factorsvariables

Factor variables, or categorical variables, take on a limited number of categories that identify groups rather than measure magnitude. They differ from numeric variables and are common in statistics and data science. Factor variables can be nominal, with no inherent order (for example, color: red, blue, green), or ordinal, with a meaningful sequence (such as education level: high school, bachelor’s, master’s, PhD). Some analyses treat ordered factors specially to reflect the order.

In data processing, a factor is described by its levels or categories. Analyses typically use indicator or contrast coding to include factors in models. The most common approach is dummy (one-hot) coding, where k−1 binary variables indicate membership in non-reference categories; the reference category is absorbed by the intercept. Other schemes include effect coding and sum-to-zero coding.

Software treats factors differently from numeric data. In R, a factor has levels and an order; in Python’s pandas, categoricals can be encoded with get_dummies or scikit-learn’s OneHotEncoder. When factors have many levels (high cardinality), the resulting design matrix can be sparse, prompting alternatives such as target encoding or grouping rare categories.

Careful choice of reference level, level order, and handling of missing values affects interpretation and model performance. Factors are fundamental in regression, ANOVA, logistic regression, and many machine learning workflows where group membership explains variation among observations.