extendedmodelformulasinrmultiplepartsandmultiple.PDFVIP

Extended Model Formulas in R: Multiple Parts and Multiple Responses Achim Zeileis Yves Croissant Universit¨at Innsbruck Universit′ede la R′eunion Abstract This introduction to the R package Formula is a (slightly) modi?ed version of Zeileis and Croissant (2010), published in the Journal of Statistical Software. 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 con?ned 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., di?erent equations for di?erent model parameters (such as mean and dispersion), regressors and instruments in instru- mental variable regressions, two-part models such as hurdle models, or alternative-speci?c and individual-speci?c variables in choice models among many others. The R package For- mula 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. Keywords: formula processing, model frame, model matrix, R. 1. Introduction Since publication of the seminal “white book” (Chambers and Hastie 1992) the standard approach for ?tting statistical models in the S language is to apply some model-?tting function (such as lm() or glm()) to a “formula” description of the variables involved in the model and typically stored in a “data.frame”. The semantics of formu