  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.
