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**Linde, A. van der and Tutz, Gerhard (2004): On association in regression: the coefficient of determination revisited. Collaborative Research Center 386, Discussion Paper 391 [PDF, 390kB]**

## Abstract

Universal coefficients of determination are investigated which quantify the strength of the relation between a vector of dependent variables Y and a vector of independent covariates X. They are defined as measures of dependence between Y and X through theta(x), with theta(x) parameterizing the conditional distribution of Y given X=x. If theta(x) involves unknown coefficients gamma the definition is conditional on gamma, and in practice gamma, respectively the coefficient of determination has to be estimated. The estimates of quantities we propose generalize R^2 in classical linear regression and are also related to other definitions previously suggested. Our definitions apply to generalized regression models with arbitrary link functions as well as multivariate and nonparametric regression. The definition and use of the proposed coefficients of determination is illustrated for several regression problems with simulated and real data sets.

Item Type: | Paper |
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Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |

Subjects: | 500 Science > 510 Mathematics |

URN: | urn:nbn:de:bvb:19-epub-1761-1 |

Language: | English |

Item ID: | 1761 |

Date Deposited: | 10. Apr 2007 |

Last Modified: | 04. Nov 2020, 12:45 |