Objectives to be profiled


Objectives to be used in profileModel.


ordinaryDeviance(fm, dispersion = 1)

RaoScoreStatistic(fm, X, dispersion = 1)



the restricted fit.


the model matrix of the fit on all parameters.


the dispersion parameter.


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).


A scalar.


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


Ioannis Kosmidis <email: ioannis@stats.ucl.ac.uk>


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

See Also

profiling, prelim.profiling, profileModel.

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