  Assessing the impact of an intervention using time-series observational data
on multiple units and outcomes is a frequent problem in many fields of
scientific research. In this paper, we present a novel method to estimate
intervention effects in such a setting by generalising existing approaches
based on the factor analysis model and developing a Bayesian algorithm for
inference. Our method is one of the few that can simultaneously: deal with
outcomes of mixed type (continuous, binomial, count); increase efficiency in
the estimates of the causal effects by jointly modelling multiple outcomes
affected by the intervention; easily provide uncertainty quantification for all
causal estimands of interest. We use the proposed approach to evaluate the
impact that local tracing partnerships (LTP) had on the effectiveness of
England's Test and Trace (TT) programme for COVID-19. Our analyses suggest
that, overall, LTPs had a small positive impact on TT. However, there is
considerable heterogeneity in the estimates of the causal effects over units
and time.
