observed variables may be meaningfully interpreted as arising after marginalising over the latent variables. A major goal of this project is to investigate a statistical modelling approach that correctly represents all and only the dependence relations holding among the observed variables, reflecting the influence of the latent variables. My approach will consider the nature of the observed measurements, discrete or continue, and propose suitable sampling distributions for modelling accordingly.