The purpose of the reduced model
The two main uses for reduced models are for simulation (to simulate new
scenarios and for design) or estimation (to be used in software like
NONMEM for estimating parameters for new populations).
For simulation, any method can be used if the simulation is based on
sets of input variables (e.g. doses, dose intervals, observation times)
that were considered when the model reduction was conducted. For
instance, if pseudo-data were simulated from the full-order model to
develop a reduced model then the reduced model can only be used to
interpolate within the range of pseudo-data inputs. In contrast, any
fully parametric method, can be used to simulate under (in theory) any
set of input variables. In this context, semiparametric methods such as
balanced truncation behave like nonparametric methods.
However, if the purpose of the reduced model is to be used for
estimation then any fully parametric method could be used for
model-order reduction. The utility of the Empirical Approximation will
depend on the circumstance. Importantly, though if it was desirable for
the parameters to provide some mechanistic meaning then only the fully
parametric methods would be of value.