Likelihood Inference for Models with Unobservables: Another View

TL;DR

This paper discusses likelihood inference for models with unobservables, introducing hierarchical likelihood as a framework to handle probabilistic modeling of unobservables and enabling natural likelihood-based inference.

Contribution

It presents hierarchical likelihood as an extended framework for likelihood inference in models with unobservables, bridging modeling and inference.

Findings

Hierarchical likelihood enables likelihood-based inference for complex models with unobservables.

The approach creates new probabilistic models incorporating unobservables.

Hierarchical likelihood broadens the scope of models suitable for likelihood inference.

Abstract

There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily having a probabilistic basis and statistical models having unobservables with a probabilistic basis. Another concerns likelihood-based inference for statistical models with unobservables. This needs an extended-likelihood framework, and we show how one such extension, hierarchical likelihood, allows this to be done. Modeling of unobservables leads to rich classes of new probabilistic models from which likelihood-type inferences can be made naturally with hierarchical likelihood.