naginterfaces.library.correg.glm_​constrain

naginterfaces.library.correg.glm_constrain(v, c, b, s)[source]

glm_constrain calculates the estimates of the parameters of a generalized linear model for given constraints from the singular value decomposition results.

For full information please refer to the NAG Library document for g02gk

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g02/g02gkf.html

Parameters
vfloat, array-like, shape

The array as returned by glm_normal(), glm_binomial(), glm_poisson() or glm_gamma().

cfloat, array-like, shape

Contains the constraints stored by column, i.e., the th constraint is stored in the th column of .

bfloat, array-like, shape

The parameter estimates computed by using the singular value decomposition, .

sfloat

The estimate of the scale parameter.

For results from glm_normal() and glm_gamma() then is the scale parameter for the model.

For results from glm_binomial() and glm_poisson() then should be set to .

Returns
bfloat, ndarray, shape

The parameter estimates of the parameters with the constraints imposed, .

sefloat, ndarray, shape

The standard error of the parameter estimates in .

covfloat, ndarray, shape

The upper triangular part of the variance-covariance matrix of the parameter estimates given in . They are stored packed by column, i.e., the covariance between the parameter estimate given in and the parameter estimate given in , , is stored in .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

does not give a model of full rank.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

glm_constrain computes the estimates given a set of linear constraints for a generalized linear model which is not of full rank. It is intended for use after a call to glm_normal(), glm_binomial(), glm_poisson() or glm_gamma().

In the case of a model not of full rank the functions use a singular value decomposition to find the parameter estimates, , and their variance-covariance matrix. Details of the SVD are made available in the form of the matrix :

as described by glm_normal(), glm_binomial(), glm_poisson() and glm_gamma(). Alternative solutions can be formed by imposing constraints on the parameters. If there are parameters and the rank of the model is then constraints will have to be imposed to obtain a unique solution.

Let be a matrix of constraints, such that

then the new parameter estimates are given by:

and the variance-covariance matrix is given by

provided exists.

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore

McCullagh, P and Nelder, J A, 1983, Generalized Linear Models, Chapman and Hall

Searle, S R, 1971, Linear Models, Wiley