The Links in our Mind: Multivariate Statistical Methods for Psychological Data

Psychopathological processes are characterized by multiple interacting dimensions, that in order to be understood properly have to be studied simultaneously. In this thesis multivariate statistical methods, such as item response theory and graphical models, have been proposed to model psychological observables for explaining complex mental phenomena. After introducing the chronology of multivariate analysis in the behavioural sciences, we describe mixed graphical models for cross-sectional data from two cohort studies, in order to study the relationship between functional somatic symptoms and psychotic experiences in adolescence. Then we focus on the statistical modelling of psychological time-series data and specifically on the class of Graphical Vector Autoregressive (GVAR) models. We implemented GVARs in open-source software that can be used for fitting these models to psychological data with different characteristics. Next, we apply the GVAR to time series data from psychopathology for studying the development of psychosis according to subsequent stages of illness severity. The topic of multivariate time series analysis in psychopathology is concluded by a newly developed hierarchical extension of the traditional GVAR model. This extension can be used for modelling simultaneously time series data from multiple individuals taking into account individual heterogeneity. The thesis is concluded with a software implementation of the nonparametric item response theory model for unfolding processes MUDFOLD, which has been extended to provide uncertainty quantification in parameter estimation using bootstrap, and which handles missing values using multiple imputation by chained equations.