Abstract
A novel method has been proposed that extends the use of regularisation to structural equation modelling (SEM). Traditionally, SEM is used in psychological research to estimate latent theoretical constructs via their effect on directly measurable variables, and to incorporate those latent factors into wider models with researcher-specified causal relations. Regularised regression is a supervised statistical learning method often used in precision medicine to predict risk of diagnosis, prognosis, and treatment response. It is increasingly common in psychological and psychiatric research for models to contain many variables relative to sample size and low number of events per variable. Regularisation can handle such scenarios, where traditional statistics struggles. Within a latent variable model context, regularisation allows for a mixture of exploratory and confirmatory approaches, as it can be applied to particular sections of the model. This is explored in the context of psychometric scale development and behavioural genetics models, where underlying complex traits that cannot be directly measured are often of interest. Where the fundamental solution is more sparsely populated than the proposed model, we expect regularised SEM to perform variable selection and reduce the variance of the estimators, thereby producing more parsimonious latent factor solutions.This thesis will investigate regularised SEM in comparison with traditional SEM in simulation studies and three empirical examples. First, regularised SEM will be applied to a large psychometrics dataset, with the aim of recovering an equally parsimonious factor solution compared to a previously validated one in that dataset for aggression. Second, regularised SEM will be applied to a longitudinal birth cohort study containing childhood behavioural measures, again looking at psychometric data, but now extending the measurement model to see if we can optimise a large scale based on prediction of later outcome. Third, regularised SEM will be used for the analysis of genetic models of body mass index and parental feeding behaviour in a longitudinal dataset, which includes genomic, clinical, and behavioural measures. Monte Carlo simulations will be generated to compare the respective performances of regularised SEM with traditional SEM for model scenarios that reflect the second and third analyses before regularised SEM is applied to the real data.
The simulation studies and real-world applications presented in this thesis demonstrate that while regularised SEM holds promise for certain psychometric applications, in terms of genetics, there are considerable challenges that have yet to be overcome. Limitations of the method, potential future applications, and overarching conclusions are discussed in the final chapter.
| Date of Award | 1 Feb 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Cedric Ginestet (Supervisor), Daniel Stahl (Supervisor) & Silia Vitoratou (Supervisor) |