- 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 14: Nonlinear Models
14.1.1 Linear Models versus Nonlinear Models
Regression models are widely used in practice. A (univariate) regression model describes a possible relationship between a response variable and a set of predictors. The predictors may also be called the covariates or explanatory variables or independent variables. In this chapter, we use the term ‘covariates’ for convenience. That is, in a regression model covariates are used to partially explain the systematic variation in the response. The remaining unexplained variation in the response is treated as a random error. In regression models, a main goal is to understand the dependence of the response on the covariates. However, the true relationship between the response and the covariates is typically unknown, may ...