  A stochastic epidemic model is defined in which each individual belongs to a
household, a secondary grouping (typically school or workplace) and also the
community as a whole. Moreover, infectious contacts take place in these three
settings according to potentially different rates. For this model we consider
how different kinds of data can be used to estimate the infection rate
parameters with a view to understanding what can and cannot be inferred, and
with what precision. Among other things we find that temporal data can be of
considerable inferential benefit compared to final size data, that the degree
of heterogeneity in the data can have a considerable effect on inference for
non-household transmission, and that inferences can be materially different
from those obtained from a model with two levels of mixing.
  Keywords: Basic reproduction number, Bayesian inference, Epidemic model,
Infectious disease data, Markov chain Monte Carlo, Networks.
