modeltermen

Modeltermen are the individual components that make up a mathematical or statistical model. Each term represents a specific effect or feature that contributes to the modeled relationship between variables. In a regression model, common terms include the intercept, linear terms (x1, x2, ...), higher-order terms (x1^2, x2^3), and interaction terms (x1 x2), as well as basis-function terms such as splines or one-hot encoded indicators for categorical variables.

Model terms are encoded in a design matrix where each column corresponds to a term. Estimation of coefficients assigns a weight to each term, indicating its contribution to predicted values. The choice of terms governs the model's expressive capacity and interpretability; adding more terms can reduce bias but increase variance and risk overfitting.

Term selection methods, such as forward or backward selection, regularization techniques (Lasso, Ridge, Elastic Net), and information criteria (AIC, BIC), are used to determine which terms to include. Interaction terms require caution for interpretability and can introduce multicollinearity.

Beyond statistics, the concept appears in other modeling domains, where individual contributions to a model's output are referred to as terms in the model's equation or energy function, such as in physics where Lagrangian terms represent different physical processes.