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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 ...

Penalized Splines and Multilevel Models
Penalized splines and multilevel models
GöranKauermannUniversity of Munich, Germany
TorbenKuhlenkasperGoethe University Frankfurt, Germany
18.1 Motivation

In this chapter we will extend multilevel models to include smooth, functional components. This means we will move forward from a parametric model as discussed in Chapters 3 and 8 towards non- and semiparametric modeling. To motivate the need for such a model class let us look at the following example. We record with y the wage of a person and intend to model how the wage depends on maturity and working experience recorded with x as years of professional experience. It is natural that y does depend non-linearly on x and we therefore use the smoothing model (see Chapter 17) and set

with m(.) as a smooth but otherwise ...

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