# Model selection and model averaging in MACML-estimated MNP models

## TL;DR

This paper reviews and compares model selection and averaging methods for MACML-estimated multinomial probit models, highlighting the advantages of empirical likelihood tests and demonstrating the practical application of model averaging.

## Contribution

It adapts and evaluates model selection and averaging techniques specifically for MACML-estimated MNP models, proposing empirical likelihood tests as a robust alternative.

## Key findings

- Likelihood-ratio tests and information criteria perform inconsistently with MACML models
- Empirical likelihood tests show more reliable performance in model selection
- Model averaging improves parameter recovery and is feasible for real-world large datasets

## Abstract

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.