  Canonical Correlation Analysis (CCA) and its regularised versions have been
widely used in the neuroimaging community to uncover multivariate associations
between two data modalities (e.g., brain imaging and behaviour). However, these
methods have inherent limitations: (1) statistical inferences about the
associations are often not robust; (2) the associations within each data
modality are not modelled; (3) missing values need to be imputed or removed.
Group Factor Analysis (GFA) is a hierarchical model that addresses the first
two limitations by providing Bayesian inference and modelling modality-specific
associations. Here, we propose an extension of GFA that handles missing data,
and highlight that GFA can be used as a predictive model. We applied GFA to
synthetic and real data consisting of brain connectivity and non-imaging
measures from the Human Connectome Project (HCP). In synthetic data, GFA
uncovered the underlying shared and specific factors and predicted correctly
the non-observed data modalities in complete and incomplete data sets. In the
HCP data, we identified four relevant shared factors, capturing associations
between mood, alcohol and drug use, cognition, demographics and
psychopathological measures and the default mode, frontoparietal control,
dorsal and ventral networks and insula, as well as two factors describing
associations within brain connectivity. In addition, GFA predicted a set of
non-imaging measures from brain connectivity. These findings were consistent in
complete and incomplete data sets, and replicated previous findings in the
literature. GFA is a promising tool that can be used to uncover associations
between and within multiple data modalities in benchmark datasets (such as,
HCP), and easily extended to more complex models to solve more challenging
tasks.
