The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models takes a straightforward approach to illustrating the value of the CML method for the estimation of discrete and mixed dependent variable models in Econometrics. The monograph discusses theoretical aspects of CML methods, provides an overview of developments and applications of the CML inference approach, and explains why the approach can be particularly very effective for the estimation and analysis of high-dimensional heterogeneous data. In addition, it provides a blueprint (complete with matrix notation) to apply the CML estimation technique to a wide variety of discrete and mixed dependent variable model systems.