The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models

This monograph presents the basics of the composite marginal likelihood (CML) inference approach, discussing the asymptotic properties of the CML estimator and the advantages and limitations of the approach. The composite marginal likelihood (CML) inference approach is a relatively simple approach that can be used when the full likelihood function is practically infeasible to evaluate due to underlying complex dependencies. The history of the approach may be traced back to the pseudo-likelihood approach of Besag (1974) for modeling spatial data, and has found traction in a variety of fields since, including genetics, spatial statistics, longitudinal analyses, and multivariate modeling. However, the CML method has found little coverage in the econometrics field, especially in discrete choice modeling. This monograph fills this gap by identifying the value and potential applications of the method in discrete dependent variable modeling as well as mixed discrete and continuous dependent variable model systems. In particular, it develops a blueprint (complete with matrix notation) to apply the CML estimation technique to a wide variety of discrete and mixed dependent variable models.