  This paper provides a review of model selection and model averaging methods
for multinomial probit models estimated using the MACML approach. The proposed
approaches are partitioned into test based methods (mostly derived from the
likelihood ratio paradigm), methods based on information criteria and model
averaging methods.
  Many of the approaches first have been derived for models estimated using
maximum likelihood and later adapted to the composite marginal likelihood
framework. In this paper all approaches are applied to the MACML approach for
estimation. The investigation lists advantages and disadvantages of the various
methods in terms of asymptotic properties as well as computational aspects. We
find that likelihood-ratio-type tests and information criteria have a spotty
performance when applied to MACML models and instead propose the use of an
empirical likelihood test.
  Furthermore, we show that model averaging is easily adaptable to CML
estimation and has promising performance w.r.t to parameter recovery. Finally
model averaging is applied to a real world example in order to demonstrate the
feasibility of the method in real world sized problems.
