Approximate Conditional Inference Object

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Description

Class of objects returned when performing approximate conditional inference for logistic and loglinear models.

Arguments

Objects of class cond 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 log likelihoods;

- the Wald pivots from the unconditional and conditional MLEs;

- the profile and modified likelihood roots (the latter one with a suitable continuity correction);

- the Lugannani-Rice tail area approximation (with suitable continuity correction);

- the correction term used in the higher order statistics;

- the 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 2x2 matrix containing the unconditional and approximate conditional MLEs and their standard errors.

call

function call that created the cond object.

formula

the model formula.

family

the variance function.

offset

the covariate occurring in the model formula whose coefficient represents the parameter of interest.

diagnostics

diagnostics related to the decomposition of the higher order adjustments into an information and a nuisance parameters term. A value larger than 0.2 in absolute value is an index that higher order methods are needed. See Pierce and Peters (1992) for details.

n.approx

number of output points that have been calculated exactly.

omitted.val

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 Pierce and Peters (1992) and Davison (1988). More details on the implementation and the methods considered are given in Brazzale (1999, 2000).

Generation

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

Methods

The class cond has methods for summary, plot, print, coef and family, amongst others.

References

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.

Davison, A. C. (1988) Approximate conditional inference in generalized linear models. J. R. Statist. Soc. B, 50, 445–461.

Pierce, D. A. and Peters, D. (1992) Practical use of higher order asymptotics for multiparameter exponential families (with Discussion). J. R. Statist. Soc. B, 54, 701–737.

See Also

cond.glm, summary.cond, plot.cond