Extended Model Formulas in R: Multiple Parts and Multiple Responses

Model formulas are the standard approach for specifying the variables in statistical models in the S language. Although being eminently useful in an extremely wide class of applications, they have certain limitations including being confined to single responses and not providing convenient support for processing formulas with multiple parts. The latter is relevant for models with two or more sets of variables, e.g., different equations for different model parameters (such as mean and dispersion), regressors and instruments in instrumental variable regressions, two-part models such as hurdle models, or alternative-specific and individual-specific variables in choice models among many others. The R package Formula addresses these two problems by providing a new class “Formula” (inheriting from “formula”) that accepts an additional formula operator | separating multiple parts and by allowing all formula operators (including the new |) on the left-hand side to support multiple responses.