extendedmodel

Extended model is a generic label for modeling approaches that augment a baseline representation with additional components to better capture relationships in data. The term is used across statistics, econometrics, and machine learning to denote a family of models that extend simple formulations by adding structure, parameters, or latent variables.

Common forms include extended linear models that incorporate polynomial terms and interactions; generalized additive models that replace linear terms with smooth functions; linear mixed models that add random effects; state-space or dynamic models that incorporate time-varying parameters or latent processes; and Bayesian hierarchical models that introduce latent variables and hierarchical priors. In some contexts, neural networks and other nonlinear predictors are described as extended versions of linear models because they augment linear combinations with nonlinear components.

Estimation and inference for extended models typically rely on maximum likelihood or Bayesian methods, often with regularization to prevent overfitting. Model selection uses information criteria such as AIC/BIC or cross-validation. Diagnostics assess fit, heterogeneity, and potential identifiability issues.

Applications span econometrics, engineering, environmental science, finance, and social science, wherever a baseline model is insufficient to describe complex data patterns. Limitations include increased risk of overfitting, computational demands, and potential identifiability problems when many components are added. Clear specification, prior knowledge, and validation are important when adopting an extended model.