Modellenformen

Modellenformen is a term used in statistics and related fields to refer to the different mathematical structures that describe how an outcome depends on predictor variables. A model form specifies the relationship, the scale of the response, and, if relevant, whether random effects, time dependence, or other complex features are included. It encompasses a range of approaches from simple linear relationships to more complex frameworks used to capture irregular patterns or hierarchical data.

Common model forms include linear models (for example y = Xβ + ε), generalized linear models such as logistic or Poisson regression, nonlinear models, and mixed-effects or hierarchical models. Time-series and state-space models, survival models, and probabilistic graphical models also represent distinct model forms. In Bayesian analysis, a model form is combined with prior information to produce posterior inferences, reflecting uncertainty about parameters and structures.

Key components and estimation methods define each form: the choice of predictors, the link function or outcome distribution, and assumptions about error or randomness. Estimation techniques include ordinary least squares, maximum likelihood, and Bayesian inference, often supplemented by regularization or model averaging. Model evaluation relies on goodness-of-fit, cross-validation, and information criteria such as AIC or BIC, along with diagnostic checks on residuals and assumptions.

Use and context vary by discipline, data characteristics, and research questions. The term Modellenformen is typically used to categorize, compare, and select among candidate model structures, balancing explanatory power, predictive accuracy, and computational feasibility, while being mindful of overfitting and potential misspecification.