Model selection and model averaging in MACML-estimated MNP models

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.