A powerful study design in the fields of genomics and metabolomics is the
'replicated time course experiment' where individual time series are observed
for a sample of biological units, such as human patients, termed replicates.
Standard practice for analysing these data sets is to fit each variable (e.g.
gene transcript) independently with a functional mixed-effects model to account
for between-replicate variance. However, such an independence assumption is
biologically implausible given that the variables are known to be highly
correlated.

In this article we present a skew-t-normal multi-level reduced-rank
functional principal components analysis (FPCA) model for simultaneously
modelling the between-variable and between-replicate variance. The reduced-rank
FPCA model is computationally efficient and, analogously with a standard PCA
for vectorial data, provides a low dimensional representation that can be used
to identify the major patterns of temporal variation. Using an example case
study exploring the genetic response to BCG infection we demonstrate that these
low dimensional representations are eminently biologically interpretable. We
also show using a simulation study that modelling all variables simultaneously
greatly reduces the estimation error compared to the independence assumption.