R: Approximate Marginal Inference Object

marg.object {marg}

R Documentation

Approximate Marginal Inference Object

Description

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

Arguments

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 `2\times 2` matrix containing the unconditional and approximate conditional/marginal MLEs and their standard errors.
`call`	the function call that created the `marg` object.
`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 `scale` if the parameter of interest is the scale parameter.
`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 `FALSE` there are none.

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).

Generation

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

Methods

The class marg has methods for summary, plot, print, coef and family, among others.

Note

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.

References

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.