funktionsformer
Funktionsformer refers to the assumed mathematical form that describes how a dependent variable depends on one or more explanatory variables in a statistical or mathematical model. It specifies the functional relationship and how parameters translate inputs into outputs. Choosing a functional form is a modeling decision that affects interpretability, extrapolation, and the risk of misfit. Parametric models fix a particular family of functions with a finite set of parameters, enabling estimation from data, while nonparametric approaches relax this assumption.
Common functional forms include linear (y = α + βx), polynomial (y = α + β1x + β2x^2 + ...), logarithmic (y = α + β log x),
Model selection involves theory, interpretability, and empirical fit. Criteria such as AIC, BIC, cross-validation, and residual
Limitations include misspecification, restricted extrapolation, and identifiability issues when parameters are not separately identifiable. A good
See also: parametric versus nonparametric modeling; regression; generalized linear models; nonlinear optimization.