### Abstract

Generalized linear models are considered within the larger framework of multiparameter exponential family models. This general approach shows that the link function is not a necessary feature of a computer algorithm for calculating maximum likelihood estimates for such models by iteratively reweighted least squares. It is argued that the link function is a useful component of model fitting and interpretation in situations where there is a natural link to an underlying linear model (e. g. , logistic regression). However in many instances there is no single link function (e. g. , multinomial regression) or else unlinked parameters exist (e. g. , bioassay with a spontaneous response rate). It is shown by a number of examples that a general approach via exponential family models is preferable in such situations. 16 refs.

Original language | English (US) |
---|---|

Title of host publication | Applied Statistics |

Pages | 18-24 |

Number of pages | 7 |

Volume | 33 |

Edition | 1 |

State | Published - 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Applied Statistics*(1 ed., Vol. 33, pp. 18-24)

**GENERALIZED LINEAR MODELS - THE MISSING LINK.** / Cox, Christopher.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Applied Statistics.*1 edn, vol. 33, pp. 18-24.

}

TY - CHAP

T1 - GENERALIZED LINEAR MODELS - THE MISSING LINK.

AU - Cox, Christopher

PY - 1984

Y1 - 1984

N2 - Generalized linear models are considered within the larger framework of multiparameter exponential family models. This general approach shows that the link function is not a necessary feature of a computer algorithm for calculating maximum likelihood estimates for such models by iteratively reweighted least squares. It is argued that the link function is a useful component of model fitting and interpretation in situations where there is a natural link to an underlying linear model (e. g. , logistic regression). However in many instances there is no single link function (e. g. , multinomial regression) or else unlinked parameters exist (e. g. , bioassay with a spontaneous response rate). It is shown by a number of examples that a general approach via exponential family models is preferable in such situations. 16 refs.

AB - Generalized linear models are considered within the larger framework of multiparameter exponential family models. This general approach shows that the link function is not a necessary feature of a computer algorithm for calculating maximum likelihood estimates for such models by iteratively reweighted least squares. It is argued that the link function is a useful component of model fitting and interpretation in situations where there is a natural link to an underlying linear model (e. g. , logistic regression). However in many instances there is no single link function (e. g. , multinomial regression) or else unlinked parameters exist (e. g. , bioassay with a spontaneous response rate). It is shown by a number of examples that a general approach via exponential family models is preferable in such situations. 16 refs.

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UR - http://www.scopus.com/inward/citedby.url?scp=0021292473&partnerID=8YFLogxK

M3 - Chapter

VL - 33

SP - 18

EP - 24

BT - Applied Statistics

ER -