Maximum likelihood (ML) denotes an important framework for estimation and inference. It is a theory about estimating models (i.e., recovering parameters from samples) rather than specifying models (i.e., constructing models). Its logic is premised on selecting the estimates that make the data the “most likely” (relative to the other possible estimates). Thanks to its versatility, ML is treated as the gold standard for estimating advanced models, such as multilevel and structural equation models. This entry provides an overview of ML estimation.

When explicating ML estimation, it is essential to keep distinct models, algorithms, and theory. A model defines the estimand (i.e., the parameter waiting to be estimated). An algorithm (or estimator) is the computational device used to obtain an estimate. A theory is the logical blueprint ...