Multilevel models vs GLMMs for correlated clustered data

Question

What is the difference between the Generalized Linear Mixed Model (GLMM) and a multilevel model?

Answer 1

Multilevel models are used when data are clustered within a hierarchical structure that will make them non-independent. The classic examples are measures of students who are nested in classes (i.e., same teacher), which are nested in schools, etc., or patients who are nested in doctors, who are nested in hospitals, etc. This is often contrasted with longitudinal data ("panel" in econometric terminology), in which you have multiple measurements on the same student / patient. These situations have led to a completely separate set of terms for mixed effects / longitudinal models. However, note that we can think of multiple measurements as nested within students / patients, so there isn't really a logical difference, just a traditional / terminological one.

Given that fact about the structure of the data, though, the data can be of any type (normal, binary, ordinal, counts, etc.). GLMMs are designed to deal with non-normal data types (binary, multi-category, ordinal, count data, etc.). Technically, normal data fall within the purview of GLMMs, but the term typically connotes non-normal data and people just say LMM (linear mixed effects model) for normal data.

GLMMs are more terminologically related to the longitudinal tradition, but are just as applicable in classically multilevel-type situations.