Overparameterized Model

An overparameterized model uses the indicator variable approach to represent effects for categorical predictor variables in general linear models and generalized linear/nonlinear models. To illustrate indicator variable coding, suppose that a categorical predictor variable called Gender has two levels (i.e., Male and Female). A separate continuous predictor variable would be coded for each group identified by the categorical predictor variable. Females might be assigned a value of 1 and males a value of 0 on a first predictor variable identifying membership in the female Gender group, and males would then be assigned a value of 1 and females a value of 0 on a second predictor variable identifying membership in the male Gender group.

Note that this method of coding for categorical predictor variables will almost always lead to design matrices with redundant columns in general linear models and generalized linear/nonlinear models, and thus requires a generalized inverse for solving the normal equations. As such, this method is often called the overparameterized model for representing categorical predictor variables, because it results in more columns in the design matrix than are necessary for determining the relationships of the categorical predictor variables to responses on the dependent variables.

See also categorical predictor variable, design matrix, and General Linear Models (GLM).