R: Objectives to be profiled

objectives-profileModel {profileModel} | R Documentation

## Objectives to be profiled

### Description

Objectives to be used in profileModel.

### Usage

    ordinaryDeviance(fm, dispersion = 1)

    RaoScoreStatistic(fm, X, dispersion = 1)

### Arguments

`fm` | the restricted fit.
`X` | the model matrix of the fit on all parameters.
`dispersion` | the dispersion parameter.

### Details

The objectives used in profileModel have to be functions of the restricted fit. Given a fitted object, the restricted fit is an object resulted by restricting a parameter to a specific value and then estimating the remaining parameters. Additional arguments could be used and are passed to the objective matching the ... in `profileModel` or in other associated functions. An objective function should return a scalar which is the value of the objective at the restricted fit.

The construction of a custom objective should follow the above simple guidelines (see also Example 3 in `profileModel` and the sources of either `ordinaryDeviance` or `RaoScoreStatistic`).

`ordinaryDeviance` refers to `glm`-like objects. It takes as input the restricted fit `fm` and optionally the value of the dispersion parameter and returns the deviance corresponding to the restricted fit divided by `dispersion`.

`RaoScoreStatistic` refers to `glm`-like objects. It returns the value of the Rao score statistic s(β)^Ti^{-1}(β)s(β)/φ, where s is the vector of estimating equations, φ is the dispersion parameter and

i(β) = cov(s(β)) = X' W(β) X/φ ,

in standard GLM notation. The additional argument `X` is the model matrix of the full (not the restricted) fit. In this way the original fit has always smaller or equal Rao score statistic from any restricted fit. The Rao score statistic could be used for the construction of confidence intervals when quasi-likelihood estimation is used (see Lindsay and Qu, 2003).

### Value

A scalar.

### Note

Because the objective functions are evaluated many times in `profiling`, `prelim.profiling` and `profileModel`, they should be as computationally efficient as possible.

### Author(s)

Ioannis Kosmidis <email: i.kosmidis@ucl.ac.uk>

### References

Lindsay, B. G. and Qu, A. (2003). Inference functions and quadratic score tests. Statistical Science 18, 394–410.

### See Also

`profiling`, `prelim.profiling`, `profileModel`.

[Package profileModel version 0.5-9 Index]