- Subject index
In this important new Handbook, the editors have gathered together a range of leading contributors to introduce the theory and practice of multilevel modeling.
The Handbook establishes the connections in multilevel modeling, bringing together leading experts from around the world to provide a roadmap for applied researchers linking theory and practice, as well as a unique arsenal of state-of-the-art tools. It forges vital connections that cross traditional disciplinary divides and introduces best practice in the field.
Part I establishes the framework for estimation and inference, including chapters dedicated to notation, model selection, fixed and random effects, and causal inference; Part II develops variations and extensions, such as nonlinear, semiparametric and latent class models; Part III includes discussion of missing data and robust methods, assessment of fit and ...
Chapter 3: Likelihood Estimation in Multilevel Models
Likelihood Estimation in Multilevel Models
3.1 A Brief History
Fisher (1925) introduced the notion of the intraclass coefficient. His basic example was a set of measurements on a sample of brother pairs. In terms of modern notation he defined the quantities:
where i, j index level 1 units (brothers) and level 2 units (pairs), and there are m = N/2 pairs. The implicit 2-level composite model can be written as
where the uj, ∊ij are assumed to have independent (normal) distributions. Fisher defined the intraclass correlation as , where .
Fisher extended this to the case where there were greater than two level 1 units per level 2 unit, but only considered the balanced case. His basic ...