modelMatrix

ModelMatrix refers to the design matrix used in statistical modeling. It is a numeric matrix that encodes the terms of a model so estimation procedures can operate on predictor data. In many software environments, a function with a name like modelMatrix (or the closely related model.matrix in R) constructs this matrix from a model specification and a data set.

Construction and terms

A design matrix is built from a model formula or specification and the data. It typically includes an intercept term by default, and expands categorical predictors into dummy variables using a chosen coding scheme (contrasts). Interactions between terms are produced as additional columns, for example through operators that specify interactions or main effects. The column names of the resulting matrix reflect the encoded terms, such as factor levels or interaction terms. The matrix is used across linear, generalized linear, and other regression frameworks.

Output, structure, and usage

The output is usually a numeric matrix with one row per observation and one column per encoded predictor. Attributes may accompany the matrix to record term structure, contrasts used, and the mapping from terms to columns. Data preprocessing such as handling missing values, data type conversion, and factor level ordering can influence the resulting matrix. The design matrix is central to estimation algorithms, prediction, and diagnostics, serving as the input to methods that solve for model parameters.

Notes and relations

While some environments expose a function named modelMatrix, the canonical implementation in R is model.matrix. The concept also appears in other ecosystems under names like design matrix or design matrix construction utilities, such as Patsy in Python. Understanding the design matrix is foundational to interpreting model results and the effects of different encoding schemes.