cvmgof: an R package for Cramer-von Mises goodness-of-fit tests in regression models

Many goodness-of-fit tests have been developed to assess the different assumptions of a (possibly heteroscedastic) regression model. Most of them are 'directional' in that they detect departures from a given assumption of the model. Other tests are 'global' (or 'omnibus') in that they assess whether a model fits a dataset on all its assumptions. We focus on the task of choosing the structural part of the regression function because it contains easily interpretable information about the studied relationship. We consider two nonparametric 'directional' tests and one nonparametric 'global' test, all based on generalizations of the Cramer-von Mises statistic. To perform these goodness-of-fit tests, we develop the R package cvmgof providing an easy-to-use tool for practitioners, available from the Comprehensive R Archive Network (CRAN). The use of the library is illustrated through a tutorial on real data. A simulation study is carried out in order to show how the package can be exploited to compare the three implemented tests.

Automated summary

Various goodness-of-fit tests have been developed for assessing assumptions in regression models. They include both 'directional' tests that detect departures from specific assumptions and 'global' tests that assess overall model fit. The focus of this study is on choosing the structural part of the regression function, with the development of nonparametric tests and an easy-to-use tool, cvmgof. The package is illustrated through a tutorial on real data and a simulation study is conducted to compare the three tests implemented.