Description Arguments Generation Methods Note References See Also

Class of objects returned when performing approximate conditional inference for regression-scale models.

Objects of class `marg`

are implemented as a list. The
following components are included:

`workspace` |
a list whose elements are the spline interpolations of several first order and higher order statistics. They are used to implement the following likelihood quantities: - the profile and modified profile/approximate marginal log likelihoods; - the Wald pivots from the unconditional and conditional/approximate marginal MLEs; - the profile and modified/approximate marginal likelihood roots; - the conditional/approximate marginal Lugannani-Rice tail area approximation; - the correction term used in the higher order statistics; - the conditional/marginal information and nuisance parameter aspects. Method functions work mainly on this part of the object. In order to avoid errors in the calculation of confidence intervals and tail probabilities, this part of the object should not be modified. |

`coefficients` |
a |

`call` |
the function call that created the |

`formula` |
the model formula. |

`family` |
the name of the error distribution. |

`offset` |
the covariate occurring in the model formula whose coefficient
represents the parameter of interest or |

`diagnostics` |
diagnostics related to the decomposition of the higher order adjustments into an information and a nuisance parameters term. |

`n.approx` |
the number of output points for which the statistics have been calculated exactly. |

`omitted.val` |
the range of values omitted in the spline interpolation of some of the higher order statistics considered. The aim is to avoid numerical instabilities around the maximum likelihood estimate. |

`is.scalar` |
a logical value indicating whether there are any nuisance
parameters. If |

Main references for the methods considered are the papers by Barndorff-Nielsen (1991), DiCiccio, Field and Fraser (1990) and DiCiccio and Field (1991). The theory and statistics used are summarized in Brazzale (2000, Chapters 2 and 3). More details of the implementation and of the methods considered are given in Brazzale (1999; 2000, Section 6.3.1).

This class of objects is returned from calls to the function
`cond.rsm`

.

The class `marg`

has methods for `summary`

,
`plot`

, `print`

,
`coef`

and `family`

, among
others.

If the parameter of interest is the scale parameter, all calculations are performed on the logarithmic scale, though most results are reported on the original scale.

Barndorff-Nielsen, O. E. (1991) Modified signed log likelihood
ratio. *Biometrika*, **78**, 557–564.

Brazzale, A. R. (1999) Approximate conditional inference for
logistic and loglinear models. *J. Comput. Graph. Statist.*,
**8**, 653–661.

Brazzale, A. R. (2000) *Practical Small-Sample Parametric
Inference*. Ph.D. Thesis N. 2230, Department of Mathematics, Swiss
Federal Institute of Technology Lausanne.

DiCiccio, T. J., Field, C. A. and Fraser, D. A. S. (1990)
Approximations of marginal tail probabilities and inference for
scalar parameters. *Biometrika*, **77**, 77–95.

DiCiccio, T. J. and Field, C. A. (1991) An accurate method for
approximate conditional and Bayesian inference about linear
regression models from censored data. *Biometrika*, **78**,
903–910.

`cond.rsm`

, `summary.marg`

,
`plot.marg`

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